Compare Decimals

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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 3

1. Sophia and Noah are comparing the distances they ran during gym class. Sophia ran 8.05 kilometers, and Noah ran 8.5 kilometers. Who ran a greater distance? Answer: Noah Solution: Write the two distances: Sophia = 8.05 km, Noah = 8.5 km. Step 2: Compare the whole number parts: Both are 8, so they are equal. Step 3: Compare the tenths place: Sophia has 0 tenths (0.0) and Noah has 5 tenths (0.5).
   Full step-by-step solution

   Step 1: Write the two distances: Sophia = 8.05 km, Noah = 8.5 km. Step 2: Compare the whole number parts: Both are 8, so they are equal. Step 3: Compare the tenths place: Sophia has 0 tenths (0.0) and Noah has 5 tenths (0.5). Since 5 is greater than 0, Noah's distance is greater. Step 4: To confirm, rewrite 8.5 as 8.50. Compare 8.05 and 8.50: 8.50 is larger than 8.05. Therefore, Noah ran a greater distance.

2. A rectangular swimming pool is drawn on grid paper where each square represents 0.25 square meters. The pool covers 12 squares across and 10 squares down. What is the total area of the swimming pool in square meters? Answer: 30 Solution: Calculate the total number of squares: 12 squares across × 10 squares down = 120 squares Each square represents 0.25 square meters Multiply total squares by area per square: 120 × 0.25 = 30 120 × 0.25 = 120 × 1/4 = 120 ÷ 4 = 30 The total area is 30 square meters.
   Full step-by-step solution

   Step 1: Calculate the total number of squares: 12 squares across × 10 squares down = 120 squares Step 2: Each square represents 0.25 square meters Step 3: Multiply total squares by area per square: 120 × 0.25 = 30 Step 4: 120 × 0.25 = 120 × 1/4 = 120 ÷ 4 = 30 The total area is 30 square meters.

3. 1.61 __ 1.16 = ? Answer: > Solution: Compare the whole number parts: 1 (from 1.61) and 1 (from 1.16). They are equal. Compare the tenths place digits: 6 (from 1.61) and 1 (from 1.16).
   Full step-by-step solution

   Step 1: Compare the whole number parts: 1 (from 1.61) and 1 (from 1.16). They are equal. Step 2: Compare the tenths place digits: 6 (from 1.61) and 1 (from 1.16). Since 6 is greater than 1, 1.61 is greater than 1.16. Step 3: Therefore, the correct symbol is >. The answer is >.

4. Liam measured the length of two ribbons for his art project. The first ribbon was 1.45 meters long, and the second ribbon was 1.6 meters long. Which ribbon is longer? Answer: 1.6 Solution: Write down the lengths of the two ribbons. First ribbon: 1.45 meters Second ribbon: 1.6 meters Compare the whole number part (the part before the decimal point). Both numbers have the same whole number part: 1.
   Full step-by-step solution

   Step 1: Write down the lengths of the two ribbons. First ribbon: 1.45 meters Second ribbon: 1.6 meters Step 2: Compare the whole number part (the part before the decimal point). Both numbers have the same whole number part: 1. Step 3: Compare the tenths place (the first digit after the decimal point). First ribbon: 1.45 → tenths digit is 4 Second ribbon: 1.6 → tenths digit is 6 Since 6 is greater than 4, the second ribbon is longer. Step 4: Confirm by thinking of both numbers with the same number of decimal places. 1.6 is the same as 1.60 Now compare 1.45 and 1.60: 1.60 − 1.45 = 0.15, which is positive, so 1.60 is larger. Step 5: Conclusion The ribbon that is 1.6 meters long is longer than the ribbon that is 1.45 meters long. ANSWER: 1.6

5. Isabella and Charlotte are measuring the lengths of two skipping ropes in their gym class. Isabella's rope measures 4.27 meters, and Charlotte's rope measures 4.3 meters. Which skipping rope is longer? Answer: Charlotte's rope (4.3 m) Solution: Write the two lengths: Isabella's rope = 4.27 m, Charlotte's rope = 4.3 m. Compare the whole number parts: Both have 4, so they are equal.
   Full step-by-step solution

   Step 1: Write the two lengths: Isabella's rope = 4.27 m, Charlotte's rope = 4.3 m. Step 2: Compare the whole number parts: Both have 4, so they are equal. Step 3: Compare the tenths place: Isabella has 2 tenths (0.2), Charlotte has 3 tenths (0.3). Since 3 is greater than 2, Charlotte's rope is longer. Step 4: To confirm, rewrite 4.3 as 4.30. Now compare 4.27 and 4.30. The hundredths place: 7 hundredths vs 0 hundredths, but the tenths already show 3 > 2, so the answer is clear. Therefore, Charlotte's skipping rope (4.3 m) is longer.

