Calculate the answer up to appropriate numbers of significant digits
(a) 246.24 + 238.278 + 98.3
(b) 1.4 x 2.639 + 117.25
(c) (2.66 x 10⁴) - (1.03 x10³)
(d) (112 x 0.456) / (3.2 x 120)
(e) 168.99 x 9
(f) 1023 + 8.5489
Ans [(a) 582.8 , (b) 120.9, (c) 2.56 x 10⁴, (d) 0.13 , (e) 2000 & (f) 1032 ]
Solution:
(a) 246.24 + 238.278 + 98.3
Calculation:
2 4 6 . 2 4
2 3 8 . 2 7 8
+ 9 8 . 3
----------------
5 8 2 . 8 1 8
But According to the rules of significant figures, when two or more quantities are added or subtracted, the result is as precise as the least precise of the quantities. After adding or subtracting, the result should be rounded to the least number of decimal places as given in the input given number. In the given numbers 98.3 has the lowest decimal place (one DP). So, in the result of the calculation (582.818) should be rounded to one decimal place.
Therefore,
246.24 + 238.278 + 98.3 = 582.8 --------Ans
(b) 1.4 ｘ 2.639 + 117.25
Calculation:
1.4
ｘ 2.639
--------------
3.6946
+ 117.25
--------------
120.9446
Here the rule of the significant figures for addition will be applied because the last operation is the Addition.
So the result will be rounded to the least number of decimal points (D.P.) in the given numbers. Here we have number 1.4 which has the least (1) D.P. Therefore,
1.4 ｘ 2.639 + 117.25 = 120.9 ------------Ans
(c) (2.66 x 10⁴) - (1.03 x10³)
Calculation:
these can be subtracted only when the term has the same power as the base 10. So,
1.03 x10³ = 0.103 x10⁴
(2.66 x 10⁴) - (1.03 x10³) = (2.66 x 10⁴) - (0.103 x10⁴)
= 2.557 x 10⁴
Here the rules of significant figures for subtraction should be applied, which is the same as addition. So.
the result should be round to the 2 d.p. therefore
(2.66 x 10⁴) - (1.03 x10³) = 2.56 x 10⁴ -------Ans
(d) (112 x 0.456) / (3.2 x 120)
Calculation:
112 3.2
ｘ 0.456 ｘ 120
-------------- --------------
= 51.072 = 384
Now `\frac {51.072}{384}` = 0.133
Here the last operation is division. So rules of significant figures for division should be applied.
According to the rules of significant figures, when quantities are multiplied or divided, the result has the same of significant figures as the quantity with the smallest number of significant figures. In the given numbers, 384 has the lowest 3 significant figures. So, in the result of the calculation should be rounded to the three significant figures. Here We have
(112 x 0.456) / (3.2 x 120) = 0.133 -------Ans.
(e) 168.99 x 9
Calculation:
168.99
ｘ 9
--------------
1520.91
According to the rules of significant figures, when quantities are multiplied or divided, the result has the same of significant figures as the quantity with the smallest number of significant figures. Of the given numbers, 9 has the lowest 1 significant figure. So, the result of the calculation should be rounded to one significant figure. Here We have
168.99 x 9 = 1520.9 = 2000 = 2 x 10³ -----Ans
(f) 1023 + 8.5489
Calculation:
1 0 2 3
+ 8 . 5 4 8 9
----------------
1 0 3 1 . 5 4 8 9
But According to the rules of significant figures, when two or more quantities are added or subtracted, the result is as precise as the least precise of the quantities. After adding or subtracting, the result should be rounded to the least number of decimal places as given in the input given number. In the given numbers 1023 has no decimal places (zero DP). So, the result of the calculation (1 0 3 1 . 5 4 8 9) should be rounded to zero decimal places.
Therefore,
1023 + 8.5489 = 1031.5489 = 1032 --------Ans
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