6.3 Approximating calculations This section will show you how to:
Key terms
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identify significant figures
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round numbers to a given number of significant figures
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use approximation to estimate answers and check calculations
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round a calculation at the end of a problem, to give what is considered to be a sensible answer.
approximate significant figure
Rounding to significant figures You often use significant figures (sf) when you want to approximate a number that has lots of digits in it. This table shows some numbers written to one, two and three significant figures. One sf
8
Two sf
67
4.8
Three sf
312
65.9
50
200
90 000
0.76 40.3
0.000 07
45 000
730
0.0761
7.05
0.003
0.4
0.0067
0.40
0.003 01
0.400
These are the steps for rounding a number to one significant figure. They are very similar to those used for rounding to one decimal place. ●
From the left, find the first non-zero digit. The next digit is the second digit.
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When the value of the second digit is less than 5, leave the first (non-zero) digit as it is.
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When the value of the second digit is equal to or greater than 5, add 1 to the first (non-zero) digit.
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If the original number is greater than 1, replace all other digits after the rounded digit, as far as the decimal point, with zeros. If there were some decimal values do not include them. If the original number is less than 1 (it starts 0), write down all the zeros before the rounded digit and delete everything after the rounded digit.
To round to two significant figures, you use the same method but use the third (non-zero) digit from the left. This table shows some numbers rounded to one or two significant figures. Number
Rounded to
Number
Rounded to
1 sf
2 sf
78
80
78
45 281
50 000
45 000
32
30
32
568
600
570
8054
8000
0.692
0.7
0.69
1.894
2
1.9
998
1000
0.436
1 sf
7.867
1000
0.4
99.8
0.44
0.0785
2 sf
8100
8 100
7.9 100
0.08
0.079
Exercise 6C 1
Round each number to one significant figure.
a 46 313
b 57 123
c 30 569
d 94 558
e 85 299
f 54.26
g 85.18
h 27.09
i
j
k 0.5388
l
m 0.00584
n 0.04785
o 0.000876
p 9.9
q 89.5
r 90.78
s 199
t 999.99
0.2823
96.432
167.77
6.3 Approximating calculations
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