Question

Write each answer with the correct number of significant figures.

(a)$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{+}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{+}\mathbf{3}\mathbf{.}\mathbf{4}\mathbf{+}\mathbf{5}\mathbf{.}\mathbf{8}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{3000}$

(b) 106.9 - 31.4 = 75.5000

(c)$\mathbf{107}\mathbf{.}\mathbf{868}\left(2.113\times {10}^2\right)\mathbf{+}\left(5.623\times {10}^3\right)\mathbf{=}\mathbf{5519}\mathbf{.}\mathbf{568}$

(d)$\left(26.14/37.62\right)\mathbf{\times }\mathbf{4}\mathbf{.}\mathbf{38}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{043413}$

(e$\left(26.14/\left(37.62\times {10}^8\right)\right)\mathbf{\times }\left(4.38\times {10}^{-2}\right)\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{043413}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}$

(f)$\left(26.14/3.38\right)\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{2}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5999}$

(g)$\mathit{l}\mathit{o}\mathit{g}\left(3.98\times {10}^4\right)\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5999}$

(h)${\mathbf{10}}^{\mathbf{-}\mathbf{6}\mathbf{.}\mathbf{31}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{89779}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$

Short answer

a) 12.3

b) 75.5

c)$5.520\times {10}^3$

d) 3.04

e)$3.04\times {10}^{-10}$

f) 11.9

g) 4.600

h)role="math" localid="1663324058547" $4.9\times {10}^{-7}$

Step-by-step solution

Definition of significant figure

In positional notation, significant figures are digits in a number that are dependable and essential to express the quantity of something.

Determine the significant figures

(a) $1.0+2.1+3.4+5.8=12.3000=12.3$

(b) 106.9 - 31.4 = 75.5000 = 75.5

(c) $107.868(2.113\times {10}^2)+(5.623\times {10}^3)=5519.568=5.520\times {10}^3$

(d) $(26.14/37.62)\times 4.38=3.043413=3.04$

(e)$(26.14/(37.62\times {10}^8))\times (4.38\times {10}^{-2})=3.043413\times {10}^{-10}=3.04\times {10}^{-10}$

(f)$(26.14/3.38)+4.2=4.5999=11.9337=11.9$

(g) $log(3.98\times {10}^4)=4.5999=4.600$

(h) ${10}^{-6.31}=4.89779\times {10}^{-7}=4.9\times {10}^{-7}$