Page 43 - Mathematics Coursebook

3.8 Estimating and approximating

3.8 Estimating and approximating

When solving a problem, it is always a good idea to start with a rough
estimate of what the answer should be.

To use an estimate to check if your answer is correct, follow these steps.
1 Round each of the numbers in the question. For example:
Round: numbers in the thousands to the nearest 1000 • round 4390 to 4000
• round 185 to 200
numbers in the hundreds to the nearest 100
numbers in the tens to the nearest 10 • round 32 to 30
• round 2.82 to 3.
numbers between 1 and 10 to the nearest 1.
2 Complete the calculation, using the rounded numbers to give you an approximate answer.

3 Work out the accurate answer.
4 If your approximate answer is close to your accurate answer, you have probably got the answer right!

Worked example 3.8A
×
.
Work these out. a 6210 ÷ 276 b 2133 97
19

a Estimate: 6000 ÷ 300 = 20 Round 6210 to 6000 and 276 to 300 and then divide.
Accurate: 6210 ÷ 276 = 22.5 Work out the accurate answer.
20 is close to 22.5, so the answer is probably correct.
200 × 4
b Estimate: = = 40 Round 213 to 200, 3.97 to 4 and 19 to 20.
40
20
Multiply 200 by 4 to give 800, then divide 800 by 20.
×
.
Accurate: 2133 97 = 44 5 (1 d.p.) Work out the accurate answer.
.
19
40 is close to 44.5 so the answer is probably correct.
Another way to check if an answer is correct is to use an inverse operation.
To check if your answer is correct using an inverse operation, simply follow one of these steps.
1 If your calculation involved an addition, check the answer by doing a subtraction.
2 If your calculation involved a subtraction, check the answer by doing an addition.
3 If your calculation involved a multiplication, check the answer by doing a division.
4 If your calculation involved a division, check the answer by doing a multiplication.

Worked example 3.8B

Work these out. a 723 + 476 b 2.76 × 9

a 723 + 476 = 1199 Work out the accurate answer.
Check: 1199 − 476 = 723 Check the addition by doing Or use 1199 − 723 = 476
a subtraction.
b 2.76 × 9 = 24.84 Work out the accurate answer.
Check: 24.84 ÷ 9 = 2.76 Check the multiplication Or use 24.84 ÷ 2.76 = 9
by doing a division.

42 3 Place value, ordering and rounding