Answer :
(a) ![2.1\times 10^3](/tpl/images/0174/3238/1ad93.png)
(b) ![1.7\times 10^{-1}](/tpl/images/0174/3238/ea7d2.png)
(c) ![6.5\times 10^3](/tpl/images/0174/3238/f99e1.png)
(d) ![1.42\times 10^{1}](/tpl/images/0174/3238/48487.png)
(e) ![9.18\times 10^{-1}](/tpl/images/0174/3238/39fc6.png)
(f) ![1.48\times 10^{2}](/tpl/images/0174/3238/31956.png)
(g) ![2.9\times 10^{1}](/tpl/images/0174/3238/58885.png)
(h) ![2.06\times 10^{2}](/tpl/images/0174/3238/3562d.png)
Explanation :
Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.
The rule apply for the multiplication and division is :
The least number of significant figures in any number of the problem determines the number of significant figures in the answer.
The rule apply for the addition and subtraction is :
The least precise number present after the decimal point determines the number of significant figures in the answer.
(a) The given expression is: 62.8 Γ 34
62.8 Γ 34 = 2135.2
In the given expression, 62.8 has 3 significant figures and 34 has 2 significant figures. From this we conclude that 2 is the least significant figures in this problem. So, the answer should be in 2 significant figures.
The answer will be, ![2.1\times 10^3](/tpl/images/0174/3238/1ad93.png)
(b) The given expression is: 0.147 + 0.0066 + 0.012
0.147 + 0.0066 + 0.012 = 0.1656
In the given expression, 0.147 has 3 significant figures, 0.0066 has 2 significant figure and 0.012 has 2 significant figures. From this we conclude that 2 is the least significant figures after decimal in this problem. So, the answer should be in 2 significant figures.
The answer will be, ![1.7\times 10^{-1}](/tpl/images/0174/3238/ea7d2.png)
(c) The given expression is: 38 Γ 95 Γ 1.792
38 Γ 95 Γ 1.792 = 6469.12
In the given expression, 38 and 95 has 2 significant figures and 1.792 has 4 significant figures. From this we conclude that 2 is the least significant figures in this problem. So, the answer should be in 2 significant figures.
The answer will be, ![6.5\times 10^3](/tpl/images/0174/3238/f99e1.png)
(d) The given expression is: 15 - 0.15 - 0.6155
15 - 0.15 - 0.6155 = 14.2345
In the given expression, from this we conclude that 2 is the least significant figures after decimal in this problem. So, the answer should be in 2 significant figures.
The answer will be, ![1.42\times 10^{1}](/tpl/images/0174/3238/48487.png)
(e) The given expression is: 8.78 Γ (0.0500 Γ· 0.478)
8.78 Γ (0.0500 Γ· 0.478) = 0.91841
In the given expression, 8.78 and 0.478 has 3 significant figures and 0.0500 has 3 significant figures. From this we conclude that 3 is the least significant figures in this problem. So, the answer should be in 3 significant figures.
The answer will be, ![9.18\times 10^{-1}](/tpl/images/0174/3238/39fc6.png)
(f) The given expression is: 140 + 7.68 + 0.014
140 + 7.68 + 0.014 = 147.694
In the given expression, from this we conclude that 2 is the least significant figures after decimal in this problem. So, the answer should be in 2 significant figures.
The answer will be, ![1.48\times 10^{2}](/tpl/images/0174/3238/31956.png)
(g) The given expression is: 28.7 - 0.0483
28.7 - 0.0483 = 28.6517
In the given expression, from this we conclude that 1 is the least significant figures after decimal in this problem. So, the answer should be in 1 significant figures.
The answer will be, ![2.9\times 10^{1}](/tpl/images/0174/3238/58885.png)
(h) The given expression is: (88.5 - 87.57) Γ· 45.13
(88.5 - 87.57) Γ· 45.13 = 0.02061
In the given expression, 88.5 has 3 significant figures, 87.57 has 4 significant figures and 45.13 has 4 significant figures. From this we conclude that 3 is the least significant figures in this problem. So, the answer should be in 3 significant figures.
The answer will be, ![2.06\times 10^{2}](/tpl/images/0174/3238/3562d.png)