Comparing and Ordering Decimals — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The decimals 0.4, 0.04, 0.44, and 0.404 in ascending order are 0.04, 0.4, 0.44, 0.404.
Corrected: The decimals 0.4, 0.04, 0.44, and 0.404 in ascending order are 0.04, 0.4, 0.404, 0.44.
Grade 5 ordering shows 0.400 is less than 0.404, so the original sequence is correct only after careful place value checks.
2. Fix the sentence:
When ordering 0.7, 0.17, 0.71, 0.07 from least to greatest, the sequence is 0.07, 0.7, 0.17, 0.71.
Corrected: When ordering 0.7, 0.17, 0.71, 0.07 from least to greatest, the sequence is 0.07, 0.17, 0.7, 0.71.
0.70 is greater than 0.17, so 0.7 belongs after 0.17 in ascending order on the number line.
3. Fix the sentence:
The smallest decimal among 0.5, 0.55, 0.05, 0.505 is 0.505 because it has the most digits.
Corrected: The smallest decimal among 0.5, 0.55, 0.05, 0.505 is 0.05 because it has the smallest tenths place.
0.05 has 0 tenths, while the others have 5 tenths, giving 0.05 the smallest magnitude.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Order 0.3, 0.31, 0.13, 0.03 from least to greatest. The smallest decimal is 0.03.
0.03 has 0 tenths, smaller than 0.13, 0.3, and 0.31 in ascending order.
2. Place 0.6, 0.06, 0.66, 0.606 on a number line. The greatest decimal is 0.66.
0.660 is greater than 0.606, 0.600, and 0.060 in descending magnitude.
3. Arrange 1.2, 1.02, 1.22, 1.202 in ascending order. The decimal that comes second is 1.2.
Grade 5 sequence: 1.020, 1.200, 1.202, 1.220 — so 1.2 is second.
4. On a number line from 0 to 1, between 0.4 and 0.5 you would place 0.45.
0.45 falls between 0.40 and 0.50 by Grade 5 number line magnitude.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Order 0.8, 0.08, 0.88, 0.808 from least to greatest. Show how you used place value to decide.
Sample answer: The ascending order is 0.08, 0.808, 0.88, 0.8 padded equals 0.800, so the full sequence is 0.080, 0.800, 0.808, 0.880. I padded each decimal to thousandths and compared the tenths, hundredths, then thousandths places.
Grade 5 ordering relies on aligning place values to compare magnitudes accurately.
2. Plot 0.2, 0.25, 0.5, 0.05 on a number line from 0 to 1. Which decimal is closest to 0, and which is closest to 1?
Sample answer: 0.05 is closest to 0 because it has 0 tenths and only 5 hundredths. 0.5 is closest to 1 because it has 5 tenths, the largest tenths value in the group, giving it the greatest magnitude.
Grade 5 number line work uses place value to position decimals by magnitude.