# Decimal Calculation

# Converting decimal system numbers to any other system

Suppose (12.725)_{ }is a number in decimal system which is required to be converted into octal system (8 digits)

We will first convert 12 into octal system.

(12)

Now to convert (0.725)

_{10}= (14)_{8}Now to convert (0.725)

_{10}into ( )_{8}, we will apply the following method:0.725 Ã— 8 | = 5.8 | Take out integral part from here. |

0.8 Ã— 8 | = 6.4 | Take out integral part from here. |

0.4 Ã— 8 | = 3.2 | Take out integral part from here. |

0.2 Ã— 8 | = 1.6 | Take out integral part from here. |

And keep doing this till we get decimal part as zero, i.e., the product should be an integer.
(0.725)

_{10}= (0.5632â€¦)_{8}_{}So, (12.725) = (14.5632â€¦)_{8}

# Converting any other system numbers to decimal system

Now suppose if (15.453)
We will first convert (15)

(15)

Now (0.453)

So, (15.453)

_{7 }is to be converted into decimal system, then the process is as follows:_{7}into decimal system.(15)

_{7}= 1 Ã— 7^{1}+ 5 Ã— 7^{0}= (12)_{10}Now (0.453)

_{7}= 4 Ã— 7^{-}^{1}+ 5 Ã— 7^{-}^{2}+ 3 Ã— 7^{-}^{3}= 0.6821So, (15.453)

_{7 }= (12.6821)_{10}