Question

When writing a decimal as a fraction, why does the fraction always have only 9s or 9s and 0s as digits in the denominator?

Answer 1

When decimal numbers are written as fractions, the denominator consists of 9s or 9s and 0s. This is due to the representation of decimal numbers using powers of 10 in the denominator.

Step-by-step explanation:

When writing a decimal as a fraction, the denominator will always consist of 9s or 9s and 0s. This is because the decimal representation of any number can be written as a fraction with powers of 10 in the denominator.

For example, to write 0.25 as a fraction, we can express it as 25/100. Simplifying this fraction gives us 1/4. Similarly, 0.75 can be written as 75/100, which simplifies to 3/4.

Since 100 can be expressed as 10^2, the denominator of the fraction will always have 9s or 9s and 0s.

Learn more about Decimal as a fraction