Question

Round off or add zeros to the following calculated answers to give a final answer with three significant figures: (2.2)

a. $0.00001258\mathrm{L}$

b. $3.528\times {10}^2\mathrm{kg}$

c. $125111\mathrm{m}$

d. $34.9673\mathrm{s}$

Short answer

a) The number $0.00001258L$with three significant figures is determined as $0.0000126L$

b) The number $3.528\times {10}^{2}kg$with three significant figures is determined as $3.53\times {10}^{2}kg$

c) The number $125111m$with three significant figures is determined as $125000m$

Step-by-step solution

Introduction (part a) 

The given is the numbers with significant figures

The objective is to round off the numbers with its significant figures

Explanation (part a)

a.

Write the number $0.00001258\mathrm{L}$ drop the digit $8$ and increase the digit $5$ by one with three significant figures because the first falling digit $8$ is greater than $5$. .

$0.00001258\mathrm{L}=0.0000126\mathrm{L}\left(\begin{array}{l}3\text{significant figures}\\ \text{drop}8,8>5\end{array}\right)$

Thus, the number $0.00001258\mathrm{L}$ with three significant figures will be $0.0000126\mathrm{L}$.

Introduction (part b)

The given is the numbers with significant figures

The objective is to round off the numbers with its significant figures

Explanation (part b)

b.

Write the number $3.528\times {10}^2\mathrm{kg}$drop the digit $8$and increase the digit $2$by one with three significant figures because the first falling digit 8 is greater than $5$.

$3.528\times {10}^2\mathrm{kg}=3.53\times {10}^2\mathrm{kg}\left(\begin{array}{l}3\text{significant figures}\\ \text{drop}8,8>5\end{array}\right)$

Thus, the number $3.528\times {10}^2\mathrm{kg}$with three significant figures will be $3.53\times {10}^2\mathrm{kg}$.

Introduction (part c)

The given is the numbers with significant figures

The objective is to round off the numbers with significant figures

Explanation (part c)

C.

Write the number $125111\mathrm{m}$ add three zeros $000$ in place of $111$with three significant figures because zeros at the end of a number are important if the number contains a decimal point. Because there is no decimal point in this number, adding zeros results in a number with three signiflcant flgures.

$125111\mathrm{m}=125000\mathrm{m}\left(\begin{array}{l}3\text{significant figures}\\ 125111\mathrm{m}\text{is rounded off}125000\mathrm{m}\end{array}\right)$

Thus, the number $125111\mathrm{m}$ with three signiflcant flgures will be $125000\mathrm{m}$.