Question

Represent the following terminating decimal in the form of a rational number `bb(("in fraction form" p/q)`:

42.75

Answer 1

Given: The terminating decimal number is 42.75.

Step-wise calculation:

1. Write the decimal number as a fraction with denominator a power of 10 based on the decimal places.

`42.75 = 4275/100`

There are two decimal places, so denominator is 10² = 100.

2. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD).

Find GCD of 4275 and 100.

Factors of 4275 include 25 since 25 × 171 = 4275.

Factors of 100 include 25.

So, divide numerator and denominator by 25:

`(4275 ÷ 25)/(100 ÷ 25) = 171/4`

The terminating decimal 42.75 can be expressed as the rational number `171/4` in simplest form.

So, `42.75 = 171/4`.