Convert the Fraction 7.57/10 to a Percentage: A Detailed Approach

Q: Why do we multiply by 100 to get a percentage?

Percent means "per hundred" or "out of 100". When you multiply a fraction by 100, you're finding how many parts out of 100 it represents. So $ \frac{7.57}{10} \times 100 = 75.7 $ means 75.7 out of 100, or 75.7%.

Q: Can I simplify the fraction first before converting?

You could try, but $ \frac{7.57}{10} $ is already in a convenient form! Since 7.57 is a decimal, it doesn't simplify nicely. It's easier to multiply directly by 100.

Q: What if I get confused by the decimal in the numerator?

Think of it step by step: $ \frac{7.57}{10} $ means "7.57 divided by 10". When you multiply by 100, you get $ 7.57 \times \frac{100}{10} = 7.57 \times 10 = 75.7 $. The decimal moves one place to the right!

Q: Is there a shortcut for fractions with denominator 10?

Yes! When the denominator is 10, just multiply the numerator by 10 to get the percentage. $ \frac{7.57}{10} \rightarrow 7.57 \times 10 = 75.7\% $. This works because $ \times 100 ÷ 10 = \times 10 $.

Fraction to Percentage with Decimal Numerators

Convert the fraction into a percentage:

$\frac{7.57}{10}=\text{?}$

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Understand the problem

Convert the fraction into a percentage:

$\frac{7.57}{10}=\text{?}$

Step-by-step solution

To solve this problem, we'll convert the fraction $\frac{7.57}{10}$ into a percentage by following these steps:

Step 1: Identify the fraction, which is $\frac{7.57}{10}$ .
Step 2: To convert this fraction to a percentage, we multiply by 100, according to the formula: $\text{Percentage} = \left(\frac{\text{Numerator}}{\text{Denominator}}\right) \times 100\%$ .

Applying the formula, we have:

$\left(\frac{7.57}{10}\right) \times 100 = 7.57 \times 10 = 75.7\%$ .

The fraction $\frac{7.57}{10}$ is equivalent to $75.7\%$ .

This corresponds to the choice that is labeled as 75.7%, confirming it as the correct answer.

Therefore, the solution to the problem is $75.7\%$ .

Final Answer

75.7%

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply fraction by 100 to convert to percentage
Method: $\frac{7.57}{10} \times 100 = 7.57 \times 10 = 75.7\%$
Check: Verify 75.7% equals 0.757 as decimal form ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point incorrectly when multiplying by 100
Don't just add two zeros after 7.57 to get 757%! This ignores the denominator 10. Moving the decimal wrong gives 757% instead of 75.7%. Always multiply the entire fraction by 100: $\frac{7.57}{10} \times 100$ .

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do we multiply by 100 to get a percentage?

Percent means "per hundred" or "out of 100". When you multiply a fraction by 100, you're finding how many parts out of 100 it represents. So $\frac{7.57}{10} \times 100 = 75.7$ means 75.7 out of 100, or 75.7%.

Can I simplify the fraction first before converting?

You could try, but $\frac{7.57}{10}$ is already in a convenient form! Since 7.57 is a decimal, it doesn't simplify nicely. It's easier to multiply directly by 100.

What if I get confused by the decimal in the numerator?

Think of it step by step: $\frac{7.57}{10}$ means "7.57 divided by 10". When you multiply by 100, you get $7.57 \times \frac{100}{10} = 7.57 \times 10 = 75.7$ . The decimal moves one place to the right!

How can I double-check my percentage answer?

Convert your percentage back to a decimal and see if it equals the original fraction! 75.7% = 0.757, and $\frac{7.57}{10} = 0.757$ . They match! ✓

Is there a shortcut for fractions with denominator 10?

Yes! When the denominator is 10, just multiply the numerator by 10 to get the percentage. $\frac{7.57}{10} \rightarrow 7.57 \times 10 = 75.7\%$ . This works because $\times 100 ÷ 10 = \times 10$ .

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