Chapter A2, Problem 1E

For each number, underline the zeroes that are significant and draw an x through the zeroes that are not.
a. 1,050,501 km
b. 0.0120 m
c. 0.0000000000002 s
d. 0.001090 cm

Interpretation Introduction

Interpretation: The zeroes that are significant should be underlined and $\times$

should be drawn through the zeroes that are not, for the following numbers:

  $1,050,501km$

  $0.0020m$

  $0.000000000000002s$

  $0.001090cm$

Concept introduction:

• Significant figures are the numbers which are reported in a measurement including the estimated digit.

To determine: The zeroes that are significant and draw a $\times$ through the zeroes that are not, for the following numbers,

  $1,050,501km$

  $0.0020m$

  $0.000000000000002s$

  $0.001090cm$

Answer to Problem 1E

Solution:

  $1,\underset{\_}{0}5\underset{\_}{0},5\underset{\_}{0}1km$

  $\text{x}\text{.xx}2\underset{\_}{0}m$

  $\text{x}\text{.xxxxxxxxxxxxxx}2s$

  $\text{x}\text{.xx}1\underset{\_}{0}9\underset{\_}{0}cm$

Explanation of Solution

Significant figures:

Significant figures are the numbers which are reported in a measurement including the estimated digit.

The following are the rules that decide whether a zero is significant or not:

1. Any zeroes between two or more non-zero digits are significant.

2. Trailing zeroes in the decimal number are significant.

3. Zeroes that are present at the beginning of a decimal number are not significant.

4. Zeroes used as place holders in large numbers without a decimal are not significant.

a. Given:

  $1,050,501km$

The zeroes in $1,050,501km$ are significant because the zeroes present between two non-zero digits are significant. The zeroes that are significant are underlined:

  $1,\underset{\_}{0}5\underset{\_}{0},5\underset{\_}{0}1km$

b. Given:

  $0.0020m$

The zero which is present after the number 2 in $0.0020m$ is a significant figure because a zero at the end of a decimal number is significant, while the zeroes that are present at the beginning of a decimal number are not significant, they show position of decimal. The zeroes that are significant are underlined and x is drawn for non-zero significant numbers are:

  $\text{x}\text{.xx}2\underset{\_}{0}m$

c. Given:

  $0.000000000000002s$

The zeroes in $0.000000000000002s$ are not significant because the zeroes that are present at the beginning of a decimal number are not significant, they show position of decimal. x is drawn for non-zero significant numbers are:

  $\text{x}\text{.xxxxxxxxxxxxxx}2s$

d. Given:

  $0.001090cm$

The zero which is present after the digit 9 in $0.001090cm$ is significant because a zero at the end of a decimal number is significant, and the zero present between 1 and 9 is also significant while the zeroes that are present at the beginning of a decimal number are not significant, they show position of decimal. The zeroes that are significant are underlined and x is drawn for non-zero significant numbers are:

  $\text{x}\text{.xx}1\underset{\_}{0}9\underset{\_}{0}cm$

Conclusion

Therefore, for given numbers, the zeroes that are underlined are significant and the zeroes that are crossed out are no significant,

  $1,\underset{\_}{0}5\underset{\_}{0},5\underset{\_}{0}1km$

  $\text{x}\text{.xx}2\underset{\_}{0}m$

  $\text{x}\text{.xxxxxxxxxxxxxx}2s$

  $\text{x}\text{.xx}1\underset{\_}{0}9\underset{\_}{0}cm$