Chapter C, Problem 1E

(a)

To determine

The representation of 326 as powers of 10.

Answer to Problem 1E

Solution:

$3.26\times {10}^2$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 326 as a power of 10.

$\begin{array}{c}326=326\times \frac{100}{100}\\ =\left(\frac{326}{100}\right)\times 100\\ =3.26\times 10\times 10\\ =3.26\times {10}^2\end{array}$

In this case, the number 326 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $3.26\times {10}^2$.

Conclusion:

The number 326 is written as power of 10 in the form $3.26\times {10}^2$.

(b)

To determine

The representation of 32608 as powers of 10.

Answer to Problem 1E

Solution:

$3.2608\times {10}^4$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 32608 as a power of 10.

$\begin{array}{c}32608=32608\times \frac{10000}{10000}\\ =\left(\frac{32608}{10000}\right)\times 10000\\ =3.2608\times 10\times 10\times 10\times 10\\ =3.2608\times {10}^4\end{array}$

In this case, the number 32608 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $3.2608\times {10}^4$.

Conclusion:

The number 32608 is written as power of 10 in the form $3.2608\times {10}^4$.

(c)

To determine

The representation of 1006 as powers of 10.

Answer to Problem 1E

Solution:

$1.006\times {10}^3$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 1006 as a power of 10.

$\begin{array}{c}1006=1006\times \frac{1000}{1000}\\ =\left(\frac{1006}{1000}\right)\times 1000\\ =1.006\times 10\times 10\times 10\\ =1.006\times {10}^3\end{array}$

In this case, the number 1006 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $1.006\times {10}^3$.

Conclusion:

The number 1006 is written as power of 10 in the form $1.006\times {10}^3$.

(d)

To determine

The representation of 36000008 as powers of 10.

Answer to Problem 1E

Solution:

$3.6000008\times {10}^7$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 36000008 as a power of 10.

$\begin{array}{c}36000008=36000008\times \frac{10000000}{10000000}\\ =\left(\frac{36000008}{10000000}\right)\times 10000000\\ =3.6000008\times 10\times 10\times 10\times 10\times 10\times 10\times 10\\ =3.6000008\times {10}^7\end{array}$

In this case, the number $36000008$ is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $3.6000008\times {10}^7$.

Conclusion:

The number 36000008 is written as power of 10 in the form $3.6000008\times {10}^7$.

(e)

To determine

The representation of 0.831 as powers of 10.

Answer to Problem 1E

Solution:

$8.31\times {10}^{-1}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 0.831 as a power of 10.

$\begin{array}{c}0.831=0.831\times \frac{10}{10}\\ =\left(0.831\times 10\right)\times \frac{1}{10}\\ =8.31\times \frac{1}{10}\\ =8.31\times {10}^{-1}\end{array}$

In this case, the number $0.831$ is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $8.31\times {10}^{-1}$.

Conclusion:

The number $0.831$ is written as power of 10 in the form $8.31\times {10}^{-1}$.

(f)

To determine

The representation of 0.03 as powers of 10.

Answer to Problem 1E

Solution:

$3\times {10}^{-2}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 0.03 as a power of 10.

$\begin{array}{c}0.03=0.03\times \frac{100}{100}\\ =\left(0.03\times 100\right)\times \frac{1}{100}\\ =3\times \frac{1}{100}\\ =3\times \frac{1}{10}\times \frac{1}{10}\end{array}$

Further solve.

$0.03=3\times {10}^{-2}$

In this case, the number 0.03 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $3\times {10}^{-2}$.

Conclusion:

The number 0.03 is written as power of 10 in the form $3\times {10}^{-2}$.

(g)

To determine

The representation of 0.000002 as powers of 10.

Answer to Problem 1E

Solution:

$2\times {10}^{-6}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 0.000002 as a power of 10.

$\begin{array}{c}0.000002=0.000002\times \frac{1000000}{1000000}\\ =\left(0.000002\times 1000000\right)\times \frac{1}{1000000}\\ =2\times \frac{1}{1000000}\\ =2\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\end{array}$

Further solve.

$0.000002=2\times {10}^{-6}$

In this case, the number 0.000002 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $2\times {10}^{-6}$.

Conclusion:

The number 0.000002 is written as power of 10 in the form $2\times {10}^{-6}$.

(h)

To determine

The representation of 0.000706 as powers of 10.

Answer to Problem 1E

Solution:

$7.06\times {10}^{-4}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express 0.000706 as a power of 10.

$\begin{array}{c}0.000706=0.000706\times \frac{10000}{10000}\\ =\left(0.000706\times 10000\right)\times \frac{1}{10000}\\ =7.06\times \frac{1}{10000}\\ =7.06\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\end{array}$

Further solve.

$0.000706=7.06\times {10}^{-4}$

In this case, the number 0.000706 is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $7.06\times {10}^{-4}$.

Conclusion:

The number 0.000706 is written as power of 10 in the form $7.06\times {10}^{-4}$.

(i)

To determine

The representation of $\sqrt{0.000081}$ as powers of 10.

Answer to Problem 1E

Solution:

$9.0\times {10}^{-3}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express $\sqrt{0.000081}$ as a power of 10.

$\begin{array}{c}\sqrt{0.000081}=\sqrt{0.009\times 0.009}\\ ={\left[{\left(0.009\right)}^2\right]}^{\frac{1}{2}}\\ =0.009\\ =0.009\times \frac{1000}{1000}\end{array}$

Further solve.

$\begin{array}{c}\sqrt{0.000081}=\left(0.009\times 1000\right)\times \frac{1}{1000}\\ =9.0\times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\\ =9.0\times {10}^{-3}\end{array}$

In this case, the number $\sqrt{0.000081}$ is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $9.0\times {10}^{-3}$.

Conclusion:

The number $\sqrt{0.000081}$ is written as power of 10 in the form $9.0\times {10}^{-3}$.

(j)

To determine

The representation of $\sqrt[3]{0.000027}$ as powers of 10.

Answer to Problem 1E

Solution:

$3.0\times {10}^{-2}$

Explanation of Solution

Introduction:

Any number can be expressed as the product of two numbers or as an integral power of 10. Power of 10 means the number can be expressed as the multiplication of 10 times and is indicated in exponential form.

Explanation:

Express $\sqrt[3]{0.000027}$ as a power of 10.

$\begin{array}{c}\sqrt[3]{0.000027}=\sqrt[3]{0.000027}\\ =\sqrt[3]{0.03\times 0.03\times 0.03}\\ ={\left[{\left(0.03\right)}^3\right]}^{\frac{1}{3}}\\ =0.03\times \frac{100}{100}\end{array}$

Further solve.

$\begin{array}{c}\sqrt[3]{0.000027}=\left(0.03\times 100\right)\times \frac{1}{100}\\ =3.0\times \frac{1}{100}\\ =3.0\times \frac{1}{10}\times \frac{1}{10}\\ =3.0\times {10}^{-2}\end{array}$

In this case, the number $\sqrt[3]{0.000027}$ is expressed as the product of the two numbers and as an integral power of 10. When it is expressed in the exponential form, it can be written as $3.0\times {10}^{-2}$.

Conclusion:

The number $\sqrt[3]{0.000027}$ is written as power of 10 in the form $3.0\times {10}^{-2}$.