Primary 4 Mathematics Decimals Quiz

Answer Key - Primary 4 Mathematics Quiz - Decimals

Section A: Multiple-Choice Questions (5 × 1 mark = 5 marks)

1. (B) 7 hundredths

• Explanation: In the number 23.75, the first digit after the decimal point (7) is in the tenths place, and the second digit (5) is in the hundredths place. So the digit 7 stands for 7 tenths or 0.7. Therefore, the answer is (A) — thank you for the check. Correction: In 23.75, the 7 is in the tenths place. So it stands for 7 tenths. (A) is correct.
• Key Concept: Decimal place value: tenths is the first digit to the right of the decimal point.
• Common Mistake: Students may confuse tenths and hundredths places.
• Answer: (A)

2. (C) 0.32

• Explanation: Compare the decimals using place value. Look at the tenths place first: 0.3, 0.29, 0.32, 0.301. All have 3 or 2 in the tenths place except 0.29. Arrange from largest: 0.32, 0.301, 0.3, 0.29. So 0.29 is the smallest and 0.32 is the largest. Wait, check carefully: 0.3 is 0.300, 0.32 is 0.320, 0.301 is 0.301. So 0.320 is the largest. So answer is (C).
• Key Concept: To compare decimals, align the decimal points and compare digits from left to right.
• Answer: (C)

3. (B) $6.45

• Explanation: $5.60 +$0.85 = 5.60 + 0.85. Add the hundredths: 60 + 85 = 145 hundredths = 1.45. Add the wholes: 5 + 0 + 1 (carry-over) = 6. So the total is 6.45.
• Key Concept: Adding decimals: align decimal points and add column by column, carrying over when necessary.
• Answer: (B)

4. (B) 0.08

• Explanation: $\frac{8}{100}$ means 8 parts out of 100. As a decimal, that is 0.08 (zero point zero eight). The first place after the decimal is tenths, the second is hundredths. So 8 hundredths is 0.08.
• Key Concept: A fraction with denominator 100 can be written as a two-digit decimal: numerator goes in the hundredths place.
• Common Mistake: Writing 0.8 for $\frac{8}{100}$ (which is $\frac{8}{10}$ or 0.8).
• Answer: (B)

5. (A) $\frac{35}{10}$

• Explanation: 3.5 means 3 wholes and 5 tenths. As an improper fraction, that is $\frac{35}{10}$ because 3.5 = $\frac{35}{10}$. Option (B) is $\frac{35}{100}=0.35$, which is not 3.5. Option (C) is $\frac{3}{5}=0.6$, not 3.5. Option (D) is $\frac{3}{100}+\frac{5}{10}=0.03+0.5=0.53$, not 3.5.
• Key Concept: A decimal can be written as a fraction with denominator 10, 100, etc.
• Answer: (A)

Section B: Short-Answer Questions (10 × 2 marks = 20 marks)

6. Answer: 0.28

• Explanation: The grid is 10 by 10, so 100 squares total. There are 28 shaded squares. The decimal for $\frac{28}{100}$ is 0.28. You say "0.28" or "twenty-eight hundredths."
• Key Concept: A 100-square grid represents hundredths. Each small square is 0.01.
• Marking Notes: 1 mark for correct fraction or concept, 1 mark for correct decimal.

7. Answer: 0.39, 0.401, 0.45, 0.5

• Explanation: Compare the decimals: Write them with the same number of decimal places: 0.390, 0.401, 0.450, 0.500. Order from smallest: 0.390, 0.401, 0.450, 0.500. So the order is 0.39, 0.401, 0.45, 0.5.
• Key Concept: Add zeros to the end of a decimal to compare more easily.
• Marking Notes: 1 mark for correct first or last element, 2 marks for full correct order.

8. Answer: 3.74

• Explanation: 5.03 - 1.29. Subtract hundredths: 3 - 9 cannot, so regroup 1 tenth from 0 tenths? 5.03 = 5 ones 0 tenths 3 hundredths. Regroup: 5.03 = 4 wholes + 10 tenths + 3 hundredths. Then subtract: 4.10.3 - 1.29 = 3.74.
• Key Concept: Subtracting decimals requires regrouping across place values.
• Marking Notes: 1 mark for correct method, 1 mark for correct answer.

9. Answer: 2.15 m

• Explanation: Starting length is 2.85 m. Cut off 0.7 m. 2.85 - 0.70 = 2.15 m.
• Key Concept: Subtraction of decimals in a real-world context.
• Marking Notes: 1 mark for correct operation, 1 mark for correct answer with unit.

