Q. 2.14 - An Introduction to General, Organic, and Biological Chemistry

Question

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

a. $20.05°C$              b. $5.00 m$

c. $0.000 02 g$           d. $120 000 yr$

e. $8.05\times {10}^2 L$.

Step-by-Step Solution

Answer

a. Zeroes in $20.05°C$ are significant.

b. Zeroes in $5.00 m$ are significant.

c. Zeroes in $0.000 02 g$ are not significant.

d. Zeroes in$120 000 yr$ are not significant.

e. Zeroes in $8.05\times {10}^2 L$ are significant.

Part (a) Step 1: Given Information

We need to Indicant the measurement $20.05°C$whether zeroes are significant or not.

Part (a) Step 2: Calculation

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

Table Significant figures in measured numbers

From the above table, the zeroes are significant as they are in between nonzero digits.

Part (b) Step 1: Given Information

We need to Indicant the measurement $5.00 m$ weather zeroes are significant or not.

Part (b) Step 2: Calculation

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

Table Significant figures in measured numbers

From the above table, the zeros are significant as they are at the end of the decimal number.

Part (c) Step 1: Given Information

We need to Indicant the measurement $0.000 02 g$ weather zeroes are significant or not.

Part (c) Step 3: Calculation

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

Table Significant figures in measured numbers

From the above table, the zeroes are not significant since they are just placeholders at the beginning of a decimal.

Part (d) Step 1: Given Information

We need to Indicant the measurement $120 000 yr$ weather zeroes are significant or not.

Part (d) Step 2: Calculation

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

Table Significant figures in measured numbers

From the above table, the zeroes are not significant since they are just placeholders at the number without a decimal point.

Part (e) Step 1: Given Information

We need to Indicant the measurement $8.05\times {10}^{2}L$ weather zeroes are significant or not.

Part (e) Step 2: Calculation

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

Table Significant figures in measured numbers

From the above table, the zeroes are significant since it is in between nonzero digit.