Question

How is 104.25 a rational number?

Answer 1

how is 104.25 a rational number? It a terminating decimal

Answer 2

It is a terminating decimal

Explanation:

You want to know how 104.25 is a rational number.

Rational number

A rational number is one that can be expressed as the ratio of two integers. Any terminating decimal can be expressed as such a ratio by considering the place value of the least-significant digit.

Here, the least-significant digit has a place value multiplier of 1/100, so the ratio of integers that has this value is ...

`104.25 = (10425)/(100) = (417)/(4)`

Besides terminating decimals, rational numbers also include repeating decimals. The length of the repeat is irrelevant, as long as there is one.

Some repeating decimals are ...

`(1)/(3)=0.\overline{3}\\\\(1)/(7)=0.\overline{142857}\\\\(1)/(19)=0.\overline{052631578947368421}`

The reciprocals of many prime numbers have repeating decimals with as many digits as the prime, less 1. As you can see, 1/7 has 6 repeating digits; 1/19 has 18 repeating digits.

Any terminating or repeating decimal is a rational number. 104.25 is a terminating decimal.