# Decimal number fraction

Decimal number fraction

In this we will learn how to represent a decimal number with the fractional part. For this we take the following example :

**Example 1: (75.65)**

_{10}** Step 1: **First we take the weights and put it in the format specified in the decimal number system done below

**10**^{1}** 10**^{0}** **^{ }**10**^{-1 }**10**^{-2}^{ }**← Weights**

. |

↑

Decimal point

Since the example above contains fractional part we must include the radix point or the decimal point.

__Step 2:__ Values are assigned to the corresponding weights before and after the decimal point as shown below:

**10**^{1}** 10**^{0}** **^{ }**10**^{-1 }**10**^{-2}^{ }**← Weights**

7 | 5 | . |
6 | 5 |

↑

Decimal point

__Step 3:__ Now calculate the product of the values and associated weights as shown

**7×10**

^{1}**5×10**

^{0}

^{.}**6x**

**10**

^{-1}**5x**

**10**

^{-2}

^{ }__Step 4:__Sum the products obtained in step 3 accordingly on the either side of the decimal point as illustrated below

**7×10**

^{1 }+ 5×10^{0 . }6×10^{-1 }

^{ }+ 5×10^{-2}

^{ }**= 7×10**

^{ }+ 5×1^{ . }6x(1/10)^{ }

^{ }+ 5x(1/100)

**= 70**

^{ }+ 5^{ . }(6/10)^{ }

^{ }+ (5/100)

**= 75**

^{ . }0.6^{ }

^{ }+ 0.05

**= (75**

^{ . }0.6**5)**

_{10}

**Some more examples that you can try**

- (154.97)
_{10} - (1.1)
_{10} - (0.984)
_{10} - (800.007)
_{10}