The CENTRE for EDUCATION in
MATHEMATICS and COMPUTING
NUMBER SENSE
AND
NUMERATION: DECIMALS
AND
PERCENTS
This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in
Mathematics and Computing, University of Waterloo.
Play the Builder Ted game first! Levels 2 and 3 are recommended.
Click on http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html or
go to www.wiredmath.ca for the link.
1.
Shade the approximate indicated part of each shape.
a. 0.75
2.
b. 300%
c. 1.5%
b. 0.556
3
e.
8
c. 3.5
Express as a percent.
a. 0.85
1
d.
5
4.
c. 62.5%
5
6
Express as a decimal.
a. 45%
3.
b.
Remember…
To express a decimal as a
percent, multiply by 100.
Express as a percent.
a. 6.5 out of 10
b. 15 out of 200
Did You Know?
Gauss is considered one of the three all time
greatest mathematicians. Who do you think were
the other two?
5.
The Gauss Mathematics Contest for Grade 7 and 8 students began
in the early 1970s.
a. What percent of the letters of the name Gauss are vowels?
b. What percent of the letters of the name Gauss are consonants?
c. What percent of the letters are s’s or vowels?
Interesting Fact!
Over 87 000 students
wrote the Canadian Gauss
Mathematics Contest in
2004.
Expectations: i) represent, order and compare decimals; ii) translate between equivalent forms of a number; iii) multiply and divide decimal numbers by powers
of ten; iv) solve multi-step problems arising from real-life contexts and involving decimals and percents. For more activities and resources from the University of
Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.
1
6.
Determine each of the following.
a. 16% of 84
b. 1.8% of 120
c. 15% of $456.60
d. 8% of $147.50
7. A family invested $6000 at 7.5% per annum.
How much interest did they receive at the end of the year?
8.
A student planned to save $800 from his summer earnings.
He did save 90% of this amount. How much did he save?
9.
Change each of the following to fractions.
a. 10%
b. 25%
c. 50%
d. 75%
1
e. 33 %
3
f.
2
66 %
3
10.
Determine the unknown number in each sentence if:
1
a. 25% of the number is 18.
b. 33 % of a number is 15.
3
2
c. 60% of a number is 243.
d. 66 % of a number is 120.
Recall
3
= means “is approximately equal to.”
11.
Round these numbers as indicated.
12.
13.
14.
e.g.
8.48 × 3.74 =
 31.72
a. 48391 (to the nearest ten thousand)
b. 5329 (to the nearest hundred)
c. 256938 (to the nearest thousand)
d. 0.485 (to the nearest hundredth)
e. 0.349 (to the nearest tenth)
f. 6.7 (to the nearest one)
g. 5.997 (to the nearest tenth)
h. 12.6629 (to the nearest hundredth)
Round 42.538 to
a. 1 decimal place
b. 2 decimal places
Round 0.9627 to
a. 3 decimal places
b. 2 decimal places
c. 1 decimal place
Round π = 3.14159265358... to
a. 3 decimal places
b. 2 decimal places
c. 1 decimal place
Expectations: i) represent, order and compare decimals; ii) translate between equivalent forms of a number; iii) multiply and divide decimal numbers by powers
of ten; iv) solve multi-step problems arising from real-life contexts and involving decimals and percents. For more activities and resources from the University of
Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.
2
15.
The daily temperatures, in degrees Celsius, for one week in Waterloo were
2.8, − 7.3, − 11.0, − 8.2, − 1.6, 1.2, and1.0 .
a. What was the average temperature that week?
b. Which season was it? Explain.
Did You Know?
16.
a. 0.333…
17.
18.
The horizontal bar used in
bar notation to represent
repeating digits is called a
vinculum.
E.g. 0.567567… can be
Express the following using bar notation.
b. 0.454545454…
c. 8.45626262…
written as 0.567 .
Write each fraction as a decimal.
a.
5
6
b.
7
12
c.
8
9
d.
2
11
e.
1
7
f.
4
15
g.
11
13
h.
61
333
Without using a calculator, express each of the following as a decimal.
a.
862
10
b.
428
100
c.
32
1000
d.
75
0.1
e.
8.31
0.01
f.
0.029
0.001
g.
0.9
10
h.
80.32
0.01
i.
4.5837
1000
j.
9
0.1
k.
0.04
0.001
l.
7
100
19.
TRY THIS INTERESTING PROBLEM!
a. Determine the value of x if x =
4444.44444
.
0.36
b. Find the value of 8x .
c. Describe the results found in parts a. and b.
Expectations: i) represent, order and compare decimals; ii) translate between equivalent forms of a number; iii) multiply and divide decimal numbers by powers
of ten; iv) solve multi-step problems arising from real-life contexts and involving decimals and percents. For more activities and resources from the University of
Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.
3
CHALLENGE YOURSELF!
20.
Write each as a fraction.
a. 0.45
21.
b. 0.777…
( )
2
When the numbers 0.3, 0.3, 0.3 ,
c. 0.1
d. 7.444…
e. 0.3
1 1
are arranged from smallest to largest, which is the middle
,
0.3 0.3
number?
EXTENSIONS!
41
is converted to a decimal.
333
22.
Determine the 100th digit to the right of the decimal point when
23.
Replace each numerator with different numbers so that the answer is as close to or equal to 0 as possible.
a.
24.
b.
7
−
11
c.
2
−
−
3 12
1 2 3
6
, , ,..., to decimals.
7 7 7
7
What pattern do you notice?
What is the sum of the tenths digit and the ten-thousandths digit for each decimal?
What is the sum of the hundredths digit and the hundred-thousandths digit for each decimal?
What is the sum of the thousandths digit and the millionths digit for each decimal?
n
What is the decimal equivalent of if the tenth’s digit is 4?
7
1 2
3
can you predict the decimal
By determining the decimal equivalents for , , and
11 11
11
7
35
equivalents for
and
?
11
11
a. Convert
b.
c.
d.
e.
f.
g.
25.
−
3 13
The sides of a cube are doubled in length. Determine the percentage increase in the volume of the new
cube.
26. 26. 26.
26.
Mr. Afton has an income which is five-eighths of Ms Benson’s.
Mr. Afton’s expenses are one-half those of Ms Benson, and Mr. Afton
saves 40% of his income. What percentage of her income does Ms
Benson save?
Expectations: i) represent, order and compare decimals; ii) translate between equivalent forms of a number; iii) multiply and divide decimal numbers by powers
of ten; iv) solve multi-step problems arising from real-life contexts and involving decimals and percents. For more activities and resources from the University of
Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.
4