NUMBER
Numbers
Large and
Small
Chapter
3
Big Idea
Understanding very large and very
small numbers helps me describe
and solve real-world problems.
Learning Goals
I can show my understanding of
place value for numbers greater
than one million.
I can show my understanding of
place value for numbers less than
one thousandth.
I can use technology to solve
problems involving large numbers.
Essential Question
How can understanding large and
small numbers help me understand
the world around me?
Important Words
billion
expanded form
million
millionth
period
standard form
ten thousandth
Large Numbers
Use your knowledge of large numbers to read and write
numbers in standard and expanded form, and to compare
and order large numbers.
Example:
Show the number 1 305 067 890 in many ways.
This number is one billion, three hundred five million,
sixty-seven thousand, eight hundred ninety.
I can write the number in a place value chart.
Billions
Hundred
Ten
Millions
Thousands
Units
One
Hundred
Ten
One
Hundred
Ten
One
Hundred
Ten
One
1
3
0
5
0
6
7
8
9
0
I can write the number in expanded form as
1 000 000 000 + 300 000 000 + 5 000 000 +
60 000 + 7000 + 800 + 90
Or as
(1 x 1 000 000 000) + (3 x 100 000 000) +
(5 x 1 000 000) + (6 x 10 000) + (7 x 1000) +
(8 x 100) + (9 x 10)
11. Write each number in a place value chart.
a. 497 000 000
b. 35 048 650
c. 771 000 967 000
d. 84 900 600 300
12. List the numbers in question 1 from smallest to largest. Circle the largest number. Put
a rectangle around the smallest number. How do you know those numbers are the
largest and the smallest?
13. What is the value of the 5 digit in each number below?
56
a. 511 111 111
b. 454 444 444 444
c. 252 222 222
d. 665 666 666 666
e. 335 333 333
f. CHAPTER 3: Numbers Large and Small
577 777 777 777
Large Numbers (continued)
14. Put the numbers in question 3 in order from smallest to largest. Explain the strategies
you used.
15. Use the place value chart below to answer the following questions.
Billions
Hundred
Ten
Millions
One
Hundred
Ten
Thousands
Units
One
Hundred
Ten
One
Hundred
Ten
One
8
5
8
7
7
0
1
3
8
7
6
2
5
0
6
7
5
7
0
0
5
6
6
8
8
5
0
7
9
6
5
0
6
0
4
6
5
5
0
7
8
0
0
0
7
a. Describe any patterns you see in the place values.
A period in a number is
a group of three place values:
one, ten, hundred.
b.
Each set of three place values is called a period.
Describe any patterns you see in the periods.
c.
Model one of the numbers and explain how your
model shows the pattern in the place values.
d.
Write each number in expanded form.
e.
Write each number in standard form.
f.
Read each number aloud and write it in words.
g.
One number has a 9 in the thousands period. Locate the digits 1, 2, 3, and 4 in the
chart. Name the period where each digit is found.
16. The numbers below are written in expanded form. Write each number in standard form.
Expanded form uses multiplication
to show the value of each
digit in a number.
Standard form is the way numbers
are usually written. The value of a
digit is shown by its location.
a. 60 000 000 + 20 000 + 3000 + 50
b. (8 × 1 000 000) + (6 × 100 000) + (2 × 10 000) + (4 × 100)
c. 50 000 000 000 + 300 000 000 + 50 000 + 3
d. (2 × 1 000 000 000) + (3 × 10 000 000) + (2 × 100) + (4 × 10)
CHAPTER 3: Numbers Large and Small
57
Large Numbers (continued)
17. The numbers below are written in words. Write each number in standard form.
a. five million, four hundred twenty-seven thousand, one hundred twelve
b. nine hundred seventy-eight million, six hundred thirty-four thousand
c. one hundred eighty-five billion
18. Write the number that is
a.
10 000 000 less than 150 456 000
b.
100 000 000 less than 510 207 860
c.
100 000 greater than 450
d.
1 000 000 greater than 89 345
e.
1000 less than 9 070 574
f.
10 000 greater than 1 797 704
19. Use your calculator to answer the questions below.
a. Press each calculator key in order from 1 to 8.
What number is displayed?
b. What value does each digit have in the
number displayed?
c. What is the largest number that can
be displayed in your calculator?
