Q. 2.28 - 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. $400\times 185$

b. $\frac{2.40}{\left(4\right)\left(125\right)}$

c. $0.825\times 3.6\times 5.1$

d. $\frac{\left(3.5\right)\left(0.261\right)}{\left(8.24\right)\left(20.0\right)}$

e. $\frac{\left(5\times {10}^{-5}\right)\left(1.05\times {10}^4\right)}{\left(8.24\times {10}^{-8}\right)}$

f. $\frac{\left(4.25\times {10}^2\right)\left(2.56\times {10}^{-3}\right)}{\left(2.245\times {10}^{-3}\right)\left(56.5\right)}$

Step-by-Step Solution

Answer

(a) The required answer is, $7.40\times {10}^4$

(b) The required answer is, $0.005$

(c) The required answer is, $15$

(d) The required answer is, $0.0055$

(e) The required answer is, $6\times {10}^6$

(f) The required answer is, $8.58$

Part (a) Step 1: Given information

We need to find out the value of $400\times 185$ with correct no. of significant figures. 

Part (a) Step 2: Simplify

We know that,

The calculation of $400\times 185$ is, $74000$

But the lowest significant figures are three

So, the Answer is rounded off to the three significant figures

Therefore, the required answer is, $7.40\times {10}^4$

Part (b) Step 1: Given information

We need to find out the value of $\frac{2.40}{\left(4\right)\left(125\right)}$ with correct no. of significant figures

Part (b) Step 2: Simplify

We know that,

The calculation of $\frac{2.40}{\left(4\right)\left(125\right)}$ is,

     $\frac{2.40}{500}=0.0048$

But the lowest significant figure is one

So, the Answer is rounded off to the one significant figure

Therefore, the required answer is, $0.005$

Part (c) Step 1: Given information

We need to find out the value of $0.825\times 3.6\times 5.1$ with correct no. of significant figures.  

Part (c) Step 2: Simplify

We know that,

The calculation of $0.825\times 3.6\times 5.1$ is, $15.147$

But the lowest significant figures are two

So, the Answer is rounded off to the two significant figures

Therefore, the required answer is, $15$

Part (d) Step 1: Given information

We need to find out the value of $\frac{\left(3.5\right)\left(0.261\right)}{\left(8.24\right)\left(20.0\right)}$ with correct no. of significant figures.  

Part (d) Step 2: Simplify

We know that,

The calculation of $\frac{\left(3.5\right)\left(0.261\right)}{\left(8.24\right)\left(20.0\right)}$ is, $0.005543$

But the lowest significant figures are two

So, the Answer is rounded off to the two significant figures

Therefore, the required answer is, $0.0055$

Part (e) Step 1: Given information

We need to find out the value of $\frac{\left(5\times {10}^{-5}\right)\left(1.05\times {10}^4\right)}{\left(8.24\times {10}^{-8}\right)}$ with correct no. of significant figures.

Part (e) Step 2: Simplify

We know that,

The calculation of $\frac{\left(5\times {10}^{-5}\right)\left(1.05\times {10}^4\right)}{\left(8.24\times {10}^{-8}\right)}$ is, $6.371359223\times {10}^6$

But the lowest significant figure is one

So, the Answer is rounded off to the one significant figure

Therefore, the required answer is, $6\times {10}^6$

Part (f) Step 1: Given information

We need to find out the value of $\frac{\left(4.25\times {10}^2\right)\left(2.56\times {10}^{-3}\right)}{\left(2.245\times {10}^{-3}\right)\left(56.5\right)}$ with correct no. of significant figures.  

Part (f) Step 2: Simplify

We know that,

The calculation of $\frac{\left(4.25\times {10}^2\right)\left(2.56\times {10}^{-3}\right)}{\left(2.245\times {10}^{-3}\right)\left(56.5\right)}$ is, $8.577566667$

But the lowest significant figures are three

So, the Answer is rounded off to the three significant figures

Therefore, the required answer is, $8.58$