Compare Numbers with 3/8: Sorting Fractions, Decimals, and Percentages

Q: Why should I convert to decimals instead of fractions?

Decimals are easier to compare! Converting $ \frac{3}{8} = 0.375 $ lets you quickly see that 0.36

Q: How do I convert percentages to decimals quickly?

Move the decimal point two places left! So 36% becomes 0.36 and 40% becomes 0.40. This works because percent means "out of 100."

Q: What if I get a repeating decimal like 1/3?

Use enough decimal places to make the comparison clear. $ \frac{1}{3} = 0.333... $ which is clearly less than 0.375, so 0.333 is sufficient.

Q: Can I convert everything to percentages instead?

Yes! $ \frac{3}{8} = 37.5\% $, so you'd compare to 37.5%. Either way works - just pick one format and stick with it throughout the problem.

Q: How do I remember which numbers go in which group?

Write down your reference value first: $ \frac{3}{8} = 0.375 $. Then make two columns labeled " 0.375" and sort each converted number.

Number Comparison with Mixed Forms

Organise the following values into two groups of values greater than $\frac{3}{8}$ and values less than $\frac{3}{8}$ :

$\frac{1}{3},40\%,0.42,36\%,\frac{2}{3}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Organise the following values into two groups of values greater than $\frac{3}{8}$ and values less than $\frac{3}{8}$ :

$\frac{1}{3},40\%,0.42,36\%,\frac{2}{3}$

Step-by-step solution

To solve this problem, we first convert all the values to decimals to ease comparison with $\frac{3}{8} = 0.375$ .

$\frac{1}{3} \approx 0.333$
$36\% = 0.36$
$\frac{2}{3} \approx 0.667$
$40\% = 0.40$
$0.42$ remains the same.

Next, we compare each of these converted values to 0.375:

$0.333 (\frac{1}{3}) < 0.375$
$0.36 (36\%) < 0.375$
$0.40 (40\%) > 0.375$
$0.42 > 0.375$
$0.667 (\frac{2}{3}) > 0.375$

Therefore, the values less than $\frac{3}{8}$ are $\frac{1}{3}$ and $36\%$ , while the values greater than $\frac{3}{8}$ are $40\%$ , $0.42$ , and $\frac{2}{3}$ .

The correct answer choice is:

$36\%,\frac{1}{3}<\frac{3}{8}$

$0.42,40\%,\frac{2}{3}>\frac{3}{8}$

Final Answer

$36\%,\frac{1}{3}<\frac{3}{8}$

$0.42,40\%,\frac{2}{3}>\frac{3}{8}$

Key Points to Remember

Essential concepts to master this topic

Convert First: Change all numbers to same format before comparing
Decimal Method: Convert 3/8 = 0.375, then compare each value
Check Work: Verify 36% = 0.36 < 0.375 and 40% = 0.40 > 0.375 ✓

Common Mistakes

Avoid these frequent errors

Comparing different number formats directly
Don't compare 1/3 to 3/8 and 40% to 3/8 in their original forms = confusion and wrong groupings! Different formats make comparison nearly impossible. Always convert all numbers to the same format (decimals work best) before comparing.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{11}{50}$ written as a percentage?

FAQ

Everything you need to know about this question

Why should I convert to decimals instead of fractions?

Decimals are easier to compare! Converting $\frac{3}{8} = 0.375$ lets you quickly see that 0.36 < 0.375 < 0.42. With fractions, you'd need common denominators for each comparison.

How do I convert percentages to decimals quickly?

Move the decimal point two places left! So 36% becomes 0.36 and 40% becomes 0.40. This works because percent means "out of 100."

What if I get a repeating decimal like 1/3?

Use enough decimal places to make the comparison clear. $\frac{1}{3} = 0.333...$ which is clearly less than 0.375, so 0.333 is sufficient.

Can I convert everything to percentages instead?

Yes! $\frac{3}{8} = 37.5\%$ , so you'd compare to 37.5%. Either way works - just pick one format and stick with it throughout the problem.

How do I remember which numbers go in which group?

Write down your reference value first: $\frac{3}{8} = 0.375$ . Then make two columns labeled "< 0.375" and "> 0.375" and sort each converted number.

What if two numbers are very close to 3/8?

Be extra careful with your conversions! For example, 36% = 0.36 and $\frac{3}{8} = 0.375$ , so 36% is definitely smaller, but only by 0.015.

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