Compare Numbers with 6/7: Sorting Decimals, Percentages, and Fractions

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

Converting to decimals is usually easier because you can directly compare decimal values. Converting fractions like $ \frac{6}{7} $ to percentages would give messy numbers!

Q: How do I convert 6/7 to a decimal quickly?

Divide 6 by 7 using long division or a calculator: $ 6 ÷ 7 = 0.857142... $. For comparison, 0.857 is accurate enough.

Q: What if I get confused with percentages?

Remember: 84% means 84 out of 100, so 84% = 0.84. Just move the decimal point two places left or divide by 100!

Q: How precise should my decimal conversion be?

For $ \frac{6}{7} $, using 0.857 is precise enough. You need enough decimal places to clearly distinguish it from your other values like 0.84 and 0.9.

Fraction Comparison with Mixed Number Types

Organise the following into two groups of parts smaller than

$\frac{6}{7}$ and parts larger than $\frac{6}{7}$ :

$84\%,10\%,0.4,\frac{14}{50},0.9$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Organise the following into two groups of parts smaller than

$\frac{6}{7}$ and parts larger than $\frac{6}{7}$ :

$84\%,10\%,0.4,\frac{14}{50},0.9$

Step-by-step solution

To solve this problem, we will convert all given values into decimals to compare with $\frac{6}{7}$ .

Step 1: Convert $\frac{6}{7}$ into a decimal.
Calculate $\frac{6}{7} \approx 0.857$ .

Step 2: Convert each value into a decimal.
- 84% = 0.84.
- 10% = 0.10.
- 0.4 is already a decimal.
- $\frac{14}{50} = 0.28$ .
- 0.9 is already a decimal.

Step 3: Compare each value to $\frac{6}{7}$ .
- $0.84 < 0.857$ , so 84% is less than $\frac{6}{7}$ .
- $0.10 < 0.857$ , so 10% is less than $\frac{6}{7}$ .
- $0.4 < 0.857$ , so 0.4 is less than $\frac{6}{7}$ .
- $0.28 < 0.857$ , so $\frac{14}{50}$ is less than $\frac{6}{7}$ .
- $0.9 > 0.857$ , so 0.9 is greater than $\frac{6}{7}$ .

Therefore, the solution is:

$84\%,\frac{14}{50},0.4,10\%<\frac{6}{7}$

$0.9>\frac{6}{7}$

Final Answer

$84\%,\frac{14}{50},0.4,10\%<\frac{6}{7}$

$0.9>\frac{6}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert all values to same format before comparing
Technique: Change 6/7 to 0.857 then compare 84% = 0.84 < 0.857
Check: Verify by converting back: 0.9 > 6/7 because 0.9 > 0.857 ✓

Common Mistakes

Avoid these frequent errors

Comparing different number formats directly
Don't compare 84% directly to 6/7 without converting = wrong groupings! You can't determine which is larger when formats differ. Always convert all values 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?

Converting to decimals is usually easier because you can directly compare decimal values. Converting fractions like $\frac{6}{7}$ to percentages would give messy numbers!

How do I convert 6/7 to a decimal quickly?

Divide 6 by 7 using long division or a calculator: $6 ÷ 7 = 0.857142...$ . For comparison, 0.857 is accurate enough.

What if I get confused with percentages?

Remember: 84% means 84 out of 100, so 84% = 0.84. Just move the decimal point two places left or divide by 100!

Can I use cross-multiplication instead?

Cross-multiplication works for comparing two fractions, but here you have mixed formats (percentages, decimals, fractions). Converting to decimals handles all types at once.

How precise should my decimal conversion be?

For $\frac{6}{7}$ , using 0.857 is precise enough. You need enough decimal places to clearly distinguish it from your other values like 0.84 and 0.9.

What if two values are very close?

Be extra careful with your conversions! For example, if comparing 0.857 and 0.856, you need to be precise with your decimal calculations to avoid grouping errors.

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