Compare Decimals

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Answer Key & Explanations

Compare Decimals · Grade 4 · Worksheet 1

1. Matiu and Hana are training for a swimming race. Matiu swam 12.75 meters in one breath, and Hana swam 12.8 meters in one breath. Who swam the greater distance? Answer: Hana Solution: Write both distances with the same number of decimal places. Matiu: 12.75. Hana: 12.8 = 12.80.
   Full step-by-step solution

   Step 1: Write both distances with the same number of decimal places. Matiu: 12.75. Hana: 12.8 = 12.80. Step 2: Compare the whole number parts. Both have 12, so they are equal. Step 3: Compare the tenths place. Matiu has 7 tenths (0.7) and Hana has 8 tenths (0.8). Since 8 tenths is greater than 7 tenths, Hana's distance is greater. Step 4: We do not need to check the hundredths place because the tenths place already shows which is larger. Therefore, Hana swam the greater distance: 12.8 meters.

2. Aroha and Tane are comparing the distances their toy cars rolled down a ramp. Aroha's car rolled 1.39 meters, and Tane's car rolled 1.4 meters. Whose car rolled a greater distance? Answer: Tane's car Solution: Write the distances: Aroha's car = 1.39 meters, Tane's car = 1.4 meters. Compare the whole number parts: Both have 1 whole, so they are equal.
   Full step-by-step solution

   Step 1: Write the distances: Aroha's car = 1.39 meters, Tane's car = 1.4 meters. Step 2: Compare the whole number parts: Both have 1 whole, so they are equal. Step 3: Compare the tenths place: Aroha's car has 3 tenths (0.3), Tane's car has 4 tenths (0.4). Since 4 is greater than 3, Tane's car rolled farther. Step 4: Check the hundredths place for Aroha's car: 1.39 has 9 hundredths. Tane's car can be written as 1.40, which has 0 hundredths. Even though 9 hundredths is more than 0, the tenths place comparison already decides that 1.4 is greater than 1.39. Therefore, Tane's car rolled a greater distance.

3. A rectangular garden is drawn with length 3.5 meters and width 2.25 meters. What is the area of the garden in square meters? Answer: 7.875 Solution: To find the area of a rectangle, we multiply its length by its width. Write down the given measurements. Length = 3.5 meters Width = 2.25 meters Write the multiplication expression for the area.
   Full step-by-step solution

   To find the area of a rectangle, we multiply its length by its width. Step 1: Write down the given measurements. Length = 3.5 meters Width = 2.25 meters Step 2: Write the multiplication expression for the area. Area = Length × Width Area = 3.5 × 2.25 Step 3: To make the multiplication easier, we can convert the decimal numbers into fractions. 3.5 is the same as 35/10. 2.25 is the same as 225/100. Step 4: Multiply the two fractions. Area = (35/10) × (225/100) Step 5: Multiply the numerators together and the denominators together. Numerator: 35 × 225 Denominator: 10 × 100 Step 6: Calculate the numerator. First, calculate 35 × 200 = 7000 Then, calculate 35 × 25 = 875 Now add them together: 7000 + 875 = 7875 So, the numerator is 7875. Step 7: Calculate the denominator. 10 × 100 = 1000 So, the denominator is 1000. Step 8: Write the result as a fraction. Area = 7875 / 1000 Step 9: Simplify the fraction. Since both the numerator and denominator end in 0 or 5, we can divide both by 25. 7875 ÷ 25 = 315 1000 ÷ 25 = 40 So, the area is 315/40. Step 10: Simplify further by dividing both numerator and denominator by 5. 315 ÷ 5 = 63 40 ÷ 5 = 8 So, the area is 63/8. Step 11: Convert the improper fraction 63/8 to a decimal by performing the division. 63 ÷ 8 = 7.875 Therefore, the area of the rectangular garden is 7.875 square meters.

4. 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 <.

5. Hana draws two number lines to compare the lengths of two ribbons. The first number line is divided into 10 equal parts from 0 to 1, and the second number line is divided into 100 equal parts from 0 to 1. On the first number line, she marks a point at 0.7. On the second number line, she marks a point at 0.65. Which ribbon is longer? Use >, <, or = to compare 0.7 and 0.65. Answer: 0.7 > 0.65 Solution: To compare 0.7 and 0.65, write both numbers with the same number of decimal places. 0.7 can be written as 0.70 because 0.7 means 7 tenths, which is the same as 70 hundredths. Now compare 0.70 and 0.65.
   Full step-by-step solution

   Step 1: To compare 0.7 and 0.65, write both numbers with the same number of decimal places. 0.7 can be written as 0.70 because 0.7 means 7 tenths, which is the same as 70 hundredths. Step 2: Now compare 0.70 and 0.65. 0.70 has 70 hundredths, and 0.65 has 65 hundredths. Step 3: Since 70 hundredths is greater than 65 hundredths, 0.70 > 0.65, so 0.7 > 0.65. Step 4: Therefore, the ribbon that is 0.7 meters long is longer than the ribbon that is 0.65 meters long. Answer: 0.7 > 0.65

6. 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

7. 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.