What is the fraction form of 0.15? a. 15/100 b. 10/15 c. 3/20 d. 20/3
The Correct Answer and Explanation is:
Thought for 7 seconds
Answer: c. 3/20
Converting the decimal 0.15 into a fraction begins by recognizing its place value. Since there are two digits to the right of the decimal point, 0.15 represents “fifteen hundredths.” In fraction form, that is written as
CopyEdit15
──
100
or 15/100. This initial fraction is valid, but it can be simplified further by removing any common factors shared by the numerator and the denominator.
To simplify 15/100, identify the greatest common divisor (GCD) of 15 and 100. Both numbers are divisible by 5. Dividing numerator and denominator by 5 gives:
CopyEdit15 ÷ 5 100 ÷ 5
────── = ──────
3 20
So the fraction reduces to 3/20. At this point, 3 and 20 share no common factors aside from 1, which means the fraction is in its simplest form.
You can check this result by performing the division 3 ÷ 20 on a calculator or by hand. It yields 0.15 exactly, confirming that 3/20 is mathematically equivalent to the original decimal. Thus option c, 3/20, is the correct answer in simplest form.
Let us briefly review the other choices:
- 15/100 (option a) is equivalent in value to 0.15 but it is not fully simplified.
- 10/15 (option b) simplifies to 2/3, which equals approximately 0.666…, not 0.15.
- 20/3 (option d) equals approximately 6.666…, which is far larger than 0.15.
Understanding how to convert a decimal into a fraction and then reduce it by dividing both numerator and denominator by their GCD is a fundamental skill in algebra and number theory. It ensures that answers are presented in the most concise and standard form.
