Compare Decimals

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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 3

1. 4.56 __ 4.65 = ? Answer: < Solution: Write the numbers one above the other, lining up the decimal points: 4.56 4.65 Compare the whole number parts: both are 4, so they are equal. Compare the tenths place: 4.56 has 5 tenths, and 4.65 has 6 tenths.
   Full step-by-step solution

   Step 1: Write the numbers one above the other, lining up the decimal points: 4.56 4.65 Step 2: Compare the whole number parts: both are 4, so they are equal. Step 3: Compare the tenths place: 4.56 has 5 tenths, and 4.65 has 6 tenths. Step 4: Since 5 is less than 6, 4.56 is less than 4.65. Step 5: Therefore, the correct symbol is <. The answer is <.

2. Charlotte and Mason are comparing the lengths of two ribbons they have for a craft project. Charlotte's ribbon is 5.27 meters long, and Mason's ribbon is 5.72 meters long. Whose ribbon is longer? Answer: Mason's ribbon (5.72 meters) Solution: Write the two lengths: Charlotte's ribbon = 5.27 meters, Mason's ribbon = 5.72 meters. Compare the whole number parts. Both are 5, so they are equal.
   Full step-by-step solution

   Step 1: Write the two lengths: Charlotte's ribbon = 5.27 meters, Mason's ribbon = 5.72 meters. Step 2: Compare the whole number parts. Both are 5, so they are equal. Step 3: Compare the tenths place. Charlotte has 2 tenths (0.2), and Mason has 7 tenths (0.7). Since 7 is greater than 2, Mason's ribbon is longer. Step 4: You can check by writing both with two decimal places: 5.27 and 5.72. Comparing digit by digit: the whole numbers are the same, then 2 vs 7 in the tenths place. Since 7 > 2, 5.72 > 5.27. Therefore, Mason's ribbon (5.72 meters) is longer.

3. 0.67 > 0.59 = ? Answer: B. true Solution: Compare the tenths place: 0.67 has 6 tenths, 0.59 has 5 tenths Since 6 > 5, 0.67 is greater than 0.59 The statement '0.67 > 0.59' is true The answer is true.
   Full step-by-step solution

   Step 1: Compare the tenths place: 0.67 has 6 tenths, 0.59 has 5 tenths Step 2: Since 6 > 5, 0.67 is greater than 0.59 Step 3: The statement '0.67 > 0.59' is true The answer is true.

4. Ava and Noah are measuring the water they collected in two different rain gauges after a storm. Ava's gauge shows 2.16 inches of rain, and Noah's gauge shows 2.6 inches of rain. Whose gauge shows more rainfall? Answer: Noah Solution: Write the two amounts: Ava's = 2.16 inches, Noah's = 2.6 inches. Compare the whole number parts: Both are 2, so they are equal. Compare the tenths place: Ava has 1 tenth (0.1), Noah has 6 tenths (0.6).
   Full step-by-step solution

   Step 1: Write the two amounts: Ava's = 2.16 inches, Noah's = 2.6 inches. Step 2: Compare the whole number parts: Both are 2, so they are equal. Step 3: Compare the tenths place: Ava has 1 tenth (0.1), Noah has 6 tenths (0.6). Since 6 is greater than 1, Noah's amount is larger. Step 4: To confirm, rewrite 2.6 as 2.60 and compare to 2.16: 2.60 is greater than 2.16. Therefore, Noah's gauge shows more rainfall at 2.6 inches.

5. A rectangular swimming pool is drawn on grid paper where each square represents 0.25 square meters. The pool covers 12 squares across and 9 squares down. What is the total area of the swimming pool in square meters? Answer: 27 Solution: Find the total number of squares: 12 squares across × 9 squares down = 108 squares Each square represents 0.25 square meters Multiply total squares by area per square: 108 × 0.25 = 27 108 × 0.25 = 108 × 1/4 = 108 ÷ 4 = 27 The total area is 27 square meters.
   Full step-by-step solution

   Step 1: Find the total number of squares: 12 squares across × 9 squares down = 108 squares Step 2: Each square represents 0.25 square meters Step 3: Multiply total squares by area per square: 108 × 0.25 = 27 Step 4: 108 × 0.25 = 108 × 1/4 = 108 ÷ 4 = 27 The total area is 27 square meters.

