Chapter 2, Problem 78A

(a)

Interpretation Introduction

Interpretation:

The given addition problem needs to be completed and represented in scientific notation.

$\left(6.23\times {10}^6\text{kL}\right)+\left(5.34\times {10}^6\text{kL}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete addition of the given problem is $\text{1}\text{.16}\times {10}^7\text{kL}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\begin{array}{c}\left(6.23\times {10}^6\text{kL}\right)+\left(5.34\times {10}^6\text{kL}\right)=\left(6.23+5.34\right)\times {10}^6\text{kL}\\ \text{=11}\text{.6}\times {10}^6\text{kL}\text{or}\text{1}\text{.16}\times {10}^7\text{kL}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The given addition problem needs to be completed and represented in scientific notation.

$\left(3.1\times {10}^4\text{mm}\right)+\left(4.87\times {10}^5\text{mm}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete addition of the given problem is $\text{5}\text{.2}\times {10}^5\text{mm}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$3.1\times {10}^4\text{mm}\text{=}0.31\times {10}^5\text{mm}$

$\begin{array}{c}\left(0.31\times {10}^5\text{mm}\right)+\left(4.87\times {10}^5\text{mm}\right)=\left(0.31+4.87\right)\times {10}^5\text{mm}\\ \text{=}\text{5}\text{.2}\times {10}^5\text{mm}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The given addition problem needs to be completed and represented in scientific notation.

$\left(7.21\times {10}^3\text{mg}\right)+\left(43.8\times {10}^2\text{mg}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete addition of the given problem is $1.16\times {10}^4\text{mm}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$43.8\times {10}^2\text{mg}\text{=}4.38\times {10}^3\text{mg}$

$\begin{array}{c}\left(7.21\times {10}^3\text{mg}\right)+\left(4.38\times {10}^3\text{mg}\right)=\left(7.21+4.38\right)\times {10}^3\text{mm}\\ \text{=}11.6\times {10}^3\text{mm}\\ =1.16\times {10}^4\text{mm}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The given addition problem needs to be completed and represented in scientific notation.

$\left(9.15\times {10}^{-4}\text{cm}\right)+\left(3.48\times {10}^{-4}\text{cm}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete addition of the given problem is $1.26\times {10}^{-3}\text{cm}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\begin{array}{c}\left(9.15\times {10}^{-4}\text{cm}\right)+\left(3.48\times {10}^{-4}\text{cm}\right)=\left(9.15+3.48\right)\times {10}^{-4}\text{cm}\\ \text{=}12.6\times {10}^{-4}\text{cm}\text{or}1.26\times {10}^{-3}\text{cm}\end{array}$

(e)

Interpretation Introduction

Interpretation:

The given addition problem needs to be completed and represented in scientific notation.

$\left(4.68\times {10}^{-5}\text{cg}\right)+\left(3.5\times {10}^{-6}\text{cg}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete addition of the given problem is $5.0\times {10}^{-5}\text{cg}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$3.5\times {10}^{-6}\text{cg}\text{=}0.35\times {10}^{-5}\text{cg}$

$\begin{array}{c}\left(4.68\times {10}^{-5}\text{cg}\right)+\left(0.35\times {10}^{-5}\text{cg}\right)=\left(4.68+0.35\right)\times {10}^{-5}\text{cg}\\ \text{=}5.0\times {10}^{-5}\text{cg}\end{array}$

(f)

Interpretation Introduction

Interpretation:

The given subtraction problem needs to be completed and represented in scientific notation.

$\left(3.57\times {10}^2\text{mL}\right)-\left(1.43\times {10}^2\text{mL}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete subtraction of the given problem is $2.14\times {10}^2\text{mL}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\begin{array}{c}\left(3.57\times {10}^2\text{mL}\right)-\left(1.43\times {10}^2\text{mL}\right)=\left(3.57-1.43\right)\times {10}^2\text{mL}\\ \text{=}2.14\times {10}^2\text{mL}\end{array}$

(g)

Interpretation Introduction

Interpretation:

The given subtraction problem needs to be completed and represented in scientific notation.

$\left(9.87\times {10}^4\text{g}\right)-\left(6.2\times {10}^3\text{g}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete subtraction of the given problem is $9.2\times {10}^4\text{g}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$6.2\times {10}^3\text{g}\text{=}0.62\times {10}^4\text{g}$

$\begin{array}{c}\left(9.87\times {10}^4\text{g}\right)-\left(0.62\times {10}^4\text{g}\right)=\left(9.87-0.62\right)\times {10}^4\text{g}\\ \text{=}9.2\times {10}^4\text{g}\end{array}$

(h)

Interpretation Introduction

Interpretation:

The given subtraction problem needs to be completed and represented in scientific notation.

$\left(7.52\times {10}^5\text{kg}\right)-\left(5.43\times {10}^5\text{kg}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete subtraction of the given problem is $2.09\times {10}^5\text{kg}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\begin{array}{c}\left(7.52\times {10}^5\text{kg}\right)-\left(5.43\times {10}^5\text{kg}\right)=\left(7.52-5.43\right)\times {10}^5\text{kg}\\ \text{=}2.09\times {10}^5\text{kg}\end{array}$

(i)

Interpretation Introduction

Interpretation:

The given subtraction problem needs to be completed and represented in scientific notation.

$\left(6.48\times {10}^{-3}\text{mm}\right)-\left(2.81\times {10}^{-3}\text{mm}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete subtraction of the given problem is $3.67\times {10}^{-3}\text{mm}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\begin{array}{c}\left(6.48\times {10}^{-3}\text{mm}\right)-\left(2.81\times {10}^{-3}\text{mm}\right)=\left(6.48-2.81\right)\times {10}^{-3}\text{mm}\\ \text{=}3.67\times {10}^{-3}\text{mm}\end{array}$

(j)

Interpretation Introduction

Interpretation:

The given subtraction problem needs to be completed and converted in scientific notation.

$\left(5.72\times {10}^{-4}\text{dg}\right)-\left(2.3\times {10}^{-5}\text{dg}\right)$

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 78A

The complete subtraction of the given problem is $5.5\times {10}^{-4}\text{dg}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same.

$\left(2.3\times {10}^{-5}\text{dg}\right)=\left(0.23\times {10}^{-4}\text{dg}\right)$

$\begin{array}{c}\left(5.72\times {10}^{-4}\text{dg}\right)-\left(0.23\times {10}^{-4}\text{dg}\right)=\left(5.72-0.23\right)\times {10}^{-4}\text{dg}\\ \text{=}5.5\times {10}^{-4}\text{dg}\end{array}$