58
CHAPTER 3: Numbers Large and Small
A billion is a thousand millions,
or 10 × 100 000 000.
Large Numbers (continued)
10. Write each of the following numbers in standard form.
a. 15 billion
b. 13.5 thousand
c. 75.5 million
d. 1205 billion
e. 3150 thousand
f. 8709 million
11. Compare each pair of numbers by writing a statement using the greater than (>), less
than (<), or equal (=) symbol.
a. 34 600 000 and 3.4 million
b. Eighty-four thousand and 84 000 000
c. 2.5 million and 2500 thousand
12. Find the number described in each riddle.
a.
I am a number between 1 and 1 000 000.
•
I have six digits and the hundred digit is the same as the hundred thousands digit.
•
There are six thousands.
•
The digit in the tens is half the digit in the thousands.
•
The tens digit is two more than the ones digit.
•
If you add the digit in the thousands place to the number of tens and then subtract the number of ones you get the ten thousands digit.
•
The hundreds digit is three less than the ten thousands digit.
b. I am a number between 1 and 50 000 000.
•
I have eight digits, and no digits are repeated.
•
There is one ten and three ten millions in the number.
•
The digit in the thousands place is twice the digit in the tens place.
•
The thousands digit is half the digit in the millions place.
•
The digit in the ten thousands place is less than the digit in the tens place.
•
The digit in the hundred thousands is twice the number of ten millions.
•
The sum of the digits in the millions period is the digit in the hundreds place.
•
The ones digit is two less than the hundreds digit.
CHAPTER 3: Numbers Large and Small
59
Large Numbers (continued)
c. I am a number between 1 million and 1 billion.
•
I have nine digits. The millions digit and the hundreds digit are the same.
•
There is one ten thousand.
•
The digit in the ten millions place is double the digit in the tens place.
•
The ten millions digit is half of the digit in the hundred millions place.
•
There is a two in the tens place.
•
The hundred thousands digit is three more than the ones digit.
•
The digit in the ones is four more than the digit in the tens.
•
The millions is the difference between the hundred thousands and the ones.
•
The digits in the ten thousands place and the thousands place are consecutive.
13. Write your own riddle for a number between 1 million and
100 billion. Exchange with a partner and try to find each
other’s number. Compare the strategies you each used to
find the number.
14. Explain how the patterns in place values could be important
in knowing about numbers.
15. Our number system is sometimes called a base ten system.
Use what you know about place value to explain why that is
a good name for our number system.
I can show my understanding of place value for numbers greater than one million.
60
CHAPTER 3: Numbers Large and Small
Numbers Around Us
Use your knowledge of large numbers to work with numbers from
contexts such as sky science, populations, money, and technology.
Example:
In 1998, the music industry sold seven hundred eleven million CDs.
Of these, they sold approximately:
•
one hundred sixty million, nine thousand R & B albums.
•
three hundred eighty-one million, thirty thousand rap albums.
•
one hundred million, four hundred thousand alternative albums.
•
two hundred seventeen million country albums.
a. Write each number in standard form.
R & B Rap A lt Country 160 009
381 030
100 400
217 000
000
000
000
000
b. Order the numbers from smallest to largest.
A lt 100 400 000
R & B
160 009 000
These both have 1 hundred million, but R & B has
6 ten mil l ions so it sold more than A l ternative.
Country 217 000 000
Rap 381 030 000
Rap is the highest because it has 3 hundred millions.
c. Explain when you might choose to write numbers in each of
these forms.
I woul d al ways write the digits. I think numbers are
easier to compare when they’re written in standard
form. The numbers might need to be written in words
if they were starting a sentence.
CHAPTER 3: Numbers Large and Small
61
Numbers Around Us (continued)
11. The following headlines include large numbers.
•
City of Edmonton plans to spend more than $1.5 million to fix roads
•
Walk-a-thon raises almost a quarter-million for cancer research
•
Wednesday lottery draw an estimated $50 million
•
China’s population passes 1.3 billion
•
Crowd of over 56K attends Stampede game
a. Write each number in standard form.
b. Explain why headlines might write numbers in this way.
