Question

Hi please do these three or you can just do one, two problems for me so, I can look back at it if I need help cuz I don't really get this and please explain how you got the answer don't just tell me the answer.

Write each decimal as a fraction in simplest form

Say it, Write it, Simply it.



1. 0.5 = ?
2. 0.7 = ?
3. 0. 875 = ?​

Answer 1

1)
`(1)/(2)`

2)
`(7)/(10)`

3)
`(7)/(8)`

Explanation:

Any decimal can be written as a fraction by just putting the given number over 1.

For example, take the first problem.

0.5 can be written as:

`(0.5)/(1)`

Then, to simplify it, multiply both the top and bottom by 2.

`(0.5 * 2)/(1 * 2)`

`= (1)/(2)`

The reason this doesn't change the value of the fraction is because any number over itself is 1. Look at the 2's we just multiplied by in the numerator and denominator. We are really just multiplying the entire fraction by 2/2, which equals 1. Here's a way of writing the above step that makes it clearer:

`(0.5)/(1) * (2)/(2)`

`=(1)/(2)`

So, the answer to the first problem is
`(1)/(2)`.

We can repeat these steps for the second problem.

`0.7 = (0.7)/(1)`

But this time, multiply by 10/10 instead of 2/2. Remember that 10/10 is still equal to 1.

`= (0.7)/(1) * (10)/(10)`

`= (7)/(10)`

So, the answer to the second problem is
`(7)/(10)`.

Finally, repeat the steps from the previous problems.

`0.875 = (0.875)/(1)`

But this time, multiply by 1,000/1,000.

`= (0.875)/(1) * (1,000)/(1,000)`

`= (875)/(1,000)`

And this time, some extra simplification is necessary. Divide by 25/25.

`= (875)/(1,000) / (25)/(25)`

`= (35)/(40)`

Then, divide by 5/5.

`= (35)/(40) / (5)/(5)`

`= (7)/(8)`

So, the answer to the third problem is
`(7)/(8)`.