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:
A pen costs $0.45 and a pencil costs $0.5. The pencil is cheaper because 5 is less than 45.
Corrected: A pen costs $0.45 and a pencil costs $0.5. The pen is cheaper because $0.45 is less than $0.50.
In Grade 5, $0.5 equals $0.50, which has a greater magnitude than $0.45 in the hundredths place.
2. Fix the sentence:
Juice is $1.7 and milk is $1.07, so milk is more expensive because it has more digits.
Corrected: Juice is $1.7 and milk is $1.07, so juice is more expensive because $1.70 is greater than $1.07.
Padding $1.7 to $1.70 shows the tenths place holds 7, while $1.07 only has 0 tenths.
3. Fix the sentence:
Apples cost $2.30 and pears cost $2.3. The apples are cheaper because $2.30 is smaller.
Corrected: Apples cost $2.30 and pears cost $2.3. The apples and pears cost the same because $2.30 equals $2.30.
Grade 5 place value shows $2.3 and $2.30 are equivalent — both have 2 ones and 3 tenths.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A bagel is $1.25 and a muffin is $1.52. The cheaper item is the bagel.
In Grade 5, $1.25 has 2 tenths while $1.52 has 5 tenths, so the bagel has a smaller magnitude.
2. A notebook costs $3.08 and a folder costs $3.8. The cheaper item costs $3.08.
$3.08 is less than $3.80 because 0 tenths is less than 8 tenths in ascending order.
3. Yogurt is $0.79 and pudding is $0.97. The price with the smaller magnitude is $0.79.
Grade 5 place value: 7 tenths is less than 9 tenths, so $0.79 is the cheaper price.
4. Crackers cost $4.6 and chips cost $4.06. The cheapest snack is the chips.
$4.06 has 0 tenths while $4.60 has 6 tenths, so chips have the smaller magnitude.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Mia sees three drinks: water for $1.25, juice for $1.5, and tea for $1.05. Which drink is cheapest, and how do you know?
Sample answer: Tea is cheapest at $1.05. I padded $1.5 to $1.50, then compared the tenths place. Tea has 0 tenths, water has 2 tenths, and juice has 5 tenths, so $1.05 is the smallest in ascending order.
Grade 5 students use place value to compare decimal magnitudes when one price has fewer digits.
2. Two stores sell the same eraser. Store A charges $0.6 and Store B charges $0.60. Which store is cheaper? Explain your reasoning.
Sample answer: Neither store is cheaper because $0.6 and $0.60 are equal. The trailing zero in $0.60 does not change the value — both prices have 6 tenths and 0 hundredths, so they have the same magnitude.
Grade 5 place value confirms equivalent decimals have the same value regardless of trailing zeros.