# Decimals: Tenths, Hundredths and Thousandths

### Tenths

0.5, 0.7 and 0.2 are decimals or decimal numbers.

Divide 1 whole 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).

 Two parts are 2 10 or 2 tenths or 0.2.

What decimals do the following shaded parts represent?

a.
4 tenths
 4 10 =  0.4

b.
3 tenths
 3 10 =  0.3

c.
10 tenths
 10 tenths = 1 whole = 1

10 tenths make 1 whole.
d.
 2 3 10 = 2  + 3 10 = 2  + 0.3 = 2.3

e.
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 = 1 6 10 = 1 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.

 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
 4 100 =  0.04

b.
10 hundredths
 10 hundredths = 1 tenth = 0.1

10 hundredths make 1 tenth.
c.
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 23 100 = 1  + 23 100 = 1  + 0.23 = 1.23

e.
 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

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 = 1 55 100 = 1 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?
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.
 9 3  100 l = 9 l  + 3  100 l = 9 l  + 0.03 l = 9.03 l

### Thousandths

Divide 1 whole 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.
 26071000
 26071000 = 2.0001e+07 + 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.

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

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.

A  =  2.973
B  =  2.988
C  =  2.995
D  =  3

 1  = 1010 = 100100 = 10001000

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,  ______ Rule: Add 0.003 to get the next decimal number. b. 14.72,  13.62,  _______,  11.42,  ______,  9.22 Rule: Subtract 1.1 to get the next decimal.