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Numbers are often rounded to avoid reporting insignificant figures. Significant figures are often used in connecting with rounding.
Rounding 15.543 or 4.756 to 1 decimal place (d.p) seems sensible. The rounded figure is very close to an actual value.
15.543 = 15.5 (1 d.p)
4.756 = 4.8 (1 d.p)
But what happens if you round a very small number to 1 d.p?
0.00789 = 0.0 (1 d.p)
0.00456 = 0.0 (1 d.p)
This is not a useful answer. Another way to find an approximate answer with very small numbers is to use significant figures.
Significant figures start at the first non-zero number, so ignore the zeros at the front, but not the ones in between. Look at the following examples:
0.0067 (Here, 6 is the first significant figure and 7 is the second significant figure)
0.0508 From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count. Here, 5 is the first significant figure, 0-second significant figure and 8 is the third significant figure.
Examples
Solution:
a) 5700
b) 5735
c) 4740
Here, 5735 is the nearest whole number to 5734.7
Solution:
i)2.007
ii)0.003
iii) 0.20
Here, 2.007 has 4 significant figures.
Solution:
i) 7.02 ii) 7.01 iii) 7.06
Here, 7.01 is the correct answer.
Solution:
12.756
= 12.8 ( 1 d.p)
Therefore, 12.756 = 12.8
Solution:
0.00456
=0.0
Therefore, 0.00456 = 0.0
Solution:
To round to 1 decimal place, look at the second decimal place, It's 4 and it is smaller than 5.So round up,
4.543 = 4.5(1 d.p.)
Therefore, 4.543 = 4.5(1 d.p.)
Solution:
0.00213
= 0.0 (1 d.p.)
This is not useful answer.
Solution:
a) 4.6 b) 4.644 c) 4.64
Here, 4.644 is the correct answer.
Solution:
0.07245
=0.0725
Therefore, 0.07245 = 0.0725( 3 s.f)
Solution:
0.0037
=0.004(1 s.f)
Therefore, 0.0037 = 0.004.
Round 0.0524591 to 3 significant figures.
Round 0.2300105 to four significant figures.
Round off the following numbers to the significant figures.
24.7(2 s.f)
Round off the following numbers to the significant figures.
0.0432 (2 s.f)
Round 7.00521 to 3 s.f
Express (frac{1}{3}) in decimal upto 3 s.f.
Express (frac{6}{7}) in decimal upto 4 s.f.
Round 2.99 to 2 s.f.
Round 3.643 to 2 decimal number.
Which number has 4 significant figures?
Round off the following numbers to the Significant figures.
0.2607 (3 s.f)
Round 45.53m to the nearest ten meters.
Round 5734.7 to the nearest whole number.
Round off the following numbers to the Significant figures.
0.00357 (2 s.f)
Round off the following numbers to the Significant figures.
0.00483 (2 s.f)
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