12. Write a headline using each of the following numbers.
a. 7 457 000
b. 500 000 000
c. 250 000
d. 1 520 000 000
13. Estimate or research to gather the following data:
•
the number of legs on a dog
•
the number of students in our class
•
the number of students in the school
•
the number of books in the library
•
the cost of a new car
•
the cost of a house
•
the amount you could win in the lottery
•
the number of people who live in Canada
•
the distance from Mars to the Sun
•
the number of people who live in India
a. What sorts of numbers did you find?
b. In which period is each number?
c. Which number is largest? smallest?
62
CHAPTER 3: Numbers Large and Small
Numbers Around Us (continued)
14. The population for each of the ten most populous countries is given in the table below.
Country
Population (2010)
China
1 333 940 000
India
1 172 170 000
United States
307 860 000
Indonesia
231 369 500
Brazil
191 991 000
Pakistan
167 871 500
Bangladesh
162 221 000
Nigeria
154 729 000
Russia
141 881 000
Japan
127 560 000
a. Write each population in a place value chart.
A million is a thousand thousands,
or 10 × 100 000.
b. Japan’s population is about 127.6 million. Write each population in millions.
15. The number of transistors used in a computer chip in each decade since their
invention in the 1950s is shown in the table below.
Decade
Number of transistors
1950s
one
1960s
16
1970s
4500
1980s
275 thousand
1990s
3.1 million
2000s
0.592 billion
a. Write each number in standard form.
b. What observations can you make about the number of transistors used in a
computer chip in each decade?
c. Predict how many transistors there might be in one computer chip in the 2010s.
CHAPTER 3: Numbers Large and Small
63
Numbers Around Us (continued)
16. The diameter of each of the first four planets in our solar system is shown below.
Planet
Diameter (millions of metres)
Mercury
4.88
Venus
12.100
Earth
12.758
Mars
6.794
a. Write each number in standard form.
b. Write each number in expanded form.
c. List the planets in order from the one having the smallest diameter to the one
having the largest diameter.
17. The largest bill still printed in Canada is the $100 bill. In the last century, some countries
have printed bills with large numbers on them.
Country
Bill
Angola
5 000 000 kwanzas readjustos
Argentina
1 000 000 pesos
Bolivia
10 million pesos bolivianos
Bosnia-Herzegovina
500 000 000 000 dinara
China
180 000 000 yuan
Germany
100 000 000 000 000 marks
Hungary
100 quintillion pengo
Zimbabwe
100 trillion dollars
a. Write the number on the bill from Bolivia in standard form.
b. A quintillion is a 1 with 18 zeros after it. Write the number for the bill from Hungary.
c. A trillion is a 1 with 12 zeros after it. Write the number for the bill from Zimbabwe.
d. Name the country that had the bill with the highest number.
e. Explain whether you can tell from the numbers which bill is worth the most.
64
CHAPTER 3: Numbers Large and Small
Numbers Around Us (continued)
18. The average distance from the sun to each of the eight planets is given in the table below.
Planet
Average distance from the sun (kilometres)
Earth
149 000 000
Jupiter
806 000 000
Mars
227 000 000
Mercury
..57 900 000
Neptune
4 500 000 000...
Saturn
1 425 000 000...
Uranus
2 850 000 000...
Venus
108 500 000
a. Write four of the distances in another form, such as in millions of kilometres.
b. List the planets in order from the one closest to the Sun to the one farthest from
the Sun.
19. Explain whether one ten million is the same as ten millions.
10. Explain the strategies you used to order large numbers.
11. Why might there be many ways to write the same number?
I can show my understanding of place value for numbers greater than one million.
CHAPTER 3: Numbers Large and Small
65
Small Numbers
Use your knowledge of small numbers to read and write numbers in
standard and expanded form and to compare and order small numbers.
Example:
Show the number 0.0375 in many ways.
This number is zero and three hundred seventy-five
ten thousan d ths.
I can write it in a place value chart.
. Tenths
0
. 0
Ones
Ten
Hundred
Hundredths Thousandths Thousandths Thousandths
3
7
Mil l ionths
Ten
Millionths
Hundred
Millionths
5
I can write the number in expanded form as
0. 03 + 0.007 + 0. 0005
Or as (3 x 0. 01) + (7 x 0. 001) + (5 x 0. 0001)
3
7
5
Or as
+
+
100
1000
10 000
I can write this number as a fraction.
