Convert 14 out of 90 to a Percentage: A Quick Calculation

Q: What does the repeating decimal 0.1̄5 mean?

The bar over the 5 means that digit repeats forever. So $ 0.1\overline{5} = 0.15555555... $ where the 5s continue infinitely.

Q: Why isn't the answer just 14%?

Don't confuse the numerator with the percentage! You must divide first: $ \frac{14}{90} \neq 14\% $. The fraction equals about 15.56%, not 14%.

Q: Should I simplify the fraction first?

You can! $ \frac{14}{90} = \frac{7}{45} $ after dividing both by 2. But either way, the percentage result is the same: 15.555...%.

Q: How do I write repeating decimals as percentages?

Convert the repeating decimal to a percentage by multiplying by 100, keeping the repeating pattern: $ 0.1\overline{5} \times 100 = 15.\overline{5}\% $

Q: Can I use a calculator for this?

Yes! But remember calculators show limited decimal places. You'll see 0.1555556 or similar. Recognize this represents the repeating decimal $ 0.1\overline{5} $.

Fraction-to-Percentage Conversion with Repeating Decimals

Calculate 14 over 90 as a percentage:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate 14 percent of 90

00:05 Convert from a percentage to a fraction, divide 14 by 90

00:09 Multiply by 100 to find the solution

00:17 Break down 90 into factors of 9 and 10

00:21 Break down 100 into factors of 10 and 10

00:25 Reduce wherever possible

00:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 14 over 90 as a percentage:

Step-by-step solution

To solve the problem of converting $\frac{14}{90}$ to a percentage, let's proceed as follows:

Step 1: Calculate $\frac{14}{90}$ as a decimal.
Step 2: Multiply the decimal by 100 to convert it to a percentage.

Step 1: Divide 14 by 90 to obtain $\frac{14}{90} = 0.155555555...$ . This is a repeating decimal indicated as $0.1\overline{5}$ .

Step 2: Convert this decimal to a percentage by multiplying by 100:
$0.155555... \times 100 = 15.555...$ . This represents the percentage as $15.555...\%$ .

Therefore, the fraction $\frac{14}{90}$ as a percentage is $15.555... \%$ , which matches the choice labeled as "15.555...%".

Final Answer

15.555...%

Key Points to Remember

Essential concepts to master this topic

Process: Divide numerator by denominator, then multiply by 100
Technique: $\frac{14}{90} = 0.1\overline{5} = 15.555...\%$
Check: Verify 15.555...% of 90 equals 14: 0.15555... × 90 = 14 ✓

Common Mistakes

Avoid these frequent errors

Rounding too early in the calculation
Don't round 0.15555... to 0.16 before converting to percentage = 16% instead of 15.555...%! This loses important precision and gives the wrong answer. Always keep full decimal accuracy until the final step, then express as repeating decimal notation.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

What does the repeating decimal 0.1̄5 mean?

The bar over the 5 means that digit repeats forever. So $0.1\overline{5} = 0.15555555...$ where the 5s continue infinitely.

Why isn't the answer just 14%?

Don't confuse the numerator with the percentage! You must divide first: $\frac{14}{90} \neq 14\%$ . The fraction equals about 15.56%, not 14%.

Should I simplify the fraction first?

You can! $\frac{14}{90} = \frac{7}{45}$ after dividing both by 2. But either way, the percentage result is the same: 15.555...%.

How do I write repeating decimals as percentages?

Convert the repeating decimal to a percentage by multiplying by 100, keeping the repeating pattern: $0.1\overline{5} \times 100 = 15.\overline{5}\%$

Can I use a calculator for this?

Yes! But remember calculators show limited decimal places. You'll see 0.1555556 or similar. Recognize this represents the repeating decimal $0.1\overline{5}$ .

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