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

a. 45.7×0.034

b.0.00278×5

c.34.561.25

d. (0.2465)(25)1.78

e. (2.8×104)(5.05×10-6)

f.(3.45×10-2)(1.8×105)(8×103)

Short Answer

Expert verified

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 1.4×10-1.

f. The required answer is 8×10-1.

Step by step solution

01

Part (a) Step 1: Given information  

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

02

Part (a) Step 2: Simplify  

We know that,

The calculation of45.7×0.034=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.

03

Part (b) Step 1: Given information   

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

04

Part (b) Step 2: Simplify   

We know that,

The calculation of0.0278×5=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.

05

Part (c) Step 1: Given information   

We need to find out the value of 34.561.25with correct no. of significant figures.

06

Part (c) Step 2: Simplify   

We know that,

The calculation of 34.561.25=27.648=27.627.648=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.

07

Part (d) Step 1: Given information   

We need to find out the value of (0.2465)(25)1.78with correct no. of significant figures.

08

Part (d) Step 2: Simplify  

We know that,

The calculation of (0.2465)(25)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.

09

Part (e) Step 1: Given information  

We need to find out the value of (2.8×104)(5.05×10-6)with correct no. of significant figures.

10

Part (e) Step 2: Simplify   

We know that,

The calculation of (2.8×104)(5.05×10-6)=1.414×10-1

1.414×10-1has four significant figures.

Therefore, the required answer is, 1.4×10-1.

11

Part (f) Step 1: Given information 

We need to find out the value of (3.45×10-2)(1.8×105)(8×103)with correct no. of significant figures.

12

Part (f) Step 2: Simplify 

We know that,

The calculation of (3.45×10-2)(1.8×105)(8×103)=7.7625×10-1

8×10-1has one significant figures.

Therefore, the required answer is,8×10-1.

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