375
10 000
11. What is the value of the 5 digit in each number?
a. 1.511
b. 4.444 544
c. 2.252
d. 6.666 656
e. 3.335
f. 7.777 775
12. The numbers below are written in expanded form. Write each number in standard form.
a. 0.060 + 0.002 + 0.0003 + 0.000 050
b. (8 × 0.1) + (6 × 0.01) + (2 × 0.001) + (4 × 0.0001)
c. 0.5 + 0.003 + 0.0005 + 0.000 03
d. 66
2
100
+
3
1000
+
2
10 000
+
4
1 000 000
CHAPTER 3: Numbers Large and Small
Small Numbers (continued)
13. Use the place value chart to answer the following questions.
Ones
0
0
5
1
.
.
.
.
.
Tenths
0
7
0
9
Ten
Hundred
Hundredths Thousandths Thousandths Thousandths Millionths
3
0
6
7
7
9
6
0
Ten
Millionths
Hundred
Millionths
5
0
2
9
0
8
0
7
4
6
a. Describe any patterns you see in the place values.
b.
Model one of the numbers and explain how your model shows the pattern in the
place values.
c. Write each number in expanded form.
d. Write each number in standard form.
e. Read each number aloud and write each number using words.
14. Write each number in a place value chart.
a.
0.034
c. 0.7259
b. 0.816 08
d. 0.090 712
15. List the numbers in question 4 from smallest to largest. Circle the largest number.
Put a rectangle around the smallest number. How do you know the numbers are the
largest and the smallest?
16. Write each of the following numbers in words.
a.
200.2002
c. 0.106 106
e.
b. 0.1082
d. 4.070 65
9.003
17. Order the numbers from question 6 from smallest to largest.
CHAPTER 3: Numbers Large and Small
67
Small Numbers (continued)
18. Write each of the following as numbers in standard form.
a. two and three hundred sixty eight thousandths
One millionth is
one part when a whole is
divided into one million parts.
b. four hundred and ninety-three ten thousandths
c. four hundred ninety-three ten thousandths
d. sixteen and seven hundred four thousand, nine hundred twenty-five millionths
19. You have been given the digits 2, 5, and 8, a decimal
point, and four 0 digits. Use all of these digits
to make a number:
One ten thousandth is
one part when a whole is
divided into ten thousand parts.
a. less than one
b. close to one
c. close to 0.5
d. less than one thousandth
e. close to 0.005
f. close to one ten thousandth
g. close to one quarter
10. Arrange the numbers you made in question 9 from smallest to largest.
68
CHAPTER 3: Numbers Large and Small
Small Numbers (continued)
11. Compare each pair of numbers by writing a statement using the greater than (>), less
than (<), or equal (=) symbol.
a. 0.000 315 and 0.000 513
b. 3 millionths and 0.000 03
c. 0.000 08 and 8 hundred thousandths
12. Solve each riddle to discover the mystery number.
a. My number has four digits.
•
My number is greater than one.
•
The digit in the hundredths is the same as the number of toes on one foot.
•
The ones digit is two greater that the hundredths digit.
•
The digit in the tenths place is three less than the digit in the ones place.
•
The thousandths digit is half the tenths digit.
b.
My number has five digits.
•
My number is less than 10.
•
The first two digits are consecutive numbers.
•
The ones digit is the same as the number of legs on a dog.
•
The digit in the ten thousandths place is the same as the number of tails
on a dog.
•
The hundredths digit is seven more than the ten thousandths digit.
•
The thousandths is five less than the sum of the ten thousandths and
the hundredth.
13. Write the number that is:
a.
0.001 less than 510.207 860.
b.
0.0001 greater than 8.9345.
c.
0.000 01 less than 150.456 000.
d.
0.000 001 greater than 450.
e.
0.1 less than 9.070 574.
f.
0.01 greater than 1.797 704.
CHAPTER 3: Numbers Large and Small
69
Small Numbers (continued)
14. Numbers can be expressed as decimals or fractions.
a. Copy and complete the table below.
Place value
Decimal
Ones
1
Tenths
0.1
Hundredths
0.01
Fraction
1
1
10
1
100
Thousandths
Ten thousandths
Hundred thousandths
Millionths
What fraction might be used to represent:
b.