6. A construction company needs to compare the lengths of two steel beams. The first beam measures 4.35 meters and the second beam measures 4.4 meters. Which beam is longer? Write the length of the longer beam. Answer: 4.4 Solution: Compare the whole number parts: Both beams have 4 as the whole number part, so we need to compare the decimal parts.
   Full step-by-step solution

   Step 1: Compare the whole number parts: Both beams have 4 as the whole number part, so we need to compare the decimal parts. Step 2: Compare the tenths place: The first beam has 3 in the tenths place, the second beam has 4 in the tenths place. Step 3: Since 4 is greater than 3 in the tenths place, 4.4 is greater than 4.35. Step 4: The second beam measuring 4.4 meters is longer than the first beam measuring 4.35 meters. The answer is 4.4.

7. Hana and Matiu are comparing the distances they threw a softball during practice. Hana threw the ball 15.6 meters, and Matiu threw the ball 15.26 meters. Who threw the softball farther? Answer: Hana Solution: Write the two distances: Hana = 15.6 meters, Matiu = 15.26 meters. Compare the whole number parts: Both have 15, so they are equal. Compare the tenths place: Hana has 6 tenths (0.6) and Matiu has 2 tenths (0.2).
   Full step-by-step solution

   Step 1: Write the two distances: Hana = 15.6 meters, Matiu = 15.26 meters. Step 2: Compare the whole number parts: Both have 15, so they are equal. Step 3: Compare the tenths place: Hana has 6 tenths (0.6) and Matiu has 2 tenths (0.2). Since 6 is greater than 2, Hana's distance is greater. Step 4: To double-check, rewrite 15.6 as 15.60 and compare to 15.26: 15.60 is greater than 15.26. Therefore, Hana threw the softball farther.

8. Mere and Hana are comparing the distances they each walked during a charity walkathon. Mere walked 4.26 kilometers, and Hana walked 4.3 kilometers. Who walked the greater distance? Answer: Hana Solution: Write the two distances side by side: Mere = 4.26 km, Hana = 4.3 km. Compare the whole number parts: Both are 4, so they are equal. Compare the tenths place: Mere has 2 tenths (0.2), Hana has 3 tenths (0.3).
   Full step-by-step solution

   Step 1: Write the two distances side by side: Mere = 4.26 km, Hana = 4.3 km. Step 2: Compare the whole number parts: Both are 4, so they are equal. Step 3: Compare the tenths place: Mere has 2 tenths (0.2), Hana has 3 tenths (0.3). Since 3 is greater than 2, Hana's distance is greater. Step 4: To double-check, rewrite 4.3 as 4.30 and compare to 4.26: 4.30 is greater than 4.26. Therefore, Hana walked the greater distance (4.3 km).

9. Sophia and Noah are comparing the weights of their backpacks for a hiking trip. Sophia's backpack weighs 7.28 kilograms, and Noah's backpack weighs 7.3 kilograms. Whose backpack is heavier? Answer: Noah Solution: Write the weights side by side: Sophia's = 7.28 kg, Noah's = 7.3 kg. Compare the whole number parts: Both are 7, so they are equal. Compare the tenths place: Sophia has 2 tenths (0.2) and Noah has 3 tenths (0.3).
   Full step-by-step solution

   Step 1: Write the weights side by side: Sophia's = 7.28 kg, Noah's = 7.3 kg. Step 2: Compare the whole number parts: Both are 7, so they are equal. Step 3: Compare the tenths place: Sophia has 2 tenths (0.2) and Noah has 3 tenths (0.3). Since 3 is greater than 2, Noah's backpack is heavier. Step 4: Check the hundredths place if needed: Sophia has 8 hundredths, but Noah's 3 tenths is already larger than 2 tenths, so no further comparison is needed. Therefore, Noah's backpack is heavier at 7.3 kg.