Decimals worksheet

Part A: Working out and filling in

1. 1. 6.4

   6 to 7 is cut into 10 steps of 0.1. Count the steps from 6 to the arrow.

   Each step is 0.1; 4 steps from 6 is 6.4.

2. 2. 9, 9

   Look at the two digits after the point in 0.99: the first is tenths, the second hundredths.

   The tenths digit 9 is 910; the hundredths digit 9 is 9100.

3. 3. 54

   First turn 510 into hundredths: multiply the numerator and denominator by 10.

   510 = 50100, and 50100 + 4100 = 54100.

4. 4. In 4.379, the 3 is worth 0.3

   In 4.379 the 3 is in the tenths, worth 3 × 0.1: 3 × 0.1 = 0.3

5. 5. 5.158: thousandths digit = 8

   5.158: after the point come the tenths, then the hundredths, then the thousandths; the thousandths hold 8 × 0.001: 8 × 0.001 = 0.008, so the digit is 8

6. 6. 3.055

   1000 mL = 1 L. What do you divide 3055 by, and which way does the point move?

   1000 mL = 1 L: 3055 ÷ 1000 moves the point three places left, giving 3.055.

7. 7. 9.5 + 3.5 = 13

   9.5 + 3.5: both have one place, so work as whole numbers, 95 + 35 = 130, then put the point back one place → 13.0 = 13

Part B: Choose, or true or false

1. 8. D

   How many whole rows is 210? How many squares is 7100?

   210 is 2 rows (20 squares), plus 7 squares: 27 in all.

2. 9. False

   For 28 ÷ 100, how many places left should the point move? Now see how far it has moved in 2.8.

   Dividing by 100 moves the point two places left: 28 ÷ 100 = 0.28.

3. 10. D. 0.35

   Turn 725 into a decimal first; with all four as decimals, compare from the tenths.

   725 = 0.28; write them all as decimals and compare from the tenths: the biggest is 0.35.

4. 11. False

   With adding and subtracting, go left to right: 8.25 − 0.12 first, then check whether the next step adds or subtracts.

   Left to right: 8.25 − 0.12 first, then add 1.7: 9.83.

5. 12. B. 25%

   A percentage is a fraction out of 100. What do you multiply the numerator and denominator of 14 by to make the denominator 100?

   Write 14 out of 100: 14 = 25100 = 25%.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 0.55

   Each sweet is 1100 of the box, 0.01. 55 sweets are 55 hundredths.

   Each sweet is 1100 = 0.01 of the box, so Tsz-ching eats 55100 = 0.55 of it.

2. 14. A decimal has 6 in the ones place, 6 in the tenths place and 2 in the hundredths place. What is the decimal? (Answer: 6.62)

   6 + 6 ÷ 10 + 2 ÷ 100 = 6.62

3. 15. 0.32 L

   Scale 825 up to a fraction over 100, write it as a decimal, then compare with 0.2.

   Turn 825 into a decimal first: 825 = 32100 = 0.32. Compared with 0.2, the fuller one holds 0.32 L.

4. 16. In the long jump, Tsz-hin jumped 2.69 m and Ka-yan jumped 1.95 m. How many metres further did Tsz-hin jump than Ka-yan? (Answer: 0.74 m)

   2.69 − 1.95 = 0.74

5. 17. 49.1 L

   Used means subtract, poured in means add. Left to right: 61.3 − 18.4 first.

   Used means subtract, poured in means add, left to right: 61.3 − 18.4 = 42.9, 42.9 + 6.2 = 49.1 L.

6. 18. 23 chocolates

   25% is a quarter. Share the 92 chocolates into 4 equal parts: Tsz-ching eats one part.

   25% is a quarter: 92 ÷ 4 = 23.