Question

0.09

What is the fraction for the decimal expansion above?


A



1 over 11
B



1 ninth
C



1 over 90
D

Answer 1

The decimal \(0.09\) can be expressed as a fraction.

We can write \(0.09\) as \(\frac{9}{100}\) because it is in the hundredths place.

Next, we simplify \(\frac{9}{100}\). The greatest common divisor (GCD) of \(9\) and \(100\) is \(1\), meaning it cannot be simplified further.

Thus, the simplified fraction for \(0.09\) is \(\frac{9}{100}\), which is not listed in the options provided. However, let's check the listed options:

A. \( \frac{1}{11} \)
B. \( \frac{1}{9} \)
C. \( \frac{1}{90} \)
D. (option not provided)

None of these fractions equal \(0.09\) (or \(\frac{9}{100}\)). Therefore, the correct answer is not present among the choices you provided.

However, if you're looking for the decimal representation of these fractions:
- \( \frac{1}{11} \approx 0.090909... \) (repeating decimal)
- \( \frac{1}{9} \approx 0.1111... \) (repeating decimal)
- \( \frac{1}{90} \approx 0.0111... \) (repeating decimal)

None of these are equal to \(0.09\).