6. Liam is comparing the weights of two rocks he found. The first rock weighs 0.87 kilograms and the second rock weighs 0.92 kilograms. Which rock is heavier? Answer: 0.92 Solution: Identify the weights of the two rocks. - First rock weight: 0.87 kilograms - Second rock weight: 0.92 kilograms Compare the two numbers digit by digit, starting from the left.
   Full step-by-step solution

   Step 1: Identify the weights of the two rocks. - First rock weight: 0.87 kilograms - Second rock weight: 0.92 kilograms Step 2: Compare the two numbers digit by digit, starting from the left. Both numbers have the same whole number part (0), so we compare the decimal parts. Step 3: Compare the tenths place (the first digit after the decimal point). - First rock: 0.87 has 8 in the tenths place. - Second rock: 0.92 has 9 in the tenths place. Since 9 is greater than 8, the second rock is heavier. Step 4: Conclusion. Because 0.92 is greater than 0.87, the second rock is heavier. Final Answer: 0.92

7. Hana and Matiu are comparing the distances they walked on a nature trail. Hana walked 15.07 kilometers, and Matiu walked 15.7 kilometers. Who walked the greater distance? Answer: Matiu (15.7 km) Solution: Write the two distances side by side: Hana = 15.07 km, Matiu = 15.7 km. Compare the whole number parts: Both have 15, so they are equal. Compare the tenths place: Hana has 0 tenths (0.0), Matiu has 7 tenths (0.7).
   Full step-by-step solution

   Step 1: Write the two distances side by side: Hana = 15.07 km, Matiu = 15.7 km. Step 2: Compare the whole number parts: Both have 15, so they are equal. Step 3: Compare the tenths place: Hana has 0 tenths (0.0), Matiu has 7 tenths (0.7). Since 7 is greater than 0, Matiu's distance is greater. Step 4: To confirm, rewrite 15.7 as 15.70 and compare to 15.07: 15.70 is greater than 15.07. Therefore, Matiu walked the greater distance at 15.7 km.

8. Mere and Hana are comparing their savings. Mere has saved $6.80, and Hana has saved $6.08. Who has saved more money? Answer: Mere Solution: Write both amounts clearly: Mere has $6.80, Hana has $6.08. Compare the whole number parts (the digits before the decimal point). Both are 6, so they are equal.
   Full step-by-step solution

   Step 1: Write both amounts clearly: Mere has $6.80, Hana has $6.08. Step 2: Compare the whole number parts (the digits before the decimal point). Both are 6, so they are equal. Step 3: Compare the tenths place (the first digit after the decimal point). Mere has 8 tenths (0.8), Hana has 0 tenths (0.0). Since 8 is greater than 0, Mere has more money. Step 4: We do not need to check the hundredths place because the tenths place already tells us which number is larger. Conclusion: Mere has saved more money than Hana. Answer: Mere

9. Mason and Isabella are comparing the lengths of two pieces of string for their craft project. Mason's string is 4.27 meters long, and Isabella's string is 4.3 meters long. Whose string is longer? Answer: Isabella's string (4.3 meters) Solution: Write the lengths: Mason's string = 4.27 meters, Isabella's string = 4.3 meters. Compare the whole number parts: Both have 4, so they are equal.
   Full step-by-step solution

   Step 1: Write the lengths: Mason's string = 4.27 meters, Isabella's string = 4.3 meters. Step 2: Compare the whole number parts: Both have 4, so they are equal. Step 3: Compare the tenths place: Mason's string has 2 tenths (0.2), Isabella's string has 3 tenths (0.3). Since 3 is greater than 2, Isabella's string is longer. Step 4: To confirm, rewrite 4.3 as 4.30 and compare to 4.27: 4.30 is greater than 4.27. Therefore, Isabella's string (4.3 meters) is longer.