Discover Mathematics P5: Term 1, Unit 1, Lessons 10–13
GoalEstimate a difference by rounding, then subtract decimals to thousandths exactly.
New words
estimate · a close guess found by roundingplace holder zero · a zero added at the end of a decimal so that two numbers have the same number of places
Explanation
Before subtracting, estimate: round both numbers to the same easy place and subtract. For 8.74 − 3.18 round to whole numbers: 9 − 3 = 6, so the answer should be a little under 6. Now subtract exactly: 8.74 − 3.18 = 5.56. The exact answer is close to the estimate, so it is reasonable. When the numbers do not have the same number of decimal places, add zeros to the shorter one: 7 − 2.368 becomes 7.000 − 2.368. A 0 on top needs regrouping from the nearest non-zero digit on its left, and the regrouping passes along the zeros one place at a time: 7.000 − 2.368 = 4.632.
Estimate
Exact
8.74 − 3.18
9 − 3 = 6
5.56
7 − 2.368
7 − 2 = 5
4.632
15.2 − 6.847
15 − 7 = 8
8.353
Worked examples
Estimate and then subtract 8.74 − 3.18. Estimate: 9 − 3 = 6. Exact: hundredths 4 − 8 needs regrouping: 14 − 8 = 6; tenths 6 − 1 = 5; ones 8 − 3 = 5. So the difference is 5.56. It is close to 6, so it is reasonable.
Ones
Tenths
Hundredths
Thousandths
after regrouping
6
9
9
10
−
2
3
6
8
=
4
6
3
2
Subtract 7 − 2.368. Write 7.000 − 2.368. Regroup 1 one as 10 tenths, then 1 tenth as 10 hundredths, then 1 hundredth as 10 thousandths. Now the top digits are 6, 9, 9, 10. Thousandths 10 − 8 = 2; hundredths 9 − 6 = 3; tenths 9 − 3 = 6; ones 6 − 2 = 4. The answer is 4.632. Check: 4.632 + 2.368 = 7.
A water pipe is 15.2 m long and 6.847 m is cut off. Estimate: 15 − 7 = 8. Exact: 15.200 − 6.847 = 8.353 m. Check by adding: 8.353 + 6.847 = 15.200. The exact answer is close to the estimate.
Class activity
Zero hunt. Choose a whole number such as 6 or 20. Write it with zeros after a decimal point: 6.000. Take away a decimal such as 2.457 on squared paper, regrouping step by step. Check by adding. Then try again with a different decimal. Notice what happens to the digits that were zeros.
Practice
1
Estimate 9.8 − 4.1 by rounding to whole numbers.
10 − 4 = 6. (The exact answer is 5.7.)
2
Subtract 12.5 − 0.875.
12.500 − 0.875 = 11.625.
3
Subtract 4 − 1.729.
4.000 − 1.729 = 2.271. Check: 2.271 + 1.729 = 4.
4
Seif says 6.3 − 2.45 = 4.15. Check by adding, then give the right answer.
4.15 + 2.45 = 6.6, not 6.3, so he is wrong. The right answer is 6.30 − 2.45 = 3.85, and 3.85 + 2.45 = 6.30.