0.0008?
c.
0.000 48?
d.
0.000 167?
15. How could you use fractions to write a decimal number in expanded form?
16. Write your own mystery number riddle using a number between
one millionth and one. Exchange with a partner and try to find
each other’s number. Compare the strategies you each used to
find the number.
17. Explain how the patterns in place values could be important in
knowing about numbers.
18. Our number system is sometimes called a base ten system. Use
what you know about place value to explain why that is a good
name for our number system.
I can show my understanding of place value for numbers less than one thousandth.
70
CHAPTER 3: Numbers Large and Small
Numbers in the World
Use your knowledge of small numbers to read and write numbers in
standard and expanded form. The numbers are taken from contexts
such as statistics, body science, and measurement.
Example:
The anthrax bacteria causes a disease that can affect humans and
livestock. The bacteria are between 0.000 001 and 0.000 009 metres
long. Show this number in many ways.
I can read these numbers as one millionth of a metre and
nine mil l ionths of a metre.
I can show these numbers in a place value chart.
Ones
0
0
Tenths
.
.
Ten
Hundred
Hundredths Thousandths Thousandths Thousandths
Mil l ionths
0
0
0
0
0
1
0
0
0
0
0
9
Ten
Millionths
Hundred
Millionths
I can write 0. 000 009 metres as 9 x 0.000 001 metres.
I can think of 0.000 001 m as 0.001 mm.
11. Coach Nichols collected the statistics below about the kids on his baseball team.
He wants to calculate the batting average of each player. The batting average is the
number of hits divided by the number of times at bat.
Name
Number of hits
Number of times at bat
Amal
30
65
Curtis
16
56
Erica
35
55
Jared
26
65
Krista
21
66
Nina
25
70
Thomas
15
65
a. Use a calculator to find the batting average of each player.
b. Arrange the players in order from highest to lowest batting average.
CHAPTER 3: Numbers Large and Small
71
Numbers in the World (continued)
12. Environment Canada, a department of the Government of Canada, tracks the
precipitation in cities across Canada. The average precipitation (in metres) in each city
in four specific months is shown in the table below.
City
January (m)
April (m)
July (m)
October (m)
Victoria, BC
0.1411
0.0419
0.0176
0.0744
Edmonton, AB
0.0229
0.0218
0.101
0.0177
Winnipeg, MB
0.0193
0.0359
0.072
0.0295
Ottawa, ON
0.58
0.069
0.0881
0.0748
Fredericton, NB
0.0933
0.0834
0.0845
0.0931
St. John’s, NL
0.1478
0.1104
0.1212
0.1517
Whitehorse, YK
0.0169
0.0083
0.0393
0.23
a. Which city gets the most precipitation in January? the least?
b. Which city gets the most precipitation in April? the least?
c. Which city gets the most precipitation in July? the least?
d. Which city gets the most precipitation in October? the least?
e. In which city would you like to live? Why?
13. The dimensions of different parts of the average human body are shown in the table below.
Body part
Dimension
Hair
0.000 08 m wide
Front tooth
0.006 m wide
Red blood cells
0.000 008 m wide
Liver cell
0.000 05 m long
Ovum
0.0002 m long
Fingernail
0.01 m wide
a. Write each number in a place value chart.
b. Write each number in expanded form.
c. Compare expanded form and place value charts for showing numbers.
d. Arrange the body parts from smallest to largest.
72
CHAPTER 3: Numbers Large and Small
Numbers in the World (continued)
14. One of the longest bugs is a stick bug which can grow to 36 cm, or 0.36 m. The length
of some of the smallest bugs is shown in the table below.
Bug
Length
Dust mite
0.000 25 m
Red ant
0.005 m
Fairy fly
0.000 21 m
Feather-winged beetle
0.000 25 m
Nanosellini beetle
0.0006 m
Flea
0.0015 m
a. Write each number in expanded form.
b. Compare expanded form and standard form for showing numbers.
c. Name the shortest insect whose length is shown in this table.
15. Silk, cotton, and wool have been used for clothing for thousands of years. The width of
four fibers is shown in the table below.
