Question

Indicate if the zeros are significant in each of the following measurements:

a. $0.0038m$ b. $5.04cm$

c. $800L$ d. $3.0\times {10}^{-3}kg$

e.$85000g$

Short answer

a. In $0.0038m$there are two significant figures which are $3$and $8$.

b. In $5.04cm$there are three significant figures which are $5,0and4$.

c. In $800L$there are three significant figures which are $8$and two non-zero digits.

d. In $3.0\times {10}^{-3}kg$there are two significant figures which are $3\mathrm{and}0$.

e. In $85000g$there are two significant figures which are $8\mathrm{and}5$.

Step-by-step solution

Part (a) Step 1: Given Information 

We need to find the number of significant figures in$0.0038m$.

Part (a) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

TableSignificant figures in measured numbers

There are two significant figures, the non-zero digits $3$and $8$, since the rest digits are the placeholders.

Part (b) Step 1: Given Information

We need to find the number of significant figures in$5.04cm$.

Part (b) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

TableSignificant figures in measured numbers

There are three significant figures, that is$5,0and4$.

Part (c) Step 1: Given Information

We need to find the number of significant figures in$800L$.

Part (c) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

TableSignificant figures in measured numbers

There are three significant figures, the non-zero digit $8$and the two zeros which denote the uncertainty at one digit.

Part (d) Step 1: Given Information

We need to find the number of significant figures in$3.0\times {10}^{-3}kg$.

Part (d) Step 1: Explanation

Considering the rules in significant figures as summarized by the table is

TableSignificant figures in measured numbers

There are two significant figures, the non-zero digit $3$and one zero which denotes the uncertainty at the $10th$digit.

Part (e) Step 1: Given Information

We need to find the number of significant figures in$85000g$.

Part (e) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

TableSignificant figures in measured numbers

There are two significant figures, the non-zero digits $8$and $5$, and the remaining digits are just placeholders.