Compare Decimals

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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 2

1. 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.

2. 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.

3. Liam and Emma are comparing the heights of two sunflowers they grew in their gardens. Liam's sunflower is 1.43 meters tall, and Emma's sunflower is 1.4 meters tall. Whose sunflower is taller? Answer: Liam's sunflower (1.43 meters) Solution: Write the heights: Liam's sunflower = 1.43 meters, Emma's sunflower = 1.4 meters. Compare the whole number parts: Both have 1, so they are equal.
   Full step-by-step solution

   Step 1: Write the heights: Liam's sunflower = 1.43 meters, Emma's sunflower = 1.4 meters. Step 2: Compare the whole number parts: Both have 1, so they are equal. Step 3: Compare the tenths place: Liam has 4 tenths (0.4), Emma has 4 tenths (0.4). They are the same. Step 4: Since the tenths are equal, compare the hundredths place: Liam has 3 hundredths (0.03), Emma has 0 hundredths (0.00). You can rewrite 1.4 as 1.40 to see this clearly. Step 5: 3 hundredths is greater than 0 hundredths, so 1.43 is greater than 1.4. Therefore, Liam's sunflower (1.43 meters) is taller than Emma's sunflower (1.4 meters).

4. Matiu and Mere are comparing the distances they walked during a school field trip. Matiu walked 103.45 meters from the bus to the museum entrance, and Mere walked 103.5 meters from the bus to the gift shop. Who walked the greater distance? Answer: Mere Solution: Write the two distances side by side: Matiu = 103.45 meters, Mere = 103.5 meters. Step 2: Compare the whole number parts: Both have 103, so they are equal.
   Full step-by-step solution

   Step 1: Write the two distances side by side: Matiu = 103.45 meters, Mere = 103.5 meters. Step 2: Compare the whole number parts: Both have 103, so they are equal. Step 3: Compare the tenths place: Matiu has 4 tenths (0.4) and Mere has 5 tenths (0.5). Since 5 is greater than 4, Mere's distance is greater. Step 4: To confirm, rewrite 103.5 as 103.50 and compare to 103.45: 103.50 is greater than 103.45. Therefore, Mere walked the greater distance.

5. Compare: 9.45 __ 9.54 = ? Answer: < Solution: Compare the whole number parts: 9 (from 9.45) and 9 (from 9.54). They are equal. Compare the tenths place digits: 4 (from 9.45) and 5 (from 9.54).
   Full step-by-step solution

   Step 1: Compare the whole number parts: 9 (from 9.45) and 9 (from 9.54). They are equal. Step 2: Compare the tenths place digits: 4 (from 9.45) and 5 (from 9.54). Since 4 is less than 5, 9.45 is less than 9.54. Step 3: Therefore, the correct symbol is <. The answer is <.

6. 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 <.

7. A rectangular garden is drawn on grid paper. The longer sides measure 12.5 meters each, and the shorter sides measure 8.75 meters each. What is the perimeter of the garden? Answer: 42.5 Solution: A rectangle has two pairs of equal sides: two longer sides and two shorter sides. Identify the lengths of the sides. The longer sides are each 12.5 meters.
   Full step-by-step solution

   A rectangle has two pairs of equal sides: two longer sides and two shorter sides. Step 1: Identify the lengths of the sides. The longer sides are each 12.5 meters. The shorter sides are each 8.75 meters. Step 2: Recall the formula for the perimeter of a rectangle. The perimeter is the total distance around the garden, which is the sum of all four sides. Perimeter = (2 × longer side) + (2 × shorter side) Step 3: Substitute the given values into the formula. Perimeter = (2 × 12.5) + (2 × 8.75) Step 4: Perform the multiplications. First, calculate 2 × 12.5. 2 × 12.5 = 25.0 Next, calculate 2 × 8.75. 2 × 8.75 = 17.5 Step 5: Add the two results together. 25.0 + 17.5 = 42.5 Step 6: State the final answer. Therefore, the perimeter of the rectangular garden is 42.5 meters.

8. Olivia and Emma are comparing the weights of their pumpkins at the school fair. Olivia's pumpkin weighs 7.03 kilograms, and Emma's pumpkin weighs 7.3 kilograms. Whose pumpkin weighs more? Answer: Emma's pumpkin (7.3 kg) Solution: Write both weights: Olivia = 7.03 kg, Emma = 7.3 kg. Compare the whole number parts: Both have 7, so they are equal. Compare the tenths place: Olivia has 0 tenths (0.0), Emma has 3 tenths (0.3).
   Full step-by-step solution

   Step 1: Write both weights: Olivia = 7.03 kg, Emma = 7.3 kg. Step 2: Compare the whole number parts: Both have 7, so they are equal. Step 3: Compare the tenths place: Olivia has 0 tenths (0.0), Emma has 3 tenths (0.3). Since 3 is greater than 0, Emma's pumpkin is heavier. Step 4: To double-check, rewrite 7.3 as 7.30. Now compare 7.03 and 7.30: the tenths place still shows 0 vs 3, so the answer is clear. Therefore, Emma's pumpkin (7.3 kg) weighs more than Olivia's pumpkin (7.03 kg).

9. 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).