Chapter L, Problem 25PS

(a)

Interpretation Introduction

Interpretation: The correct number of significant figure for $1.52$ and $9.44\times {10}^{-3}$ has to be provided.

Concept Introduction:

Significant of zeroes:

• Zeroes between two other significant digits are significant.
• Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
• Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

Answer to Problem 25PS

$\text{9}\text{.44}\times {\text{10}}^{-3}$; The number of significant figures is three.

Explanation of Solution

In $1.52$, the decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 3.

In $6.21\times {10}^{-3}$, the decimal numbers with no zeroes and has only the significant numbers. So, the significant number is 3.

The multiplication of $1.52$ and $9.44\times {10}^{-3}$:

  $\underset{\_}{\begin{array}{l}\times \underset{\_}{\begin{array}{l}\text{ 1}\text{.52}\text{ significant}\text{figure}\text{3}\\ (\text{6}\text{.21}\times {10}^{-3})\text{significant}\text{figure}\text{3}\end{array}}\\ \text{=}\text{9}\text{.4392}\times {10}^{-3}\end{array}}$

The number of significant figures should the answer contain is the fewest number of significant figures of the given quantity.  Both the quantity possesses same significant figures.  Hence, the answer should be written as $\text{9}\text{.44}\times {10}^{-3}$.  The significant figure is three.

(b)

Interpretation Introduction

Interpretation: The correct number of significant figure for $6.217\times {10}^3-5.23\times {10}^2$ has to be provided.

Concept Introduction:

Significant of zeroes:

• Zeroes between two other significant digits are significant.
• Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
• Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

Answer to Problem 25PS

$5694$; The number of significant figures is four.

Explanation of Solution

In $6.217\times {10}^3$, written as $6217$ no decimal numbers; has only the significant numbers.  So, the significant number is 4.

In $5.23\times {10}^2$, written as $523$ no decimal numbers and has only the significant numbers.  So, the significant number is 3.

The subtraction of $6217$ and $523$:

  $\underset{\_}{\begin{array}{l}\text{- }\underset{\_}{\begin{array}{l}6217\text{ decimal places}\text{0}\\ 523\text{ decimal places }\text{0}\end{array}}\\ \text{=}\text{5694 decimal places 0 }\end{array}}$

The number of decimal places should the answer contain is the fewest decimal places of the given quantity.  Both the quantity possesses zero decimal places.  Hence, the answer should be written as $5694$.  The significant figure is four.

(c)

Interpretation Introduction

Interpretation: The correct number of significant figure for $6.217\times {10}^3÷5.23\times {10}^2$ has to be provided.

Concept Introduction:

Significant of zeroes:

• Zeroes between two other significant digits are significant.
• Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
• Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

Answer to Problem 25PS

$11.9$; The number of significant figures is three.

Explanation of Solution

In $6.217\times {10}^3$, writes as $6217$ has no decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 4.

In $5.23\times {10}^2$, written as $523$ has no decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 3.

The division of $6217$ and $523$:

  $\underset{\_}{\begin{array}{l}÷\underset{\_}{\begin{array}{l}6217\text{ significant}\text{figure}\text{4}\\ 523\text{significant}\text{figure}\text{3}\end{array}}\\ \text{=}11.887\end{array}}$

The number of significant figures should the answer contain is the fewest number of significant figures of the given quantity.  Out of both the quantity $523$ possesses 3 significant figures.  Hence, the answer should be written as $\text{11}\text{.9 (rounding off)}$.  The significant figure is three.

(d)

Interpretation Introduction

Interpretation: The correct number of significant figure for $\text{(0}\text{.0546)(16}\text{.0000)}\left[\frac{\text{7}\text{.779}}{\text{55}\text{.85}}\right]$ has to be provided.

Concept Introduction:

Significant of zeroes:

• Zeroes between two other significant digits are significant.
• Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
• Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

Answer to Problem 25PS

$0.122$; The number of significant figures is three.

Explanation of Solution

The division and multiplication of:

  $\begin{array}{l}\text{(0}\text{.0546)(16}\text{.0000)}\left[\frac{\text{7}\text{.779}}{\text{55}\text{.85}}\right]\\ \underset{\_}{\text{Multiplication of 0}\text{.0546 and 16}\text{.0000:}}\\ \underset{\_}{\begin{array}{l}\text{×}\underset{\_}{\begin{array}{l}\text{ 0}\text{.0546}\text{ significant}\text{figure}\text{3}\\ \text{16}\text{.0000 significant}\text{figure}\text{6}\end{array}}\\ \text{=}\text{0}\text{.874 significant}\text{figure}\text{3 }\end{array}}\\ \\ \underset{\_}{\text{Division of 7}\text{.779 and 55}\text{.85:}}\\ \underset{\_}{\begin{array}{l}\text{÷}\underset{\_}{\begin{array}{l}\text{ 7}\text{.779 significant}\text{figure}\text{4}\\ \text{55}\text{.85}\text{significant}\text{figure}\text{4}\end{array}}\\ \text{=}\text{0}\text{.1393 significant}\text{figure}\text{4 }\end{array}}\\ \text{Finally,}\\ \underset{\_}{\text{Mutiplication of 0}\text{.874 and 0}\text{.1393:}}\\ \underset{\_}{\begin{array}{l}\text{×}\underset{\_}{\begin{array}{l}\text{ 0}\text{.874}\text{ significant}\text{figure}\text{3}\\ \text{0}\text{.1393 significant}\text{figure}\text{4}\end{array}}\\ \text{=}\text{0}\text{.12174 }\end{array}}\\ \end{array}$

Finally, on the multiplication of $\text{0}\text{.874 and 0}\text{.1393}$ gives the value $\text{0}\text{.12174}$.  Out of the two obtained quantity $\text{0}\text{.874}$ possesses 3 significant figures.  Hence, the answer should be written as $\text{0}\text{.122 (rounding off)}$.  The significant figure is three.