Question

How do you change `398.4374` into a fraction?

Answer 1

See below.

Explanation:

Decimals are just another way to write fractions. In essence, `0.1` is the same as `1/10`, `0.01` is the same as `1/100`, and `1.023` is the same as `1023/1000` (for example).

Now, let's tackle the problem at hand. This is a decimal which has 4 places, so the last digit is in the ten-thousandths place. This means that the fraction in our answer has to be out of `10,000`. Now that we know the denominator (bottom) of the fraction, let's write the actual fraction:

`3984374/10000`

This is our final answer. Since the question doesn't specify whether or not the answer has to be in simplest form, we are done. (Note that the numerator no longer has any decimal.)

I hope that helps! P.S. If you find any part of my answer confusing, please leave a comment. Thank you!

Answer 2

`398.4374 = 1992187/5000`

Explanation:

A terminating decimal can be written as a multiple of a negative power of `10` then simplified:

`398.4374 = 3984374/10000 = (color(red)(cancel(color(black)(2))) * 1992187) / (color(red)(cancel(color(black)(2))) * 5000) = 1992187/5000`