Decimals: Tenths, Hundredths and Thousandths

1. Understanding Tenths

square metre or square meter
0.5, 0.7 and 0.2 are decimals or decimal numbers.

Divide 1 whole into 10 equal parts.

square metre or square meter
In the fraction form, each part has a value equal to
1
10
or 1 tenth.
In the decimal form, each part has a value equal to 0.1 (read as zero point one).

square metre or square meter
Two parts are
2
10
or 2 tenths or 0.2.
The dot in a decimal number is called a decimal point.

2. What decimals do the following shaded parts represent?

a)
square metre or square meter
4 tenths
4
10
= 0.4
b)
square metre or square meter
3 tenths
3
10
 =  0.3
c)
square metre or square meter
10 tenths
10 tenths  =  1 whole
=  1
10 tenths make 1 whole.
d)
square metre or square meter
2 3
10
  =   2  + 
3
10

=  2  +  0.3
=  2.3
e)
square metre or square meter
2 fifths
2
5
  =  
4
10

=    0.4
2 fifths  =  4 tenths

3. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.

a)   0.3
      0.3  = 
3
10
b)   0.5
      0.5  = 
5
10

1
2
c)   1.6
      1.6  =  
1 6
10

=  
1 3
5

4. What is the value of each digit in 736.5?

square metre or square meter
In 736.5,
  • the digit 7 is in the hundreds place, its value is 7 × 100 or 700
  • the digit 3 is in the tens place, its value is 3 × 10 or 30
  • the digit 6 is in the ones place, its value is 6 × 1 or 6
  • the digit 5 is in the tenths place, its value is 5 × 0.1 or 0.5
700   +   30   +   6   +   0.5  =  736.5

5. Understanding Hundredths

Divide 1 whole into 100 equal parts.

square metre or square meter
In the fraction form, each part has a value equal to
1
100
or 1 hundredth.

In the decimal form, each part has a value equal to 0.01 (read as zero point zero one).

6. What decimals do the following shaded parts represent?

a)
square metre or square meter
4 hundredths
4
100
 =   0.04
b)
square metre or square meter
10 hundredths
10 hundredths  =  1 tenth
=  0.1
10 hundredths make 1 tenth.
c)
square metre or square meter
50 hundredths
50
100
  =   0.50

Or,

50
100
  =  
5
10

=    0.5

The decimals 0.5 and 0.50 have the same value.
d)
square metre or square meter
1 23
100
  =   1  + 
23
100

=  1  +  0.23
=  1.23
e)
square metre or square meter
3 12
25
  =   3  + 
12
25

=   3  + 
48
100

=   3  +  0.48
=   3.48
Change the denominator to a multiple of 10.

25  ×  4 = 100

7. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.

a)   0.03
      0.03  = 
3
100
b)   0.5
      0.25  = 
25
100

1
4
c)   1.55
      1.55  =  
1 55
100

=  
1 11
20

8. What is the value of each digit in 73.65?

square metre or square meter
In 73.65,
  • the digit 7 is in the tens place, its value is 7 × 10 or 70
  • the digit 3 is in the ones place, its value is 3 × 1 or 3
  • the digit 6 is in the tenths place, its value is 6 × 0.1 or 0.6
  • the digit 5 is in the hundredths place, its value is 5 × 0.01 or 0.05
70   +   3   +   0.6   +   0.05  =  73.65

9. What is the value of each digit in 73.65?

square metre or square meter
A  =  2.82
B  =  2.95
C  =  3.03

10. Do the following.

a)   Change $10 and 35 ¢ to dollars.

      $10   and   35 ¢  =  $10  +  $0.35
=  $10.35
100 ¢  =  $1
1 ¢  = 
1
100
of $1

=  $0.01

b)   Write 4 m 65 cm in m.

      4 m   65 cm  =  4 m  +  65 cm
=  4.65 m
100 cm  =  1 m
1 cm  = 
1
100
m

=  0.01 m
c)   Express
9 3
100
litres in decimal.


     
9 3
100
  L   =   9 L  + 
3
100
L
=   9 L   +   0.03 L
=   9.03 L

11. Understanding Thousandths

Divide 1 whole into 1000 equal parts.

square metre or square meter
In the fraction form, each part has a value equal to
1
1000
or 1 thousandth.

In the decimal form, each part has a value equal to 0.001 (read as zero point zero zero one).

12. What decimals do the following fractions or mixed numbers represent?

a)   8 thousandths
      8 thousandths  = 
8
1000
 =  0.008
b)  
2607
1000

     
2607
1000
 = 
2000
1000
 + 
607
1000

 =  2  +  0.607
 =  2.607
c)  
5 300
1000

     
5 300
1000
  =   5  + 
300
1000

 =   5  +  0.300
 =   5.300

Or,

     
5 300
1000
  =   5  + 
300
1000

 =   5  + 
3
10

 =   5  +  0.3
 =   5.3

The decimals 5.300 and 5.3 have the same value.

13. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.

a)   0.003
      0.003   = 
3
1000
b)   0.250
      0.250   = 
250
1000

 = 
25
100

 = 
1
4
c)   1.775
      1.775   = 
1 775
1000

 = 
1 33
40

14. What is the value of each digit in 7.365?

square metre or square meter
In 7.365,
  • the digit 7 is in the ones place, its value is 7 × 1 or 7
  • the digit 3 is in the tenths place, its value is 3 × 0.1 or 0.3
  • the digit 6 is in the hundredths place, its value is 6 × 0.01 or 0.06
  • the digit 5 is in the thousandths place, its value is 5 × 0.001 or 0.005
7   +   0.3   +   0.06   +   0.005   =   7.365

15. Write a decimal for each letter on the number line below.

square metre or square meter
A  =  2.973
B  =  2.988
C  =  2.995
D  =  3

1 Whole

1  = 
10
10
 = 
100
100
 = 
1000
1000


Or,

1 whole  =  10 tenths
1 whole  =  100 hundredths
1 whole  =  1000 thousandths

1 tenth  =  0.1
1 hundredth  =  0.01
1 thousandth  =  0.001

16. Compare the numbers 3.687, 3.678 and 3.876 and 3.786.
a) Which number is the smallest?
b) Which number is the greatest?
c) Arrange the numbers in increasing order.
d) Arrange the numbers in decreasing order.

square metre or square meter
a)   3.678 is the smallest number.

b)   3.876 is the greatest number.

c)   Increasing order:
      3.678,    3.687,    3.786,    3.876

d)   Decreasing order:
      3.876,    3.786,    3.687,    3.678
Compare the numbers digit by digit starting with the digit in the highest place value.

17. Complete the number patterns below.

a)    3.591,    3.594,    ______,    3.6,    ______

square metre or square meter
Rule: Add 0.003 to get the next decimal number.

     b)    14.72,    13.62,    ______,    11.42,    ______,    9.22

square metre or square meter
Rule: Subtract 1.1 to get the next decimal.