Q. 2.26 - An Introduction to General, Organic, and Biological Chemistry

Question

Round off or add zeros to each of the following to two significant figures: 

a. $3.2805 m$                       b. $1.855\times {10}^{2}g$

c. $0.002 341 mL$               d. $2 L$.

Step-by-Step Solution

Answer

a. The value of $3.2805 m$ in two significant figures is $3.3 m$.

b. The value of $1.855\times {10}^{2}g$ in two significant figures is $1.9\times {10}^{2}g$

c. The value of $0.002 341 mL$ in two significant figures is $0.0023 mL$.

d. The value of $2 L$ in two significant figures is $2.0 L$.

Part (a) Step 1: Given Information

We need to round off or add zeros in $3.2805 m$ to two significant figures.

Part (a) Step 2: Explanation

Considering the rules for rounding off numbers.

• If the digit to be rejected is $5$ or greater, the last remaining digit is increased by one.
• If the digit to be rejected is less than $5$ , the last remaining digit is left as it is.

Now, rounding off $3.2805$ to three significant figures with considering the rules.

$3.2805$ has five significant figures, so we have to drop the last three-digit which is $805$ . The last remaining digit which is $2$ will increase by $1$ as the last rejected digit is $8$ which is greater than $5$.

Hence, $3.2805$ is round off to two significant figures, that is $3.3$.

Part (b) Step 1: Given Information

We need to round off or add zeros in $1.855\times {10}^{2}g$to two significant figures.

Part (b) Step 2: Explanation

Considering the rules for rounding off numbers.

• If the digit to be rejected is $5$ or greater, the last remaining digit is increased by one.
• If the digit to be rejected is less than $5$ , the last remaining digit is left as it is.

Now, rounding off $1.855\times {10}^2$ to three significant figures with considering the rules.

$1.855\times {10}^2$ has four significant figures, so we have to drop the last two digit which is $55$ . The last remaining digit which is $8$ will increase by $1$ as the last rejected digit is $5$.

Hence, $1.855\times {10}^2$ will round off to two significant figures, that is  $1.9\times {10}^2$.

Part (c) Step 1: Given Information

We need to round off or add zeros in $0.002 341 mL$ to two significant figures.

Part (c) Step 2: Explanation

Considering the rules for rounding off numbers.

• If the digit to be rejected is $5$ or greater, the last remaining digit is increased by one.
• If the digit to be rejected is less than $5$ , the last remaining digit is left as it is.

Now, rounding off $0.002 341$ to three significant figures with considering the rules.

$0.002341$ has four significant figures, so we have to drop the last two digit which is $41$ . The last remaining digit which is $3$ will left as it is as the last rejected digit which is $4$ is less than $5$.

Hence, $0.002 341$ will round off to two significant figures, that is  $0.0023$.

Part (d) Step 1: Given Information

We need to round off or add zeros in $2 L$ to two significant figures.

Part (d) Step 2: Explanation

Considering the rules for rounding off numbers.

• If the digit to be rejected is $5$ or greater, the last remaining digit is increased by one.
• If the digit to be rejected is less than $5$ , the last remaining digit is left as it is.

Now, rounding off $2$ to two significant figures with considering the rules.

$2$ has one significant figure, so we have to add one zero to get two significant figures. and we will add a decimal point between the number to retain the original number.

Hence, $2$ is round off to two significant figures, that is $2.0$.