# Decimals

A decimal point separates whole numbers from numbers with value less than 1.

## Example: 3.232

Thousands | Hundreds | Tens | Units | Tenths | Hundredths | Thousandths |

3 | 2 | 3 | 2 |

The number 3, which is to the right, is a whole number and the numbers to the left are as follows:

- Tenths = 2/10
- Hundredths = 3/100
- Thousandths = 2/1000

# More Examples!

## Example 1

6.22

Six is a whole number (6 units) and .22 is less than one

2/10 + 2/100 = 22/100.

Th | H | T | U | 1/10 | 1/100 | 1/1000 |

6 | 2 | 2 |

## Example 2

56.134

56 is a whole number (5 tens and 6 units) and .134 is less than one

1/10 + 3/100 + 4/1000 = 134/1000.

Th | H | T | U | 1/10 | 1/100 | 1/1000 |

5 | 6 | 1 | 3 | 4 |

## Example 3

734.356

734 is a whole number (7 hundreds,3 tens and 4 units) and .356 is less than one

3/10 + 5/100 + 6/1000 = 356/1000.

Th | H | T | U | 1/10 | 1/100 | 1/1000 |

7 | 3 | 4 | 3 | 5 | 6 |

# Addition

We have to align the decimal points, before we add up.

U | 1/10 | |
---|---|---|

2. | 4 | + |

5. | 1 | |

7. | 5 | |

U | 1/10 | 1/100 | |
---|---|---|---|

4. | 2 | 9 | |

2. | 3 | 8 | + |

6. | 6 | 7 | |

1 |

T | U | 1/10 | 1/100 | |
---|---|---|---|---|

1 | 6. | 5 | 2 | |

3 | 5. | 2 | 4 | + |

5 | 1. | 7 | 6 | |

1 |

# Subtraction

Just like addition, we have to align the decimal points.

# Multiplication

Example 1: 2.5 x 3 = ?

1. Remove the decimal point

and multiply as normal.**Note!** 2.5 has only one number after the decimal

point.

2 5 | x |

3 | |

7 5 | |

1 |

2. Add a decimal point after the 7.

Hence, the answer has one number after
the

decimal point.

Answer=7.5

Example 2: 4.2 x 2.1=?

1. Remove the decimal points and multiply

as normal.**Note! **4.2 has one number
after the decimal

point and 2.1 has one number after the decimal

point 1+1=2.

4 | 2 | x | |

2 | 1 | ||

4 | 2 | ||

8 | 4 | 0 | |

8 | 8 | 2 | |

2. The answer should have two numbers

after the decimal point. Hence, add the

decimal point after the 8.

Answer=8.82

# Multiply by 10

If we multiply by 10 we move the decimal point one place to the right.

## Example 1

3.5 × 10= ?

Answer=35

## Example 2

4.678 × 10= ?

Answer=46.78

## Example 3

45.43 × 10= ?

Answer=454.3

# Multiply by 100

If we multiply by 100 we move the decimal point two places to the right.

## Example 1

4.56 x 100= ?

Answer=456

## Example 2

13.23 x 100= ?

Answer=1323

## Example 3

3.384 x 100= ?

Answer=338.4

# Multiply by 1000

If we multiply by 1000 we move the decimal point three places to the right.

## Example 1

0.64 x 1000= ?

Answer=640

## Example 2

1.230 x 1000= ?

Answer=1230

## Example 3

7.254 x 1000= ?

Answer=7254

# Division

Divide as normal but the decimal point for the answer should be aligned to the decimal point inside the division bracket.

## Example 1

Divide 5.5 by 5

## Example 2

Divide 12.3 by 3

In the above division we divided decimal numbers by whole numbers. Now we are going to divide decimal numbers by decimal numbers.

## Example 1

7.5 ÷ 2.5 = ?

- Multiply both the numbers by 10 to make it easier for us to divide.

7.5 x 10 = 75

2.5 x 10 = 25 - Divide 75 by 25

Dividing 75 by 25 is the same as dividing 7.5 by 2.5. Therefore the answer is **3**

## Example 2

1.4412 ÷ 0.12=?

- Multiply both the numbers by 100 to make it easier for us to divide.

1.4412 x 100 = 144.12

0.12 x 100 = 12 - Divide 144.12 by 12.

It helps if you know

your 12 times table!

Dividing 144.12 by 12 is the same as dividing 1.4412 by 0.12 Therefore the answer is **12.1**.

# Divide by 10

If we divide by 10 we move the decimal point one place to the left.

## Example 1

44 ÷ 10= ?

Answer=4.4

## Example 2

67.42 ÷ 10= ?

Answer=6.742

## Example 3

4.54 x 10= ?

Answer=0.454

# Divide by 100

If we divide by 100 we move the decimal point two places to the left.

## Example 1

236.2 ÷ 100= ?

Answer=2.362

## Example 2

12.34 ÷ 100= ?

Answer=0.1234

## Example 3

3.45 ÷ 100= ?

Answer=0.0345

# Divide by 1000

If we divide by 1000 we move the decimal point three places to the left.

## Example 1

435.2 ÷ 1000= ?

Answer=0.4352

## Example 2

12382.5 ÷= ?

Answer=12.3825

## Example 3

5325.34 ÷= ?

Answer=5.32534

# Recurring Decimal Number

A recurring decimal number is a number that is continously repeated. For example dividing 2 by 3 will give us a continous repeated decimal number 6.

2/3 = 0.6666666666666

0.66666666666 can be shortened to

# Decimals to Percentages

Multiply the decimal number by 100 for example 0.5 x 100= 50%

0.546 x 100 = 54.6%

0.035 x 100 = 3.5%

To convert the percentages back to decimals **divide by 100**.

# Fractions to Decimals

2/5 means 2 divide by 5

2/5 = 0.4

# Decimals to Fractions

0.4 means 4/10

.Th | H | T | U | 1/10 | 1/100 | 1/1000 |

4 |

We can say 4/10 equals 2/5 by dividing the top and bottom numbers by 2.

0.75 means 7/10 + 5/100 = 75/100

Th | H | T | U | 1/10 | 1/100 | 1/1000 |

7 | 5 |

We can say 75/100 = 3/4 by dividing the top and bottom number by 25.

# Whole Numbers

Whole numbers can be converted into fractions. For example we know 0.4 means 4/10 so 1.4 would mean 10/10 + 4/10 = 14/10.

## More Examples!

2.4 in fractions means 20/10 + 4/10 = 24/10

3.6 in fractions means 30/10 + 6/10 = 36/10

1.75 in fractions means 100/100 + 75/100 = 175/100

2.75 in fraction means 200/100 + 75/100 = 275/100