Comparing Decimal Numbers
Understanding and comparing money helps us understand and compare decimals.
Examples
We know that:
• ten cents is more money than seven cents
$0.10 > $0.07
•
sixty-seven cents is more money than sixty-two cents
$0.67 > $0.62
The greater the number, the greater the value of the money.
This pattern works the same for decimal numbers that are not money values.
We can represent and compare decimal numbers using diagrams, grids and number
lines.
Diagrams/Grids:
Seven of the 10 squares are shaded.
0.7 is shaded.
Four of the 10 squares are shaded.
0.4 is shaded.
0.7 has more shaded squares than 0.4. Therefore, 0.7 > 0.4.
To compare a number out of 100 with a number out of 10, add a zero to the end of the
number out of 10. The additional zero is a place holder and does not change the value
of the number.
For example: 50 cents can be expressed as $0.50 or $0.5.
Both can be expressed as 50/100.
0.50 = 0.5
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Decimals:
Comparing Decimal Numbers
1/5
Examples
•
Compare 0.5 and 0.30.
Ignore the decimal point and the zero to the left of the decimal point.
Which number has the greater value, 30 or 50?
50 is greater.
0.50 is greater than 0.30.
0.5 > 0.30
•
Compare 0.65 and 0.4.
Which number has the greater value, 65 or 40?
65 is greater.
0.65 is greater than 0.40.
0.65 > 0.4
•
Compare 0.07 and 0.7.
Which number has the greater value, 7 or 70?
70 is greater.
0.70 is greater than 0.07.
0.7 > 0.07
Examples
Some decimal numbers can be difficult to put in order because
many of the digits are the same. For example:
12.3
12.03
12.31
To determine which is greater, begin by comparing the digits farthest left and move to
the right, comparing each place value. A chart can help.
Number
12.3
12.03
12.31
Tens
1
1
1
Ones
2
2
2
•
•
•
•
Tenths
3
0
3
Hundredths
0
3
1
Hint: Tenths are bigger than hundredths.
To compare similar numbers, follow the steps on the next page. Refer to the numbers in
the above chart.
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Decimals:
Comparing Decimal Numbers
2/5
1.
2.
3.
4.
5.
Explanation
Add zeros to the right to ensure
that all numbers have the same
number of digits after the
decimal.
Compare the digits in the tens
position.
Compare the digits in the ones
position.
Compare the digits in the tenths
position.
Compare the digits of the
remaining 2 numbers in the
hundredths position.
Example
12.3 becomes 12.30.
All of the numbers have a 1 in the tens
position.
All of the numbers have a 2 in the ones
position.
The tenths column has:
3 0 3
1 is larger than 0, so 12.31 is greater
than 12.30
The order of the numbers, from least to greatest, is: 12.03, 12.3, 12.31
Think About …
How do you think being able to tell what number is greater or smaller can help you at
home, in your community and in the workplace?
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Decimals:
Comparing Decimal Numbers
3/5
Practice: Comparing Decimals
1. Compare the following and indicate which is greater.
a)
b)
c)
d)
e)
f)
g)
h)
0.8
0.47
0.05
0.6
0.22
0.41
0.75
0.9
or
or
or
or
or
or
or
or
0.80
0.4
0.5
0.61
2.2
0.05
0.77
0.90
2. Gather information about temperatures using a variety of sources, such as
newspapers, other media, a library or the Internet. Locate a map that identifies a
variety of temperatures, either within one city over a period of time or a number of
different cities in a specific time frame.
Select temperatures that are reported to the nearest tenth of a degree (one number
to the right of the decimal).
Print or make a copy of the map you are using. Order the
temperatures from highest to lowest and list the locations.
3. Gather data about temperatures using a thermometer. Place containers of water
throughout the school, inside and outside. Take the initial temperatures. Leave the
containers for a set time and take the temperatures again. Record the initial and
final temperatures on a chart. Compare and order the temperatures.
Develop a set of questions to discuss with your classmates about the
changes in temperatures throughout the time period, such as:
•
At which location did the temperature change the most? The least?
Write a summary statement about the data collected.
Use the data to develop graphs.
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Decimals:
Comparing Decimal Numbers
4/5
4. a) Write the temperatures in the chart below.
Temp.
Tens
Ones
•
26.02°C
•
25.02°C
•
26.2°C
•
26.24°C
•
25.21°C
•
Tenths Hundredths
b) Compare and write the temperatures in order from least to greatest on the lines
below.
Order of temperatures from least to greatest:
__________, __________, __________, __________, __________
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Decimals:
Comparing Decimal Numbers
5/5