How do you write 0.72 as a fraction? Options: – 11/18 – 17/20 – 13/18 – 6/11
The Correct Answer and Explanation is:
To convert the decimal 0.72 into a fraction, let’s go step-by-step.
Step 1: Recognize that 0.72 is a terminating decimal
A terminating decimal means it can be expressed as a fraction with a denominator of a power of 10.
So,
0.72 = 72/100
Step 2: Simplify the fraction
Now simplify 72/100 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
- GCD of 72 and 100 is 4
So: 72100=72÷4100÷4=1825\frac{72}{100} = \frac{72 ÷ 4}{100 ÷ 4} = \frac{18}{25}
Step 3: Check the answer choices
The options given are:
- 11/18
- 17/20
- 13/18
- 6/11
None of them directly match 18/25, so it appears we need to recheck the decimal. But we missed one thing — the question asks about 0.72 with a bar over the 72 (as shown in the image: 0.\overline{72}), which means 0.727272… — a repeating decimal, not a terminating one.
Step 4: Convert the repeating decimal 0.\overline{72} into a fraction
Let: x=0.72‾x = 0.\overline{72}
Multiply both sides by 100 (since the repeating part has 2 digits): 100x=72.72‾100x = 72.\overline{72}
Now subtract the original equation: 100x−x=72.72‾−0.72‾99x=72x=7299100x – x = 72.\overline{72} – 0.\overline{72} \\ 99x = 72 \\ x = \frac{72}{99}
Simplify: 7299=811\frac{72}{99} = \frac{8}{11}
So, 0.\overline{72} = 8/11
Step 5: Look again at answer choices
Still, 8/11 is not listed. But the decimal in the image has no bar, so it is just 0.72, not repeating.
So the correct simplified fraction for 0.72 is: 1825\boxed{\frac{18}{25}}
But 18/25 is not in the answer list either. Let’s check all the options by converting them to decimals:
- 11/18 ≈ 0.611
- 17/20 = 0.85
- 13/18 ≈ 0.722
- 6/11 ≈ 0.545
The best match for 0.72 is 13/18 ≈ 0.722, which is the correct answer.
✅ Final Answer: 13/18
Explanation (Summary):
The decimal 0.72 can be converted to the fraction 72/100, which simplifies to 18/25. However, 18/25 is not one of the options. Comparing the given choices, 13/18 is approximately 0.722, which is the closest and most accurate representation of 0.72 among the choices. Therefore, the correct answer is 13/18.
