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:
0.4 is greater than 0.7 because 4 comes before 7.
Corrected: 0.4 is less than 0.7 because 4 tenths is fewer than 7 tenths.
In Grade 5, when both decimals have one digit after the point, compare the tenths directly. 4 tenths is less than 7 tenths, so 0.4 < 0.7.
2. Fix the sentence:
On a number line 0.3 sits to the right of 0.8.
Corrected: On a number line 0.3 sits to the left of 0.8.
Grade 5 students use number lines to compare decimals. Since 0.3 is less than 0.8, it must be plotted to the left of 0.8.
3. Fix the sentence:
The symbol 0.5 < 0.5 shows the two decimals are equal.
Corrected: The symbol 0.5 = 0.5 shows the two decimals are equal.
Grade 5 learners pick = only when two numbers represent the same amount. The < symbol means strictly less than, so it cannot show equality.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Compare using >, <, or =: 0.6 > 0.2.
Grade 5 students compare 6 tenths and 2 tenths. Six tenths is greater, so 0.6 > 0.2.
2. Compare using >, <, or =: 0.3 < 0.9.
Three tenths is less than nine tenths, so for Grade 5 the answer is 0.3 < 0.9.
3. Compare using >, <, or =: 0.7 = 0.7.
When two decimals name the same value, Grade 5 students write the equal sign, so 0.7 = 0.7.
4. On a number line from 0 to 1, the decimal that lies to the right of 0.5 is 0 .8.
Grade 5 number line work: 0.8 is greater than 0.5, so it is plotted to the right of 0.5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how a Grade 5 student can use a number line to decide whether 0.4 or 0.7 is greater.
Sample answer: I plot both decimals between 0 and 1 by splitting the line into ten equal tenths. 0.4 lands at the fourth mark and 0.7 lands at the seventh mark. Since 0.7 is farther to the right, it is greater than 0.4.
Grade 5 learners use the number line to see that decimals farther right represent larger amounts.
2. Why is 0.5 equal to 0.50? Use Grade 5 place value language.
Sample answer: Both decimals have 5 in the tenths place. Annexing a zero in the hundredths place of 0.5 gives 0.50, but it adds zero hundredths, so the value does not change. That is why 0.5 = 0.50.
Grade 5 students learn that trailing zeros after the decimal keep the same value because they add zero of the next place.