Question

Perform the following calculation and report each answer with the correct number of significant figures.

(a) 62.8 x 34
(b) 0.147 + 0.0066 + 0.012
(c) 38 x 95 x 1.792
(d) 15 - 0.15 - 0.6155
(e) 8.78 x (0.0500/0.478)
(f) 140 + 7.68 + 0.014
(g) 28.7 - 0.0483
(h) (88.5 - 87.57)/45.13

Answer 1

(a)
`2.1* 10^3`

(b)
`1.7* 10^(-1)`

(c)
`6.5* 10^3`

(d)
`1.42* 10^(1)`

(e)
`9.18* 10^(-1)`

(f)
`1.48* 10^(2)`

(g)
`2.9* 10^(1)`

(h)
`2.06* 10^(2)`

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 × 34

62.8 × 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* 10^3`

(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* 10^(-1)`

(c) The given expression is: 38 × 95 × 1.792

38 × 95 × 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* 10^3`

(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* 10^(1)`

(e) The given expression is: 8.78 × (0.0500 ÷ 0.478)

8.78 × (0.0500 ÷ 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* 10^(-1)`

(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* 10^(2)`

(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* 10^(1)`

(h) The given expression is: (88.5 - 87.57) ÷ 45.13

(88.5 - 87.57) ÷ 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* 10^(2)`

Answer 2

Step-by-step explanation:

a) 2135.2 ⇒ 2100(rounding to two significant figures)

b) 0.1656⇒0.166 ( rounding to 3 digits after decimal)

c) 6469.12⇒6500(rounding to 2 significant figures)

d) 14.2345 ⇒14.23(rounding to two digits after decimal)

e) 0.9184⇒ .918(rounding to 3 significant figures)

f) 147.694 ⇒147.69 (rounding to 2 digits after decimal)

g)28.6517⇒28.7(rounding to one digit after decimal)

h).0206⇒ .02( rounding to one significant digit)