10. Answer: 13.8

• Explanation: 4.6 × 3. Multiply: 46 × 3 = 138. Since 4.6 has one decimal place, place the decimal point so the product has one decimal place: 13.8.
• Key Concept: Multiplying a decimal by a whole number: multiply as whole numbers, then place the decimal point using the number of decimal places in the decimal factor.
• Marking Notes: 1 mark for correct method, 1 mark for correct answer.

11. Answer: 7.56

• Explanation: Round 7.563 to 2 decimal places. Look at the third decimal place (thousandths), which is 3. Since 3 is less than 5, we do not round up the second decimal place. So the answer is 7.56.
• Key Concept: Rounding rules: if the digit to the right of the rounding place is 5 or more, round up; otherwise, keep the digit the same.
• Marking Notes: 1 mark for understanding rounding, 1 mark for correct answer.

12. Answer: 0.6

• Explanation: $\frac{3}{5}$ = $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$ = 0.6. Alternatively, think: 3 ÷ 5 = 0.6.
• Key Concept: Converting a fraction to a decimal: find an equivalent fraction with denominator 10, 100, or 1000, then write as a decimal.
• Marking Notes: 1 mark for correct method, 1 mark for correct answer.

13. Answer: 0.3 L

• Explanation: 1.5 L ÷ 5. Think: 15 tenths ÷ 5 = 3 tenths = 0.3 L. Or: 1.5 ÷ 5 = 0.3.
• Key Concept: Dividing a decimal by a whole number.
• Marking Notes: 1 mark for correct method, 1 mark for correct answer with unit.

14. Answer: $\frac{7}{10}$

• Explanation: 0.7 means 7 tenths. As a fraction, that is $\frac{7}{10}$. This is already in simplest form because 7 and 10 have no common factors other than 1.
• Key Concept: Decimals can be expressed as fractions in simplest form.
• Marking Notes: 1 mark for correct fraction, 1 mark for simplest form.

15. Answer: 8.2

• Explanation: 2.05 × 4. Multiply: 205 × 4 = 820. 2.05 has two decimal places, so the product has two decimal places: 8.20 = 8.2.
• Key Concept: Multiplication of decimal by whole number with decimal point placement.
• Marking Notes: 1 mark for correct method, 1 mark for correct answer.

Section C: Word Problems (5 × 3 marks = 15 marks)

16. Answer: 4.2 m

• Explanation: Total length = 1.25 m + 0.8 m + 2.15 m. Align decimal points: 1.25 + 0.80 + 2.15 = 4.20 m = 4.2 m.
• Step-by-step:
  1. 1.25 + 0.80 = 2.05
  2. 2.05 + 2.15 = 4.20 = 4.2
• Key Concept: Adding multiple decimals.
• Marking Notes: 1 mark for each correct addition step, 1 mark for correct final answer with unit. (Total 3 marks)

17. Answer: 2.35 kg

• Explanation: Weight of cake = weight of chocolates + 1.05 kg = 0.65 kg + 1.05 kg = 1.70 kg. Total weight = chocolates + cake = 0.65 kg + 1.70 kg = 2.35 kg.
• Step-by-step:
  1. Cake weight: 0.65 + 1.05 = 1.70 kg
  2. Total: 0.65 + 1.70 = 2.35 kg
• Key Concept: Two-step word problem involving decimal addition.
• Marking Notes: 1 mark for finding cake weight, 1 mark for total, 1 mark for correct answer with unit.

18. Answer: 2.05 L

• Explanation: Juice left = 2.4 L - 0.35 L. Write 2.4 as 2.40. 2.40 - 0.35 = 2.05 L.
• Key Concept: Subtraction with regrouping: borrowing from wholes to tenths/hundredths.
• Marking Notes: 1 mark for setting up subtraction, 1 mark for correct regrouping, 1 mark for correct answer with unit.

19. Answer: 4.8 m

• Explanation: Rope B is 3 times Rope A. So Rope B = 1.6 m × 3 = 4.8 m.
• Key Concept: Multiplication word problem with decimals.
• Marking Notes: 1 mark for identifying operation (multiplication), 1 mark for calculation, 1 mark for correct answer with unit.

20. Answer: 1.15 kg

• Explanation: Total flour used = 0.75 kg + 0.6 kg = 1.35 kg. Flour left = 2.5 kg - 1.35 kg = 1.15 kg.
• Step-by-step:
  1. Total used: 0.75 + 0.60 = 1.35 kg
  2. Left: 2.50 - 1.35 = 1.15 kg
• Key Concept: Two-step word problem: addition then subtraction with decimals.
• Marking Notes: 1 mark for finding total used, 1 mark for subtraction, 1 mark for correct answer with unit.