When 0.36 is written in its simplest fractional form, what is the sum of the…

A terminating decimal is converted to a fraction by writing the digits after the decimal point over a power of 10 with as many zeros as there are decimal places, and then reducing that fraction to its lowest terms by dividing the numerator and denominator by their highest common factor (HCF).

Applying this to 0.36:

1. 0.36 has two digits after the decimal point, so it is written as the fraction 36/100.

2. Factorise: 36 = 22×32 and 100 = 22×52, so the highest common factor (HCF) of 36 and 100 is 22 = 4.

3. Divide both the numerator and the denominator by 4: 36 ÷ 4 = 9 and 100 ÷ 4 = 25, giving the fraction 9/25.

4. Since 9 = 32 and 25 = 52 share no common factor other than 1, 9/25 is already in its lowest (simplest) terms.

5. Add the numerator and the denominator of this simplest form: 9 + 25 = 34.

As an independent check, convert 9/25 back to a decimal: 9/25 = 36/100 = 0.36, which matches the original value — confirming the simplification is correct, and the required sum is 34.