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Compare Decimals

Grade 4 · Decimals · Worksheet 1

  1. 1.61 __ 1.16 = ? Answer: ______________
  2. Aroha and Tane are comparing the heights of two different tree ferns they found in the bush. One fern is 3.07 meters tall, and the other fern is 3.7 meters tall. Which fern is taller? Answer: ______________
  3. Compare: 105.50 __ 105.05 = ? Answer: ______________
  4. A rectangular swimming pool is drawn on grid paper where each square represents 0.5 meters on each side. The pool measures 15 squares long and 8 squares wide. What is the actual area of the swimming pool in square meters? Answer: ______________
  5. Compare: 12.45 __ 12.54 Answer: ______________
  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: ______________
  7. 0.75 > 0.7 = ?
    • A. false
    • B. true
  8. Aroha and Tane are comparing the heights of two trees in their backyard. The first tree is 15.28 meters tall, and the second tree is 15.3 meters tall. Which tree is taller? Answer: ______________
  9. 8.37 __ 8.73 = ? Answer: ______________
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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 1

  1. 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 >.

  2. Aroha and Tane are comparing the heights of two different tree ferns they found in the bush. One fern is 3.07 meters tall, and the other fern is 3.7 meters tall. Which fern is taller? Answer: the second fern (3.7 m) Solution: Write the heights side by side: first fern = 3.07 m, second fern = 3.7 m. Compare the whole number parts: Both have 3, so they are equal.
    Full step-by-step solution

    Step 1: Write the heights side by side: first fern = 3.07 m, second fern = 3.7 m. Step 2: Compare the whole number parts: Both have 3, so they are equal. Step 3: Compare the tenths place: The first fern has 0 tenths (0.0), and the second fern has 7 tenths (0.7). Since 7 is greater than 0, the second fern is taller. Step 4: To double-check, rewrite 3.7 as 3.70. Now compare 3.07 and 3.70. 3.70 is greater than 3.07. Therefore, the second fern at 3.7 meters is taller.

  3. Compare: 105.50 __ 105.05 = ? Answer: > Solution: Compare the whole number parts: 105 (from 105.50) and 105 (from 105.05). They are equal. Compare the tenths place digits: 5 (from 105.50) and 0 (from 105.05).
    Full step-by-step solution

    Step 1: Compare the whole number parts: 105 (from 105.50) and 105 (from 105.05). They are equal. Step 2: Compare the tenths place digits: 5 (from 105.50) and 0 (from 105.05). Since 5 is greater than 0, 105.50 is greater than 105.05. Step 3: Therefore, the correct symbol is >. The answer is >.

  4. A rectangular swimming pool is drawn on grid paper where each square represents 0.5 meters on each side. The pool measures 15 squares long and 8 squares wide. What is the actual area of the swimming pool in square meters? Answer: 30 Solution: Each square represents 0.5 meters, and the pool is 15 squares long Actual length = 15 × 0.5 = 7.5 meters The pool is 8 squares wide Actual width = 8 × 0.5 = 4 meters Area = length × width Area = 7.5 × 4 7.5 × 4 = 30 The actual area of the swimming pool is 30 square meters.
    Full step-by-step solution

    Step 1: Find the actual length of the pool Each square represents 0.5 meters, and the pool is 15 squares long Actual length = 15 × 0.5 = 7.5 meters Step 2: Find the actual width of the pool The pool is 8 squares wide Actual width = 8 × 0.5 = 4 meters Step 3: Calculate the area of the rectangular pool Area = length × width Area = 7.5 × 4 Step 4: Multiply the decimals 7.5 × 4 = 30 The actual area of the swimming pool is 30 square meters.

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

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

  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. 0.75 > 0.7 = ? Answer: B. true Solution: We are comparing two decimal numbers: 0.75 and 0.7. The symbol ">" means "greater than". Compare the numbers digit by digit from left to right.
    Full step-by-step solution

    Step 1: Understand the problem. We are comparing two decimal numbers: 0.75 and 0.7. The symbol ">" means "greater than". So the statement is: 0.75 > 0.7. Step 2: Compare the numbers digit by digit from left to right. Both numbers start with "0." so we compare the tenths place first. 0.75 has a 7 in the tenths place. 0.7 is the same as 0.70, which also has a 7 in the tenths place. Since the tenths digits are equal, we move to the next digit. Step 3: Compare the hundredths place. 0.75 has a 5 in the hundredths place. 0.7 (or 0.70) has a 0 in the hundredths place. 5 is greater than 0. Step 4: Conclusion. Since 0.75 has a greater hundredths digit than 0.70, 0.75 is greater than 0.7. Therefore, the statement "0.75 > 0.7" is true. Final answer: true

  8. Aroha and Tane are comparing the heights of two trees in their backyard. The first tree is 15.28 meters tall, and the second tree is 15.3 meters tall. Which tree is taller? Answer: second tree (15.3 m) Solution: Write the two heights: first tree = 15.28 m, second tree = 15.3 m. Compare the whole number parts: Both have 15, so they are equal. Compare the tenths place: First tree has 2 tenths (0.2), second tree has 3 tenths (0.3).
    Full step-by-step solution

    Step 1: Write the two heights: first tree = 15.28 m, second tree = 15.3 m. Step 2: Compare the whole number parts: Both have 15, so they are equal. Step 3: Compare the tenths place: First tree has 2 tenths (0.2), second tree has 3 tenths (0.3). Since 3 is greater than 2, the second tree is taller. Step 4: To confirm, rewrite 15.3 as 15.30 and compare to 15.28: 15.30 is greater than 15.28. Therefore, the second tree (15.3 m) is taller.

  9. 8.37 __ 8.73 = ? Answer: < Solution: Compare the whole number parts: 8 (from 8.37) and 8 (from 8.73). They are equal. Compare the tenths place digits: 3 (from 8.37) and 7 (from 8.73).
    Full step-by-step solution

    Step 1: Compare the whole number parts: 8 (from 8.37) and 8 (from 8.73). They are equal. Step 2: Compare the tenths place digits: 3 (from 8.37) and 7 (from 8.73). Since 3 is less than 7, 8.37 is less than 8.73. Step 3: Therefore, the correct symbol is <. The answer is <.