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 30 over 100 as a percentage:

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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