Q. 2.27 - An Introduction to General, Organic, and Biological Chemistry

Question

Perform each of the following calculations, and give an answer with the correct number of significant figures: 

a. $45.7\times 0.034$

b. $0.00278\times 5$

c. $\frac{34.56}{1.25}$

d. $\frac{(0.2465)\left(25\right)}{1.78}$

e. $(2.8\times {10}^4)(5.05\times {10}^{-6})$

f. $\frac{(3.45 \times {10}^{-2})(1.8\times {10}^5)}{(8\times {10}^3)}$

Step-by-Step Solution

Answer

a. The required answer is $1.5$.

b. The required answer is $0.01$.

c. The required answer is $27.6$.

d. The required answer is $3.5$.

e. The required answer is $1.4\times {10}^{-1}$.

f. The required answer is  $8\times {10}^{-1}$.

Part (a) Step 1: Given information

We need to find out the value of $45.7\times 0.034$ with correct no. of significant figures.  

Part (a) Step 2: Simplify

We know that, 

The calculation of $45.7\times 0.034=1.5538=1.5$

But the lowest significant figures are two

So, the answer is rounded off to the two significant figures.

Therefore, the required answer is $1.5$.

Part (b) Step 1: Given information

We need to find out the value of $0.00278\times 5$ with correct no. of significant figures.  

Part (b) Step 2: Simplify

We know that,

The calculation of $0.0278\times 5=0.0139=0.01$

But the lowest significant figures are one.

So, the answer is rounded off to the one significant figures.

Therefore, the required answer is, $0.01$.

Part (c) Step 1: Given information

We need to find out the value of $\frac{34.56}{1.25}$with correct no. of significant figures.  

Part (c) Step 2: Simplify

We know that,

The calculation of $\frac{34.56}{1.25}=27.648=27.6$$27.648=27.6$

But the lowest significant figures are three.

So, the answer is rounded off to the three significant figures.

Therefore, the required answer is, $27.6$.

Part (d) Step 1: Given information

We need to find out the value of $\frac{(0.2465)\left(25\right)}{1.78}$ with correct no. of significant figures.  

Part (d) Step 2: Simplify

We know that,

The calculation of $\frac{(0.2465)\left(25\right)}{1.78}=3.46207=3.5$ 

But the lowest significant figures are two.

So, the answer is rounded off to the two significant figures.

Therefore, the required answer is, $3.5$.

Part (e) Step 1: Given information

We need to find out the value of $(2.8\times {10}^4)(5.05\times {10}^{-6})$ with correct no. of significant figures.  

Part (e) Step 2: Simplify

We know that,

The calculation of  $(2.8\times {10}^4)(5.05\times {10}^{-6})=1.414\times {10}^{-1}$

$1.414\times {10}^{-1}$ has four significant figures.

Therefore, the required answer is, $1.4\times {10}^{-1}$.

Part (f) Step 1: Given information

We need to find out the value of $\frac{(3.45 \times {10}^{-2})(1.8\times {10}^5)}{(8\times {10}^3)}$ with correct no. of significant figures. 

Part (f) Step 2: Simplify

We know that,

The calculation of $\frac{(3.45 \times {10}^{-2})(1.8\times {10}^5)}{(8\times {10}^3)}=7.7625\times {10}^{-1}$ 

$8\times {10}^{-1}$ has one significant figures.

Therefore, the required answer is,$8\times {10}^{-1}$.