Convert Fraction 167/1000 to Percentage: Step-by-Step Solution

Q: Why do I multiply by 100 to convert fractions to percentages?

Because percentage means 'per hundred'! When you multiply by 100, you're finding how many parts out of 100 your fraction represents. $ \frac{167}{1000} $ becomes 16.7 parts out of 100, or 16.7%.

Q: Is 16.70% the same as 16.7%?

Mathematically yes, but 16.7% is the preferred answer because we don't write unnecessary trailing zeros after the decimal point. Both represent the same value, but 16.7% is more concise.

Q: What if I get a really long decimal when I divide?

For percentage problems, usually round to one decimal place unless told otherwise. If $ \frac{167}{1000} $ gave 16.666...%, you'd write 16.7%. Always check if your problem asks for a specific number of decimal places!

Q: Can I use a shortcut instead of multiplying by 100?

Yes! Since $ \frac{167}{1000} $ has 1000 in the denominator, you can think: 167 out of 1000 equals how many out of 100? Divide both by 10: $ \frac{16.7}{100} = 16.7\% $.

Q: How do I check if my percentage answer is reasonable?

Ask yourself: Is my answer smaller than 100%? Since $ \frac{167}{1000} $ is less than 1 whole, the percentage must be less than 100%. Also, 167 is about 1/6 of 1000, so ~16-17% makes sense!

Fraction to Percentage with Decimal Results

Write the fraction $\frac{167}{1000}$ as a percentage

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:05 Multiply the fraction by 100 in order to convert to a percentage

00:20 Break down 1000 into factors of 100 and 10

00:25 Reduce wherever possible

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction $\frac{167}{1000}$ as a percentage

Step-by-step solution

To convert the fraction $\frac{167}{1000}$ to a percentage, we follow these steps:

Step 1: Recall the conversion method from fraction to percentage.
Step 2: Multiply $\frac{167}{1000}$ by 100 to perform the conversion.

Now let's perform the calculations:

First, we multiply the fraction by 100:
$\frac{167}{1000} \times 100 = \frac{167 \times 100}{1000}$

Simplify the expression by multiplying and then dividing:
$\frac{167 \times 100}{1000} = \frac{16700}{1000}$

Divide 16700 by 1000 to simplify:
$16700 \div 1000 = 16.7$

Thus, the percentage equivalent of $\frac{167}{1000}$ is $16.7\%$ .

Therefore, the solution to the problem is $16.7\%$ .

Final Answer

16.7%

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Multiply any fraction by 100 to convert to percentage
Calculation Method: $\frac{167}{1000} \times 100 = \frac{16700}{1000} = 16.7$
Verification Check: Convert back: 16.7% = 0.167 = $\frac{167}{1000}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 or multiplying by the wrong amount
Don't just convert the fraction to decimal (0.167) and call it done = missing the % conversion! This gives you the decimal form, not the percentage. Always multiply by 100 to complete the fraction-to-percentage conversion.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction $\frac{75}{100}$

to a percentage:

FAQ

Everything you need to know about this question

Why do I multiply by 100 to convert fractions to percentages?

Because percentage means 'per hundred'! When you multiply by 100, you're finding how many parts out of 100 your fraction represents. $\frac{167}{1000}$ becomes 16.7 parts out of 100, or 16.7%.

Is 16.70% the same as 16.7%?

Mathematically yes, but 16.7% is the preferred answer because we don't write unnecessary trailing zeros after the decimal point. Both represent the same value, but 16.7% is more concise.

What if I get a really long decimal when I divide?

For percentage problems, usually round to one decimal place unless told otherwise. If $\frac{167}{1000}$ gave 16.666...%, you'd write 16.7%. Always check if your problem asks for a specific number of decimal places!

Can I use a shortcut instead of multiplying by 100?

Yes! Since $\frac{167}{1000}$ has 1000 in the denominator, you can think: 167 out of 1000 equals how many out of 100? Divide both by 10: $\frac{16.7}{100} = 16.7\%$ .

How do I check if my percentage answer is reasonable?

Ask yourself: Is my answer smaller than 100%? Since $\frac{167}{1000}$ is less than 1 whole, the percentage must be less than 100%. Also, 167 is about 1/6 of 1000, so ~16-17% makes sense!

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