★ DECIMALS ★

Easy to Learn! Easy to Use!
1. WHAT IS A DECIMAL?

A decimal is a way of writing a number that has a whole part and a part of a whole.

We use a dot (.) called the decimal point.

Example:
In 3.45
3
Whole part
.
4 5
Decimal part
(part of a whole)
The numbers on the right side of the decimal point are less than 1.
2. PLACE VALUE IN DECIMALS

In decimals, each place on the right of the decimal point has a value.

Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths
.
1 10
1 100
1 1000
1000 100 10 1 . 0.1 0.01 0.001
Example: 27 . 345
2 ↑ 2 Tens
7 ↑ 7 Ones
•    
3 ↑ 3 Tenths
4 ↑ 4 Hundredths
5 ↑ 5 Thousandths
3. READING DECIMALS

We read decimals by saying the whole part, then "point", then each digit on the right.

Examples:

  • 2.5 – two point five
  • 7.08 – seven point zero eight
  • 12.345 – twelve point three four five
  • 0.6 – zero point six
  • 45.67 – forty five point six seven
Read each digit after the point separately!
4. COMPARING DECIMALS

To compare decimals:

  1. First, compare the whole parts.
  2. If whole parts are same, compare the tenths.
  3. If still same, compare the hundredths, and so on.

Examples:

3.5 > 2.8 (3 is greater than 2)
6.12 > 6.02 (1 tenth is greater than 0 tenth)
4.37 < 4.4 (37 hundredths is less than 40 hundredths)
5.06 = 5.060 (Trailing zeros do not change the value)
7.0 = 7 (7.0 is equal to 7)
More digits means greater value.
5. WRITING DECIMALS

We write decimals using a decimal point.

Examples:

In Words Decimal Form Expanded Form
Three and five tenths 3.5 3 + 0.5
Seven and eight hundredths 7.08 7 + 0.08
Twelve and three hundred forty five thousandths 12.345 12 + 0.3 + 0.04 + 0.005
Zero and six tenths 0.6 0 + 0.6
Forty five and sixty seven hundredths 45.67 45 + 0.6 + 0.07
6. DECIMAL ON A NUMBER LINE

Decimals can be shown on a number line.

0 0.5 1 1.5 2 0.2 0.8 1.3 1.7
Think of decimals as small steps between whole numbers!
7. ADDING DECIMALS (Easy)

Write the numbers one below the other.

Put the decimal points in a straight line.

Add as we add whole numbers.

Example:

  3.45
+ 2.30
  5.75
Line up the points!
8. SUBTRACTING DECIMALS (Easy)

Write the numbers one below the other.

Put the decimal points in a straight line.

Subtract as we subtract whole numbers.

Example:

  6.75
- 2.40
  4.35
Line up the points!
PRACTICE TIME!

A. Write the decimals.

  1. Three and four tenths = ________
  2. Six and seven hundredths = ________
  3. Nine and five thousandths = ________
  4. Zero and eight tenths = ________
  5. Eleven and thirty two hundredths = ________

B. Read the decimals.

  1. 4.3 = ________
  2. 7.09 = ________
  3. 12.456 = ________
  4. 0.7 = ________
  5. 45.68 = ________

C. Compare (<, > or =)

  1. 3.6 _____ 3.06
  2. 7.04 _____ 7.4
  3. 5.70 _____ 5.7
  4. 12.3 _____ 12.30
  5. 0.89 _____ 0.98
QUICK REMINDERS
  • ★ Decimal point (.) separates whole part and decimal part.
  • ★ Each place on the right is 10 times smaller than the place before it.
  • ★ Read each digit after the point separately.
  • ★ Line up the decimal points when adding or subtracting.