Question

81.4 g sample of ethyl alcohol contains 0.002 g of water. The amount of pure ethyl alcohol to the proper number of significant figures is:
A. 81.398g
B. 71.40g
C. 91.4g
D. 81g

Answer 1

Hint: Significant figures are simply any number having considerable digits.
According to the rules for significant numbers, the no.of zeros that come before non-zero numbers are not considered significant digits.

Complete Step by Step Solution:
- Here in the given question, we have an 81.4g sample of ethyl alcohol that contains 0.002g of water.
- We have to find the significant numbers in the pure amount of ethyl alcohol.
- First, we have to find out the pure amount of ethyl alcohol.
- For this, we subtracted the amount of water from the amount of ethyl alcohol as ethyl alcohol has water in it.
- So, the pure amount of alcohol is \[81.4g - 0.002g = 81.398g\].
- According to the rule for significant numbers, non-zero numbers are significant.
- This is an apparent rule which states that the numbers excluding zero are significant.
- For example, in the number 543.3, there is an entirety of four significant figures.
- So, the amount of pure ethyl alcohol to the proper number of significant figures is 81.398g.
- It has five significant numbers i.e., 8,1,3,9, and 8.
So, option A is correct.

Note: When we are calculating by multiplication, subtraction, division, or addition we must round off the significant numbers to the closest and smallest decimal units. For example, 39.49 can be rounded up to 39.5.