Fiber
Width
Spider web silk
0.000 005 m
Cotton fiber
0.000 01 m
Silk fiber
0.000 07 m
Wool fiber
0.000 25 m
a. Write each number in words.
b. Explain whether you can tell from the numbers which fiber will be the smoothest.
16. Explain whether one ten thousandth is the same as ten thousandths.
17. Explain the strategies you used to compare small numbers.
18. Why might there be many ways to write the same number?
I can show my understanding of place value for numbers less than one thousandth.
CHAPTER 3: Numbers Large and Small
73
Numbers Large and Small
Use your knowledge of small and large numbers to compare
and order numbers. You will need to work with numbers in
standard and expanded form.
Example:
35.12 million
985 millionths
Explain how you know which number is bigger.
Ada’s strategy:
M il l ions are much larger than millionths so
35.12 mil l ion must be more that 985 millionths.
Bianka’s strategy:
1
2 0 0 0
0 0 0 9 8
Ten M il l ionths
One M il l ionths
Hundred Thousan d t h s
Ten Thousan d t h s
One Thousan d t h s
Hundredths
.
0 .
0 .
Tenths
Ones
Tens
Hundreds
One Thousand
5
Ten Thousands
3
Hundred Thousands
One M il l ion
Ten M il l ion
Hundred M il l ion
I put both numbers into the same place value chart
to compare them.
5
Dakota’s strategy:
I used a calculator to multiply 35.12 x 1 000 000 to
get 35 120 000. I multiplied 985 x 0.000 001 to get
0.000 985. Then I compared the numbers. 35 120 000
is much bigger than 0.000 985.
Cailyn’s strategy:
I wrote each number in expanded form to help me tell
which was b igger.
30 000 000 + 5 000 000 + 100 000 + 20 000
0. 0009 + 0. 000 08 + 0.000 005
74
CHAPTER 3: Numbers Large and Small
Numbers Large and Small (continued)
11. Write a number between:
a. 1 and 1 000 000.
b. 0 and 1.
c. 1 000 000 and 1 000 000 000.
d. 0.001 and 0.0001.
e. 10 000 000 and 100 000 000.
f. 0 and 0.001.
12. Use your calculator to find the operation that can be used to find the next number in
the table.
a. When moving from the millions place value down to the smaller number.
b. When moving from the millionths place value up to the larger number.
Place value
Millions
Hundred thousands
Ten thousands
Value
1 000 000
100 000
10 000
Thousands
1000
Hundreds
100
Tens
10
Ones
1
Tenths
0.1
Hundredths
0.01
Thousandths
0.001
Ten thousandths
0.0001
Hundred thousandths
0.000 01
Millionths
0.000 001
CHAPTER 3: Numbers Large and Small
75
Numbers Large and Small (continued)
13. Compare each pair of numbers by writing a statement using the greater than (>), less
than (<), or equal (=) symbol.
a. ten thousand and ten thousandths
b. 20 000 001 and 20.000 001
c. 2.4 and 2.4 million
d. 324 millionths and 324 000 000
14. Use a calculator to find the pattern in each set of expressions. Predict the next term in
the pattern.
b. 2 × 3
a. 45 000 000 ÷ 9
2 × 0.3
4 500 000 ÷ 9
2 × 0.03
450 000 ÷ 9
2 × 0.003
45 000 ÷ 9
2 × 0.000 3
4 500 ÷ 9
2 × 0.000 03
450 ÷ 9
2 × 0.000 003
45 ÷ 9
5. In your own words, explain standard form and expanded form.
I can show my understanding of place value for numbers greater than one million.
I can show my understanding of place value for numbers less than one thousandth.
I can use technology to solve problems involving large numbers.
76
CHAPTER 3: Numbers Large and Small
Numbers at Large
Use your knowledge of small and large numbers to estimate and
calculate answers to problems in contexts such as science,
geography, technology, money, and measurement.
Example:
Mary reads for 25 minutes each night. For how many minutes does
she read in two years? For how many hours does she read for in two
years? For how many seconds does she read in two years?
25 minutes x 365 nights x 2 years = 18 250 minutes
M ary reads for 18 250 minutes in two years.
18 250 m ÷ 60 m/hour = 304.166 667 hours
M ary reads for 304.166 667 hours in two years.
