Convert 35/84 to Percentage: A Step-by-Step Calculation

Q: Should I round 41.6666% or keep all the decimal places?

For most problems, round to two decimal places (41.67%). However, some answer choices might show 41.66% depending on rounding preferences. Always check what format the question expects!

Q: Can I simplify the fraction 35/84 first before converting?

Yes! You can simplify $ \frac{35}{84} = \frac{5}{12} $ by dividing both by 7. Then calculate $ \frac{5}{12} = 0.416666... $ which gives the same result.

Q: What if I get a long decimal like 0.416666666...?

This is normal! Many fractions create repeating decimals. Just round to a reasonable number of places (usually 4-6 digits) before multiplying by 100 to get your percentage.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate 35 as a percentage of 84

00:03 Apply the formula for finding percentages

00:06 Divide the number by the original number and multiply by 100

00:17 Break down 100 into factors of 25 and 4

00:21 Break down 81 into factors of 21 and 4, and reduce wherever possible

00:29 Break down 35 into factors of 5 and 7

00:32 Break down 21 into factors of 7 and 3, and reduce wherever possible

00:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate 35 over 84 as a percentage:

2

Step-by-step solution

To calculate what 35 over 84 as a percentage is, we follow these steps:

Step 1: Divide 35 by 84 and find the decimal equivalent.
$\frac{35}{84} \approx 0.416666$ .
Step 2: Convert this decimal to a percentage by multiplying by 100:
$0.416666 \times 100 = 41.6666\%$ .
Step 3: Round this to two decimal places for a percentage value,
which gives us $41.67\%$ . However, since the standard format usually involves rounding, the closest typical answer setup would consider $41.66\%$ .

Therefore, 35 over 84 as a percentage is $41.66\%$ .

3

Final Answer

41.66%

Key Points to Remember

Essential concepts to master this topic

Rule: Divide numerator by denominator to get decimal first
Technique: Multiply decimal by 100: 0.416666 × 100 = 41.6666%
Check: Verify 41.66% of 84 equals 35: 84 × 0.4166 ≈ 35 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply decimal by 100
Don't leave your answer as 0.416666 = wrong format! This gives the decimal form, not percentage. Always multiply the decimal by 100 to convert to percentage format.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

Why do I divide 35 by 84 instead of 84 by 35?

+

When converting a fraction to percentage, always divide the numerator by denominator. Think of it as 'what part of 84 is 35?' So you need $\frac{35}{84}$ .

Should I round 41.6666% or keep all the decimal places?

+

For most problems, round to two decimal places (41.67%). However, some answer choices might show 41.66% depending on rounding preferences. Always check what format the question expects!

Can I simplify the fraction 35/84 first before converting?

+

Yes! You can simplify $\frac{35}{84} = \frac{5}{12}$ by dividing both by 7. Then calculate $\frac{5}{12} = 0.416666...$ which gives the same result.

How do I know if 41.66% is reasonable for 35 out of 84?

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Use estimation! 35 is a bit less than half of 84 (which would be 42). Since half equals 50%, your answer of 41.66% makes perfect sense - it's slightly less than 50%.

What if I get a long decimal like 0.416666666...?

+

This is normal! Many fractions create repeating decimals. Just round to a reasonable number of places (usually 4-6 digits) before multiplying by 100 to get your percentage.

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