Question

Write the decimal expansion of the following rational number and state which type of decimal expansion has?

`17/400`

Answer 1

Given: The rational number is `17/400`.

Step-wise calculation:

1. First, consider the denominator 400.

2. Factorise 400 into its prime factors: 400 = 2⁴ × 5²

3. Since the denominator is of the form 2^m × 5ⁿ, where m and n are non-negative integers, the decimal expansion of `17/400` is terminating.

4. Convert `17/400` to a decimal by adjusting the denominator to 10’s power: 

`17/400`

= `(17 xx 25)/(400 xx 25)`

= `425/10000`

= 0.0425

The decimal expansion of `17/400` is 0.0425, which is a terminating decimal expansion.