# Q: Change 0.56 to a base 5 decimal. _____

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### 2 Answers

A decimal in base 10 is equivalent to expressing each digit in terms of decreasing powers of 10. That is:

`0.56=5 times 10^{-1}+6 times 10^{-2}`

To convert this to base 5, we need to change the decimal into decreasing powers of 5, which means we are looking for a series of the form:

`a_1 5^{-1}+a_2 5^{-2}+a_3 5^{-3}+a_4 5^{-4}+cdots`

Noting each of the corresponding powers of 5, we get:

`5^{-1}=0.2`

`5^{-2}=0.04`

This means that if we select `a_1=2` , and `a_2=4` , then

`2 times 5^{-1}+4 times 5^{-2}=0.56`

**This means that in base 5, we get `0.56_{10}=0.42_5` .**

the way to solve this problem is:

Step 1: take 0.56 and multiply by 5 (the base5) = 2.80 and 2.80 > 1

Step2: Write down the 2; the 0.8 will be use for Step3

Step3: Take the 0.8 (from step 1) and multiply by 5 = 4.0; 4.0> 1

Step4: write down 4 and since the decimal part is 0 you are done.

The answer is 0.24