Chapter 1.2, Problem 12SSC

(a)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $\text{2}\text{.54 g}$

Explanation of Solution

Given:

  $10.8\text{g}-8.264\text{g}$

Calculations:

To determine the significant figure in subtraction, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $10.8\text{g}-8.264\text{g}\text{=}\text{2}\text{.536}\text{g}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $\text{2}\text{.54 g}$

Conclusion:

Thus, the result is $\text{2}\text{.54 g}$ .

(b)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $\text{4}\text{.33 m}$

Explanation of Solution

Given:

  $4.75\text{m}-0.4168\text{m}$

Calculations:

To determine the significant figure in subtraction, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $4.75\text{m}-0.4168\text{m = 4}\text{.3332}\text{m}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $\text{4}\text{.33 m}$

Conclusion:

Thus, the result is $\text{4}\text{.33 m}$ .

(c)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $\text{3}\text{.2}\times {\text{10}}^2{\text{ cm}}^2$

Explanation of Solution

Given:

  $\text{139}\text{cm}\text{×}\text{2}\text{.3}\text{cm}$

Calculations:

To determine the significant figure in multiplication, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $\text{139}\text{cm}\text{×}\text{2}\text{.3}\text{cm}=319.7{\text{cm}}^{\text{2}}$

The least number of significant figures is 2. Thus, answer up to three correct significant digits is:

  $\text{3}\text{.2}\times {\text{10}}^2{\text{ cm}}^2$

Conclusion:

Thus, the result is $\text{3}\text{.2}\times {\text{10}}^2{\text{ cm}}^2$ .

(d)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $1.22\text{g/mL}$

Explanation of Solution

Given:

  $\frac{13.78\text{g}}{11.3\text{mL}}$

Calculations:

To determine the significant figure in division, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $\frac{13.78\text{g}}{11.3\text{mL}}=1.219469\text{g/mL}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $1.22\text{g/mL}$

Conclusion:

Thus, the result is $1.22\text{g/mL}$ .

(e)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $93\text{cm}$

Explanation of Solution

Given:

  $\text{6}\text{.021 cm + 7}\text{.4 }\text{cm + 0}\text{.68 m + 12}\text{.0 cm}$

Calculations:

To determine the significant figure in addition, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $\text{6}\text{.021 cm + 7}\text{.4 }\text{cm + 0}\text{.68 m + 12}\text{.0 cm}$

Convert m to cm.

  $\text{1m =100}\text{cm}$

  $\text{6}\text{.021 cm + 7}\text{.4 }\text{cm + 68 cm + 12}\text{.0 cm = 93}\text{.421}\text{cm}$

The least number of significant figures is 2. Thus, answer up to three correct significant digits is:

  $93\text{cm}$

Conclusion:

Thus, the result is $93\text{cm}$ .

(f)

To determine

To Solve: The given expression.

Answer to Problem 12SSC

  $1.61\times {10}^5\text{cm}$

Explanation of Solution

Given:

  $\text{1}\text{.6 km + 1}\text{.62 m + 1200 cm}$

Calculations:

To determine the significant figure in addition, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

  $\text{1}\text{.6 km + 1}\text{.62 m + 1200 cm}$

Convert m to cm and km to cm

  $\begin{array}{l}\text{1m =100}\text{cm}\\ \text{1 km = 100000 cm}\end{array}$

  $\begin{array}{l}\text{1}\text{.6 km + 1}\text{.62 m + 1200 cm}\\ \text{=160000 cm + 162 cm +1200 cm}\\ \text{=161362 cm}\end{array}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $1.61\times {10}^5\text{cm}$

Conclusion:

Thus, the result is $1.61\times {10}^5\text{cm}$ .