Fractions and decimals worksheet

Part A: Working out and filling in

1. 1. 0.84 = 2125

   0.84: write it over 100, 0.84 × 100 = 84 → 84100; simplify, dividing the numerator and denominator by their highest common factor 4: 84 ÷ 4 = 21, 100 ÷ 4 = 25 → 2125

2. 2. 750 = 0.14

   750: scale it to a denominator of 100, multiplying the numerator and denominator by 2: 7 × 2 = 14, 50 × 2 = 100 → 14100 = 0.14

3. 3. 14 = 0.25

   14: scale it to a denominator of 100, multiplying the numerator and denominator by 25: 1 × 25 = 25, 4 × 25 = 100 → 25100 = 0.25

4. 4. 0.92 = 2325

   0.92: write it over 100, 0.92 × 100 = 92 → 92100; simplify, dividing the numerator and denominator by their highest common factor 4: 92 ÷ 4 = 23, 100 ÷ 4 = 25 → 2325

5. 5. 1320 = 0.65

   1320: scale it to a denominator of 100, multiplying the numerator and denominator by 5: 13 × 5 = 65, 20 × 5 = 100 → 65100 = 0.65

6. 6. 0.9 = 910

   0.9: write it over 10, 0.9 × 10 = 9 → 910, already in simplest form

7. 7. 12 = 0.5

   12: scale it to a denominator of 10, multiplying the numerator and denominator by 5: 1 × 5 = 5, 2 × 5 = 10 → 510 = 0.5

8. 8. 58 = 0.625

   58: scale it to a denominator of 1000, multiplying the numerator and denominator by 125: 5 × 125 = 625, 8 × 125 = 1000 → 6251000 = 0.625

9. 9. 720 = 0.35

   720: scale it to a denominator of 100, multiplying the numerator and denominator by 5: 7 × 5 = 35, 20 × 5 = 100 → 35100 = 0.35

10. 10. 0.5 = 12

    0.5: write it over 10, 0.5 × 10 = 5 → 510; simplify, dividing the numerator and denominator by their highest common factor 5: 5 ÷ 5 = 1, 10 ÷ 5 = 2 → 12

11. 11. 0.44 = 1125

    0.44: write it over 100, 0.44 × 100 = 44 → 44100; simplify, dividing the numerator and denominator by their highest common factor 4: 44 ÷ 4 = 11, 100 ÷ 4 = 25 → 1125

12. 12. 0.375 = 38

    0.375: write it over 1000, 0.375 × 1000 = 375 → 3751000; simplify, dividing the numerator and denominator by their highest common factor 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8 → 38

Part B: Word problems

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

1. 13. Ka-yee ran 45 km. Written as a decimal, how many kilometres did she run? (Answer: 0.8 km)

   4 ÷ 5 = 0.8

2. 14. Chi-keung ran 34 km and Ka-yan ran 2.6 km. How many kilometres did they run altogether? (Give a decimal.) (Answer: 3.35 km)

   3 ÷ 4 + 2.6 = 3.35

3. 15. May ran 38 km and Ka-lok ran 2.2 km. How many kilometres did they run altogether? (Give a decimal.) (Answer: 2.575 km)

   3 ÷ 8 + 2.2 = 2.575

4. 16. A bottle holds 0.5 L of soy sauce. Written as a fraction in simplest form, how many litres is that? (Answer: 12 L)

5. 17. Ka-yan ran 78 km. Written as a decimal, how many kilometres did she run? (Answer: 0.875 km)

   7 ÷ 8 = 0.875

6. 18. A bottle holds 0.1 L of soy sauce. Written as a fraction in simplest form, how many litres is that? (Answer: 110 L)