Ordering Fractions Decimals and Percents Practice: 6th Grade Guide
To order fractions, decimals, and percents, convert every value into the same form—usually a decimal or a percent—then compare them. For example, 1/2, 0.45, and 55% become 0.50, 0.45, and 0.55, so the correct order is 0.45 < 1/2 < 55%. This skill shows up constantly in sixth-grade math, from number-line work to standardized tests.
The good news is that once students have a reliable conversion routine, ordering becomes almost automatic. Below you’ll find a benchmark chart, a step-by-step method, practice problems with answers, and the mistakes that cost the most points.
Reference Chart and Benchmarks
A benchmark is a familiar value students can compare other numbers against without doing a full conversion. The most useful ones are worth memorizing because they appear repeatedly.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/2 | 0.50 | 50% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.20 | 20% |
| 1/10 | 0.10 | 10% |
A printable version of this chart works well taped inside a notebook cover. When a student sees 0.75, they should recognize it as 3/4 and 75%; when they see 50%, they should know it equals 1/2 and 0.5.
To use benchmarks while ordering, compare each value to 1/2 first. Anything above 0.5 goes to the right, anything below goes to the left. Then compare values within each group. For instance, 0.6, 3/8, and 70% split into “below half” (3/8 = 0.375) and “above half” (0.6 and 0.70), and only the two larger values need direct comparison.
Converting a fraction to a decimal and percent is one routine: divide the numerator by the denominator. So 3/8 = 3 ÷ 8 = 0.375, and moving the decimal point two places right gives 37.5%.
Step-by-Step Method
The cleanest strategy is to convert everything to decimals, because decimals line up easily by place value.
- Convert each fraction by dividing numerator by denominator.
- Convert each percent by dividing by 100 (50% = 0.50).
- Rewrite every value as a decimal with the same number of places.
- Compare from left to right, digit by digit.
Worked Example
Order 5/8, 0.6, and 55% from least to greatest.
- 5/8 = 5 ÷ 8 = 0.625
- 0.6 = 0.600
- 55% = 0.55
Written uniformly: 0.625, 0.600, 0.550. Comparing the tenths place and then the hundredths place gives 0.550 < 0.600 < 0.625. So the order is 55% < 0.6 < 5/8.
A shortcut: convert everything to percents instead. 5/8 = 62.5%, 0.6 = 60%, 55% = 55%. Same result, and many students find percent form easier to eyeball. Khan Academy has a full unit on this conversion process at Khan Academy.
Ordering Practice Problems
Work each set without a calculator first, then check against the keys.
Set 1: Least to Greatest
A) 1/4, 0.3, 20% B) 2/3, 0.65, 68% C) 0.9, 7/8, 85%
Answer key:
- A) 20% (0.20) < 1/4 (0.25) < 0.3
- B) 0.65 < 2/3 (0.666…) < 68% (0.68)
- C) 85% (0.85) < 7/8 (0.875) < 0.9
Set 2: Greatest to Least
A) 0.45, 1/2, 40% B) 5/6, 0.8, 82% C) 0.125, 15%, 1/8
Answer key:
- A) 1/2 (0.50) > 0.45 > 40% (0.40)
- B) 5/6 (0.833…) > 82% (0.82) > 0.8
- C) 15% (0.15) > 0.125 = 1/8 (they are equal)
Word Problems
1. Three students ran a race. Ana finished in 0.72 of the total time, Ben in 3/4, and Cara in 70%. Who finished fastest?
Answer: Fastest means smallest time. 70% (0.70) < 0.72 < 3/4 (0.75), so Cara finished fastest.
2. A store compares discounts: 2/5 off, 35% off, and 0.45 off. Which discount saves the most?
Answer: 2/5 = 0.40, 35% = 0.35, and 0.45. The largest is 0.45 off.
Common Mistakes and Test Tips
Most lost points come from a handful of recurring errors.
- Misreading decimals by length. Students often assume 0.45 > 0.5 because “45 is bigger than 5.” Line up place values: 0.45 is 45 hundredths, 0.5 is 50 hundredths, so 0.5 is larger.
- Forgetting that percents need dividing by 100. Treating 25% as 25 instead of 0.25 ruins the whole comparison.
- Ignoring the “greatest to least” direction. Reread the instructions before writing an answer.
- Skipping conversion to guess. Comparing 3/7 and 0.4 by eye is unreliable; convert both.
For timed quizzes, convert everything to the same form in the margin before comparing—this takes seconds and prevents careless errors. Use the 1/2 benchmark to sort quickly. For multiple-choice questions, you can often eliminate answers by checking just the smallest or largest value. If two values look nearly equal (like 2/3 and 0.66), compute to three decimal places: 2/3 = 0.666…, which is greater than 0.66. Precision matters most in these close calls.
Converting Fractions to Decimals Without a Calculator
Long division is the engine behind every fraction-to-decimal conversion, so it is worth practicing until it feels routine.
Some fractions stop; others repeat forever. For a terminating decimal, the denominator’s only prime factors are 2 and 5: examples include 1/2 = 0.5, 3/8 = 0.375, and 7/20 = 0.35. Any other denominator repeats: 1/3 = 0.333…, 2/11 = 0.181818…, and 5/6 = 0.8333…. For repeating decimals, write three decimal places and an ellipsis (0.666…) or use an overbar. When comparing a repeating decimal to a terminating one, three places is almost always enough to decide the order.
To see long division in action, convert 7/12 to a decimal. Set up 7 ÷ 12: 12 does not fit into 7, so write 0 and a decimal point, giving 0.5 because 12 × 5 = 60 with a remainder of 4. Bring down a zero to make 40; 12 × 3 = 36 with remainder 4. The remainder repeats, so the decimal is 0.58333…., confirming 7/12 sits between 0.58 and 0.59.
Using a Number Line to Order Values
A number line turns an abstract comparison into a visual one, which helps students who struggle to hold several values in their head at once.
- Draw a line and mark 0 on the left and 1 on the right.
- Add a midpoint mark for 1/2 = 0.5 = 50%.
- Plot each value by estimating its distance from the nearest benchmark.
- Read the final order straight off the line, left to right.
For values greater than 1, extend the line beyond 1 and mark 2. For negative values, mirror the line to the left of 0—remember that −0.4 is greater than −0.7 because it is closer to zero.
Here’s a mixed set: place 0.35, 2/5, and 32% on the line. Since 2/5 = 0.40 and 32% = 0.32, the marks fall at 0.32, 0.35, and 0.40. Reading left to right gives 32% < 0.35 < 2/5.
For values greater than one, convert each: 150% = 1.50, 1.4 = 1.40, and 3/2 = 1.50. The order from least to greatest is 1.4 < 3/2 = 150%. Note that 3/2 and 150% are equal—recognizing equivalences prevents students from inventing a false order. If the numerator is larger than the denominator, the value exceeds 1; compare these first against whole numbers, then against each other, rather than mixing them with fractions below 1.
Key Takeaways
- To order fractions, decimals, and percents, convert all values to one form—decimals are usually easiest.
- Benchmark values like 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 3/4 = 0.75 = 75% make comparisons fast.
- Convert a fraction by dividing numerator by denominator, then shift the decimal two places for the percent.
- Line up place values before comparing; 0.5 is greater than 0.45.
- Reread whether the question wants least-to-greatest or greatest-to-least.
- Practice with mixed sets and word problems, then check your work against an answer key to catch recurring errors.
