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AQA GCSE · Question 05 · Number
Put these values in order of size, starting with the smallest.
80%, 0.7, 3/4
Put these values in order of size, starting with the smallest.
80%, 0.7, 3/4
How to approach this question
To compare these values, convert them all to the same format, either decimals or percentages.
Method 1: Convert to decimals
- 80% = 80/100 = 0.80
- 0.7 is already a decimal.
- 3/4 = 0.75
Now compare the decimals: 0.7, 0.75, 0.80.
The order from smallest to largest is 0.7, 0.75, 0.80.
Now write them back in their original form: 0.7, 3/4, 80%.
Method 2: Convert to percentages
- 80% is already a percentage.
- 0.7 = 0.7 x 100% = 70%
- 3/4 = (3/4) x 100% = 75%
Now compare the percentages: 70%, 75%, 80%.
The order from smallest to largest is 70%, 75%, 80%.
Now write them back in their original form: 0.7, 3/4, 80%.
Full Answer
0.7, 3/4, 80%
To order numbers of different types (percentages, decimals, fractions), it is easiest to convert them all into a single, consistent format. Let's convert them all to decimals.
1. **80%**: The word "percent" means "out of 100". So, 80% is 80/100, which is 0.8.
2. **0.7**: This is already in decimal form.
3. **3/4**: To convert a fraction to a decimal, you can find an equivalent fraction with a denominator of 100. 3/4 is equivalent to 75/100, which is 0.75.
Now we have the three numbers as decimals: 0.8, 0.7, and 0.75.
We can now easily order them from smallest to largest:
0.7 is the smallest.
0.75 is next.
0.8 is the largest.
Finally, we write the numbers in their original forms in this order: 0.7, 3/4, 80%.
Common mistakes
✗ Incorrectly converting between formats, e.g., thinking 3/4 is 0.34 or 80% is 0.08.\n✗ Ordering them based on the numbers they see, e.g., 0.7, 3/4, 80 because 0.7 < 3 < 80.
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