Compare Decimals

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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 2

1. Compare: 7.83 __ 7.38 = ? Answer: > Solution: Compare the whole number parts: 7 (from 7.83) and 7 (from 7.38). They are equal. Compare the tenths place digits: 8 (from 7.83) and 3 (from 7.38).
   Full step-by-step solution

   Step 1: Compare the whole number parts: 7 (from 7.83) and 7 (from 7.38). They are equal. Step 2: Compare the tenths place digits: 8 (from 7.83) and 3 (from 7.38). Since 8 is greater than 3, 7.83 is greater than 7.38. Step 3: Therefore, the correct symbol is >. The answer is >.

2. Aroha and Kaia are comparing the distances they can throw a softball. Aroha threw the ball 9.36 meters, and Kaia threw the ball 9.4 meters. Who threw the ball a greater distance? Answer: Kaia (9.4 meters) Solution: Write the two distances: Aroha = 9.36 meters, Kaia = 9.4 meters. Compare the whole number parts: Both have 9, so they are equal. Compare the tenths place: Aroha has 3 tenths (0.3), Kaia has 4 tenths (0.4).
   Full step-by-step solution

   Step 1: Write the two distances: Aroha = 9.36 meters, Kaia = 9.4 meters. Step 2: Compare the whole number parts: Both have 9, so they are equal. Step 3: Compare the tenths place: Aroha has 3 tenths (0.3), Kaia has 4 tenths (0.4). Since 4 is greater than 3, Kaia's distance is greater. Step 4: To confirm, rewrite 9.4 as 9.40 and compare to 9.36: 9.40 is greater than 9.36. Therefore, Kaia threw the ball a greater distance (9.4 meters).

3. Liam is comparing the lengths of two caterpillars he found in his garden. The first caterpillar measures 0.87 meters long, and the second caterpillar measures 0.9 meters long. Which caterpillar is longer? Answer: 0.9 Solution: Write the two lengths clearly. First caterpillar: 0.87 meters Second caterpillar: 0.9 meters Understand that 0.9 is the same as 0.90. This is because 0.9 = 9/10 = 90/100 = 0.90.
   Full step-by-step solution

   Let's compare the two lengths step by step. Step 1: Write the two lengths clearly. First caterpillar: 0.87 meters Second caterpillar: 0.9 meters Step 2: Understand that 0.9 is the same as 0.90. This is because 0.9 = 9/10 = 90/100 = 0.90. Step 3: Compare the two numbers digit by digit after the decimal point. 0.87 = 87/100 0.90 = 90/100 Step 4: Since both have the same denominator (100), compare the numerators: 87 is less than 90. Step 5: Therefore, 0.87 < 0.90, which means 0.87 < 0.9. Step 6: Conclusion: The second caterpillar (0.9 meters) is longer. ANSWER: 0.9

4. 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.

5. A construction company needs to compare the lengths of two steel beams. Beam A measures 156.38 meters and Beam B measures 156.4 meters. Which beam is longer? Write the length of the longer beam. Answer: 156.4 Solution: Write both measurements with the same number of decimal places to make comparison easier.
   Full step-by-step solution

   Step 1: Write both measurements with the same number of decimal places to make comparison easier. Step 2: Beam A = 156.38 meters Step 3: Beam B = 156.40 meters (adding a zero to the hundredths place) Step 4: Compare digit by digit from left to right: - Hundreds: both have 1 - Tens: both have 5 - Ones: both have 6 - Tenths: both have 3 - Hundredths: Beam A has 8, Beam B has 0 Step 5: Since 8 is greater than 0 in the hundredths place, 156.38 is greater than 156.40 Step 6: Wait, let's double-check: 156.38 vs 156.40 Actually, 40 hundredths is greater than 38 hundredths, so 156.40 > 156.38 Step 7: Therefore, Beam B (156.4 meters) is longer than Beam A (156.38 meters). The answer is 156.4.

6. 12.45 __ 12.54 = ? Answer: < Solution: Compare the whole number parts: both are 12, so they are equal. Compare the tenths place: 12.45 has 4 tenths, and 12.54 has 5 tenths. Since 4 is less than 5, 12.45 is less than 12.54.
   Full step-by-step solution

   Step 1: Compare the whole number parts: both are 12, so they are equal. Step 2: Compare the tenths place: 12.45 has 4 tenths, and 12.54 has 5 tenths. Step 3: Since 4 is less than 5, 12.45 is less than 12.54. Step 4: Therefore, the correct symbol is <. The answer is <.

7. Liam is comparing the lengths of two worms he found in the garden. The first worm measured 0.85 meters and the second worm measured 0.79 meters. Which worm is longer? Answer: 0.85 Solution: We are comparing two decimal numbers: 0.85 and 0.79. We need to determine which number is larger, because the larger number means the longer worm. Compare the whole number parts.
   Full step-by-step solution

   Step 1: Understand the problem. We are comparing two decimal numbers: 0.85 and 0.79. We need to determine which number is larger, because the larger number means the longer worm. Step 2: Compare the whole number parts. Both numbers have the same whole number part: 0. So we must look at the decimal parts. Step 3: Compare the decimal parts digit by digit, starting from the tenths place. - Tenths place: 0.85 has 8 in the tenths place. 0.79 has 7 in the tenths place. Since 8 is greater than 7, 0.85 is larger than 0.79. Step 4: Conclusion. The first worm (0.85 meters) is longer than the second worm (0.79 meters). Final answer: 0.85

8. Matiu and Hana are comparing their pumpkin weights from the school garden. Matiu's pumpkin weighs 4.82 kilograms, and Hana's pumpkin weighs 4.8 kilograms. Whose pumpkin is heavier? Answer: Matiu Solution: Write the weights with the same number of decimal places. Matiu's pumpkin: 4.82 kg. Hana's pumpkin: 4.8 kg = 4.80 kg.
   Full step-by-step solution

   Step 1: Write the weights with the same number of decimal places. Matiu's pumpkin: 4.82 kg. Hana's pumpkin: 4.8 kg = 4.80 kg. Step 2: Compare the whole number part (the digits before the decimal point). Both have 4, so they are equal. Step 3: Compare the tenths place (first digit after the decimal). Matiu has 8 tenths (0.8) and Hana has 8 tenths (0.8). They are equal. Step 4: Compare the hundredths place (second digit after the decimal). Matiu has 2 hundredths (0.02) and Hana has 0 hundredths (0.00). Step 5: Since 0.02 is greater than 0.00, Matiu's pumpkin is heavier. Answer: Matiu

9. Maria and Carlos are comparing their long jump distances from track practice. Maria jumped 2.35 meters and Carlos jumped 2.4 meters. Who jumped farther? Answer: B. Carlos Solution: Compare the whole number parts: Both jumps have 2 meters in the whole number part, so they are equal. Compare the tenths place: Maria has 3 tenths (0.3) and Carlos has 4 tenths (0.4).
   Full step-by-step solution

   Step 1: Compare the whole number parts: Both jumps have 2 meters in the whole number part, so they are equal. Step 2: Compare the tenths place: Maria has 3 tenths (0.3) and Carlos has 4 tenths (0.4). Since 0.4 is greater than 0.3, Carlos jumped farther. Step 3: We don't need to check the hundredths place because the tenths place already shows which number is greater. Therefore, Carlos jumped farther with 2.4 meters compared to Maria's 2.35 meters.