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:
0.45 is greater than 0.52 because 45 is bigger than 52 when you ignore the point.
Corrected: 0.45 is less than 0.52 because 4 tenths is less than 5 tenths.
Grade 5 students compare place by place. The tenths digit 4 is less than 5, so 0.45 < 0.52 even though 45 looks larger.
2. Fix the sentence:
Since 0.30 has more digits than 0.3, the decimal 0.30 is bigger.
Corrected: Since 0.30 has the same value as 0.3, the decimals are equal.
Grade 5 learners know 0.30 = 0.3 because the extra zero represents zero hundredths, so the values match.
3. Fix the sentence:
0.61 is less than 0.6 because 0.61 has more decimal places.
Corrected: 0.61 is greater than 0.6 because 0.61 = 0.60 + 0.01.
Grade 5 students rewrite 0.6 as 0.60 and then see 0.61 has one more hundredth, so 0.61 > 0.6.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Compare using >, <, or =: 0.27 < 0.31.
Grade 5 comparison: 2 tenths is less than 3 tenths, so 0.27 < 0.31 without checking hundredths.
2. Compare using >, <, or =: 0.84 > 0.48.
Grade 5 students see 8 tenths is greater than 4 tenths, so 0.84 > 0.48.
3. Compare using >, <, or =: 0.50 = 0.5.
Grade 5 learners annex a zero to 0.5 to get 0.50, showing both decimals are equal.
4. Compare using >, <, or =: 0.73 > 0.70.
Annex a zero to 0.7 to get 0.70, then compare 0.73 to 0.70 in hundredths.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe the Grade 5 left-to-right strategy for comparing 0.62 and 0.69.
Sample answer: I start at the largest place value, the tenths. Both decimals have 6 tenths, so they are tied. I move right to the hundredths and see 2 hundredths versus 9 hundredths. Since 9 hundredths is greater, 0.69 > 0.62.
Grade 5 students compare place values left to right because the leftmost digits hold the most value.
2. Why does annexing a zero help when comparing 0.4 and 0.36?
Sample answer: I rewrite 0.4 as 0.40 so both decimals show tenths and hundredths. Now I can see 0.40 has 4 tenths while 0.36 has 3 tenths, so 0.40 > 0.36 and therefore 0.4 > 0.36.
Grade 5 students annex zeros so they can compare matching place values without confusion.