Q. 2.95 - An Introduction to General, Organic, and Biological Chemistry

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. $34.9673 \mathrm{s}$

Step-by-Step Solution

Answer

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

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 $125111 m$ with three significant figures is determined as $125000 m$

Step 1 : Introduction (part a)

The given is the numbers with significant figures

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

Step 2 : 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 $0.0000126 \mathrm{L}$.

Step 3 : Introduction (part b)

The given is the numbers with significant figures

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

Step 4 : 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 $3.53\times {10}^2 \mathrm{kg}$.

Step 5 : Introduction (part c)

The given is the numbers with significant figures

The objective is to round off the numbers with significant figures

Step 6 : 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 $125000 \mathrm{m}$.