18 250 m x 60 seconds/m = 1 095 000 seconds
M ary reads for 1 095 000 seconds in two years.
11. The diameter of each of the first four planets in our solar system is shown below.
Planet
Mercury
Diameter (millions of metres)
4.88
Venus
12.100
Earth
12.758
Mars
06.794
a. Write each number in standard form.
b. Determine how much larger the diameter of Venus is than the diameter of Mercury.
c. Calculate how many times larger the diameter of Venus is than the diameter of
Mercury.
d. Explain whether you think the number from b or the number from c tells you more
about the size of Venus and Mercury.
e. Find the planet with a diameter that will fit about twice into the diameter of another
planet.
CHAPTER 3: Numbers Large and Small
77
Numbers at Large (continued)
12. Two different boxes of balloons are available
at the local party store.
a. Find the cost of one balloon from each box.
b. Explain which box is the better buy.
13. Statistics Canada tracks the population of
every region in the country. The populations are shown in the table below:
Province or Territory
2008 population (millions)
Alberta
3.585
British Columbia
4.382
Manitoba
1.208
New Brunswick
0.747
Newfoundland and Labrador
0.508
Northwest Territories
0.043
Nova Scotia
0.938
Nunavut
0.031
Ontario
12.929
Prince Edward Island
0.140
Québec
7.751
Saskatchewan
1.016
Yukon
0.033
a. Calculate the total population of Canada in millions.
b. Write the population of Canada in standard form.
c. Write the population of Canada in expanded form.
d. Calculate how many more people there are in Alberta than in Saskatchewan.
e. Calculate how many times larger Alberta’s population is than Saskatchewan’s
population.
f. Explain whether the number from d or the number from e tells you more about the
populations of Alberta and Saskatchewan.
g. Write two questions that can be answered using the numbers in this table.
78
CHAPTER 3: Numbers Large and Small
Numbers at Large (continued)
14. Environment Canada tracks the precipitation in cities across Canada. The average
precipitation (in metres) in each city in four specific months is shown in the table below.
City
January (m)
April (m)
July (m)
October (m)
Victoria, BC
0.1411
0.0419
0.0176
0.0744
Edmonton, AB
0.0229
0.0218
0.101
0.0177
Winnipeg, MB
0.0193
0.0359
0.072
0.0295
Ottawa, ON
0.58
0.069
0.0881
0.0748
Fredericton, NB
0.0933
0.0834
0.0845
0.0931
St. John’s, NL
0.1478
0.1104
0.1212
0.1517
Whitehorse, YK
0.0169
0.0083
0.0393
0.23
a. Calculate the total precipitation in each city for the months shown.
b. Which city gets the most total precipitation?
c. Which city gets the least total precipitation?
d. What is the difference in precipitation between the two cities in b and c?
e. In which city would you prefer to live? Why?
15. A million dollars sounds like a lot of money.
a. How many five cent candies can you buy for a million dollars?
b. How many eighty-five cent candy bars can you buy for a million dollars?
c. How many $27 000 cars can you buy for a million dollars?
d. How many $350 000 houses can you buy for a million dollars?
e. What would you buy with a million dollars?
16. Susannah sleeps eight hours each night.
a. How many hours does she sleep in one year?
b. Susannah is 12 years old. How many hours has she slept in her life?
c. How many minutes has Susannah slept in her life?
d. How many seconds has Susannah slept in her life?
e. How many years has Susannah slept in her life?
CHAPTER 3: Numbers Large and Small
79
Numbers at Large (continued)
Use a calculator to help you answer the following questions. Explain the steps you followed
to answer each question.
17. Explain whether you think one million tennis balls would fit into your classroom.
18. Calculate how many times your heart has beat in your life.
19. Determine which is taller, you or a million-dollar stack of ten-dollar bills.
10. Use a dictionary to estimate the number of words in the English language.
11. How did using a calculator help you answer these questions?
12. Write your own question using large or small numbers.
Exchange questions with a partner and solve each other’s
problem. Compare the solution strategies you used.
I can show my understanding of place value for numbers greater than one million.
I can show my understanding of place value for numbers less than one thousandth.
I can use technology to solve problems involving large numbers.
80
CHAPTER 3: Numbers Large and Small