Q. 2.25 - An Introduction to General, Organic, and Biological Chemistry

Question

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

a. $56.855 m$              b. $0.002 282 g$

c. $11 527 s$                d. $8.1 L$.

Step-by-Step Solution

Answer

a. The round-off value of $56.855 m$ is $56.9m$

b. The round-off value of $0.002282 g$ is $0.00228 g$.

c. The round-off value of  $11 527 s$ is  $11500 s$

d. The round-off value of  $8.1 L$ is  $8.10 L$.

Part (a) Step 1: Given Information

We need to round off or add zeros in $56.855 m$ to three 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 $56.855$ to three significant figures with considering the rules.

$56.855$ has five 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,$56.855$ is rounded off to three significant figures, that is $56.9$.

Part (b) Step 1: Given Information

We need to round off or add zeros in $0.002 282 g$ to three 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 $0.002282$ to three significant figures with considering the rules.

$0.00282$ has four significant figures, so we have to drop the last digit which is $2$. The last remaining digit which is $8$ will left as it is as the last rejected digit is less than .

Hence, $0.002282$ is rounded off to three significant figures, that is $0.00228$.

Part (c) Step 1: Given Information

We need to round off or add zeros in $11 527 s$ to three 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 $11.527$ to three significant figures with considering the rules.

$11.527$ has five significant figures, so we have to drop the last two digit which is$27$ . The last remaining digit which is $5$ will left as it is as the last rejected digit is less than $5$ and also we will add two zero to retain the value of original number.

Hence, $11.527$ is rounded off to three significant figures, that is $11500$.

Part (d) Step 1: Given Information

We need to round off or add zeros in $8.1 L$to three 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 $8.1$ to three significant figures with considering the rules.

$8.1$ has two significant figures, so we have to add one zero to get three significant figures.

Hence, $8.1$ is round off to three significant figures that is $8.10$.