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Decimals: Tenths, Hundredths and Thousandths

Tenths

Understanding tenths, hundredths and thousandths

0.5, 0.7 and 0.2 are decimals or decimal numbers.

Divide 1 whole into 10 equal parts.

1 whole divided into 10 equal parts

In the fraction form, each part has a value equal to   1 
10
  or 1 tenth.

The dot in a decimal is called a decimal point.
In the decimal form, each part has a value equal to 0.1 (read as zero point one).


2 parts are equal to 2 tenths or 0.2
Two parts are   2 
10
  or 2 tenths or 0.2.


What decimals do the following shaded parts represent?

a.  4 tenths
4 tenths
 4 
10
  =  0.4


b.  3 tenths
3 tenths
 3 
10
  =  0.3


c.  1 whole
10 tenths
10 tenths  =  1 whole
   =  1


10 tenths make 1 whole.
d.  2 wholes and 1 whole divided into 10 equal parts
 3 
10
  =  2  +  3 
10
    =  2  + 0.3
    =  2.3


e.  2 fifths = 4 tenths
2 fifths
 2 
5
  =   4 
10
2 fifths  =  4 tenths
   =  0.4


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  =   6 
10
   =   3 
5


What is the value of each digit in 736.5?

Hundreds Tens Ones Tenths
7 3 6 5


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


Hundredths

Divide 1 whole into 100 equal parts.

1 whole divided into 100 equal parts

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).


What decimals do the following shaded parts represent?

a.  4 hundredths
4 hundredths
 4 
100
  =  0.04


b.  10 hundredths
10 hundredths
10 hundredths  =  1 tenth
   =  0.1


10 hundredths make 1 tenth.
c.  50 hundredths
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.  1 whole and 1 whole divided into 100 equal parts
 23 
100
  =  1  +  23 
100
    =  1  + 0.23
    =  1.23


e.  3 wholes and 1 whole divided into 25 equal parts
 12 
25
  =  3  +  12 
25
    =  3  +  48 
100
    =  3  + 0.48
    =  3.48
Change the denominator to a multiple of 10.

25 × 4 = 100


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

a.  0.03
0.03  =   3 
100
 
b.  0.25
0.25  =   25 
100
   =   1 
4
 
c.  1.55
1.55  =   55 
100
   =   11 
20


What is the value of each digit in 73.65?

Tens Ones Tenths Hundredths
7 3 6 5


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


What decimal does each letter represent on the number line below?
decimal number line showing hundredths
A  =  2.82
B  =  2.95
C  =  3.03


Do the following.

a.  Change $10 and 35 ¢ to dollars.
100 ¢  =  $1
1 ¢  =    1  
100
 of $1
   =  $0.01
   
$10 and 35 ¢ = $10 + $0.35
  = $10.35


b.  Write 4 m 65 cm in m.
100 cm  =  1 m
1 cm  =    1  
100
 m
   =  0.01 m
   
4 m 65 cm  =  4 m + 0.65 m
   =  4.65 m


c.  
Express 9   3  
100
  litres in decimal.
   
 3  
100
  l  =  9 l  +   3  
100
l
     =  9 l  +  0.03l
     =  9.03 l


Thousandths

Divide 1 whole into 1000 equal parts.

1 whole divided into 1000 equal parts

  1  
1000
  =  1 thousandth  =  0.001

We read 0.001 as zero point zero zero one.


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.  
 300 
1000
 300 
1000
  =  5  +  300 
1000
    =  5  + 0.300
    =  5.300

       Or
 
 300 
1000
  =  5  +  300 
1000
    =  5  +  3 
10
    =  5  + 0.3
    =  5.3
The decimals 5.300 and 5.3 have the same value.


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  =   775 
1000
   =  1 33 
40


What is the value of each digit in 7.365?

Ones Tenths Hundredths Thousandths
7 3 6 5


In 73.65,
  • 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


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

decimal number line showing hundredths
A  =  2.973
B  =  2.988
C  =  2.995
D  =  3


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


Comparing and Ordering Decimals

Compare the numbers 3.687, 3.678 and 3.876 and 3.786.
  1. Which number is the smallest?
  2. Which number is the greatest?
  3. Arrange the numbers in increasing order.
  4. Arrange the numbers in decreasing order.


  Ones Tenths Hundredths Thousandths
3.687 3 6 8 7
3.678 3 6 7 8
3.876 3 8 7 6
3.786 3 7 8 6


Compare the numbers digit by digit starting with the digit in the highest place value.
  1. 3.678 is the smallest number.

  2. 3.876 is the greatest number.

  3. Increasing order:
    3.678,  3.687,  3.786,  3.876

  4. Decreasing order:
    3.876,  3.786,  3.687,  3.678


Decimal Number Patterns

Complete the number patterns below.

a.  3.591,  3.594,  ______,  3.6,  ______

Decimal number pattern

Rule: Add 0.003 to get the next decimal number.

 
b.  14.72,  13.62,  _______,  11.42,  ______,  9.22

Decimal number pattern

Rule: Subtract 1.1 to get the next decimal.