Q. 2.23 - An Introduction to General, Organic, and Biological Chemistry

Question

Round off each of the following calculator answers to three significant figures:

a. $1.854 kg$                            b. $88.2038 L$

c. $0.0004 738 265 cm$         d. $8807 m$

e. $1.832\times {10}^5 s$.

Step-by-Step Solution

Answer

a. The three significant figure of $1.854 kg$ is $1.85$.

b. The three significant figure of $88.2038 L$is $88.2$.

c. The three significant figure of $0.0004 738 265 cm$ is $0.000473$.

d. The three significant figure of $8807 m$is $8.81\times {10}^3$.

e. The three significant figure of $1.832\times {10}^{5}s$ is $1.83\times {10}^5$.

Part (a) Step 1: Given Information

We need to round off $1.854 kg$ to three significant figures.

Part (a) Step 2: Explanation

To get the three significant figures from the number $1.854$, we will use only the first three leftmost digit that should be $1.85$. And the number which is following $5$ is $4$, hence round off is not that necessary, and the number retained is $1.85$.

Part (b) Step 1: Given Information

We need to round off $88.2038 L$to three significant figures.

Part (b) Step 2: Explanation

To get the three significant figures from the number $88.2038$, we will use only the first three leftmost digits to reach at $88.2$. taking the number on the right of $2$ is less than $5$, so we don't need to round off the number to retain $88.2$.

Part (c) Step 1: Given Information

We need to round off $0.004 738 265 cm$to three significant figures.

Part (c) Step 2: Explanation

To get the three significant figures from the number $0.0004 738 265$, we use the leftmost non-zero digits from the original number to reach at $0.00473$. Taking the number on the right of $3$ is greater than $5$, we will round off the number to get $0.00474$.

Part (d) Step 1: Given Information

We need to round off $8807 m$to three significant figures.

Part (d) Step 1: Explanation

To get the three significant figures from the number $8807$, first of all convert the number to a specific notation, that is $8.807\times {10}^3$. Then use the first three leftmost digits to get $8.80\times {10}^3$.

Taking the number on the right of $0$ in the original number which is greater than $5$, we will round up the number to $8.81\times {10}^3$.

Part (e) Step 1: Given Information

We need to round off $1.832\times {10}^5 s$ to three significant figures.

Part (e) Step 2: Explanation

To get the three significant figures from the number $1.832\times {10}^5$. Now, sing the first three leftmost digits to get $1.83\times {10}^5$. Taking the number on the right of $3$ is less than $5$, so we don't need to round off the number to retain $1.83\times {10}^5$.