Comparing decimals worksheet

Part A: Working out and filling in

1. 1. 1.12

   What can you multiply the numerator and denominator of 2825 by to make the denominator 100?

   Multiply the numerator and denominator by 4 to get hundredths: 2825 = 112100 = 1.12.

2. 2. 2.02

   What can you multiply the numerator and denominator of 10150 by to make the denominator 100?

   Multiply the numerator and denominator by 2 to get hundredths: 10150 = 202100 = 2.02.

3. 3. C → B → A → D

   Compare the whole parts first to find the biggest; then compare the rest from the tenths.

   Whole parts first: 7 is biggest. Then the tenths, then the hundredths: 6.07, 6.2, 6.25, 7.

Part B: Choose, or true or false

1. 4. True

   1.26 and 1.2 have the same whole part: compare the tenths, then the hundredths if they match.

   The whole parts match; pad with zeros to two decimal places each, then compare from the tenths: 1.26 is greater than 1.2.

2. 5. C. 4.4

   All four have the same whole part, so compare the tenths first; more digits isn't bigger.

   The whole parts match, so compare the tenths: 4.4 has the biggest.

3. 6. True

   0.99 and 0.98 have the same whole part: compare the tenths, then the hundredths if they match.

   The whole parts match; pad with zeros to two decimal places each, then compare from the tenths: 0.99 is greater than 0.98.

4. 7. C. 0.34

   Turn 15 into a decimal first; with all four as decimals, compare from the tenths.

   15 = 0.2; write them all as decimals and compare from the tenths: the biggest is 0.34.

5. 8. D. 0.26

   First scale 1350 up to hundredths: what do the numerator and denominator both get multiplied by?

   Scale 1350 up to hundredths, then write it as a decimal: 0.26.

6. 9. D. 0.91

   Turn 1720 into a decimal first; with all four as decimals, compare from the tenths.

   1720 = 0.85; write them all as decimals and compare from the tenths: the biggest is 0.91.

7. 10. C. 0.8

   First scale 45 up to hundredths: what do the numerator and denominator both get multiplied by?

   Scale 45 up to hundredths, then write it as a decimal: 0.8.

8. 11. A. 0.18

   First scale 950 up to hundredths: what do the numerator and denominator both get multiplied by?

   Scale 950 up to hundredths, then write it as a decimal: 0.18.

9. 12. D. 0.31

   Turn 15 into a decimal first; with all four as decimals, compare from the tenths.

   15 = 0.2; write them all as decimals and compare from the tenths: the biggest is 0.31.

Part C: Word problems

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

1. 13. 1.72 m

   Both heights have the same whole part, so compare the tenths first.

   The whole parts match, so compare the tenths, then the hundredths if needed: 1.72 is more than 1.7, so the taller one is 1.72 m.

2. 14. 1.08 L

   Scale 1920 up to a fraction over 100, write it as a decimal, then compare with 1.08.

   Turn 1920 into a decimal first: 1920 = 95100 = 0.95. Compared with 1.08, the fuller one holds 1.08 L.

3. 15. 8.45 s

   Less time means faster. Compare the whole parts of 8.45 and 12.83 first.

   Less time means faster. Compare the whole parts, then the tenths and hundredths: 8.45 is less than 12.83, so the faster one takes 8.45 s.

4. 16. 0.68 L

   Scale 1725 up to a fraction over 100, write it as a decimal, then compare with 0.51.

   Turn 1725 into a decimal first: 1725 = 68100 = 0.68. Compared with 0.51, the fuller one holds 0.68 L.

5. 17. 9.44 s

   Less time means faster. Compare the whole parts of 9.44 and 10.61 first.

   Less time means faster. Compare the whole parts, then the tenths and hundredths: 9.44 is less than 10.61, so the faster one takes 9.44 s.

6. 18. 1.7 m

   Both heights have the same whole part, so compare the tenths first.

   The whole parts match, so compare the tenths, then the hundredths if needed: 1.7 is more than 1.64, so the taller one is 1.7 m.