Question

Underline the significant zeros in the following numbers:

(a) 0.41
(b) 0.041
(c) 0.0410
(d) 4.0100 x 104

Answer 1

a) 0.41 - No significant zeros

b) 0.041 - No significant zeros

c) 0.0410 - Trailing zero after '1' is significant

d) 0.04100 * 10^4 - The two trailing zeros after '1' are significant

Step-by-step explanation:

As per the rules governing significant zeros in the context of 'significant figures'

-Zeros between two significant digits are significant

-Any zero or trailing zeros after non-zero numbers in a decimal are significant

- Zeros after the decimal but before a non-zero number are not significant

a) 0.41

The '0' before the decimal is not significant. Hence, there are no significant zeros

b) 0.041

The '0' before the decimal and right after it are not significant. Hence, there are no significant zeros

c) 0.0410

The trailing zero after the number '1' is significant. Hence, there is one significant zero

d) 0.04100*10^4

The trailing zeros after the number '1' are significant. Hence, there are two significant zeros

Answer 2

Answer is given below

Step-by-step explanation:

According to significant figure counting rule-

zeros after decimal point are significant if a non-zero digit is present before that zero e.g. "0" is considered as a significant figure in 2.20 as 2(non-zero digit) is present before decimal point.

zero before a decimal point is insignificant if no non-zero digit is present before that zero e.g. "0" is insignificant in 0.22.

Zero placed between any two non-zero digits are always significant e.g."0" is significant in 305.

(a)Here 0.41 contains no significant zero.

(b)Here 0.041 contains no significant zero

(c) One significant zero is present-
`0.041\underline{0}`

(d) Three significant zeroes are present -
`4.\underline{0}1\underline{00}* 10^(4)`