Chapter 7.4, Problem 68PPE

a.

To determine

To write: three numbers greater than 1000 in scientific notation.

Answer to Problem 68PPE

The required answer is: numbers are $7.8\times {10}^3,3.64\times {10}^{4}and2\times {10}^4$

Explanation of Solution

Given information:

The given information: numbers greater than 1000

Calculation:

First number:

  $7800=7.8\times {10}^3$

(Scientific notation)

Second number:

  $36400=3.64\times {10}^4$

(Scientific notation)

Third number:

  $20000=2\times {10}^4$

(Scientific notation)

Hence, three numbers greater than 1000 are $7.8\times {10}^3,3.64\times {10}^{4}and2\times {10}^4$

b.

To determine

To divide: each number by 2, numbers are $7.8\times {10}^3,3.64\times {10}^{4}and2\times {10}^4$

Answer to Problem 68PPE

The required answer is: 3900, 18200 and 10000

Explanation of Solution

Given information:

The given numbers: $7.8\times {10}^3,3.64\times {10}^{4}and2\times {10}^4$

Calculation:

  $\frac{7.8\times {10}^3}{2}=\frac{7.8}{2}\times {10}^3$

  $\begin{array}{l}=3.9\times {10}^3\\ =3.9\times 1000\\ =3900\end{array}$

(Simplify)

  $\frac{3.64\times {10}^4}{2}=\frac{3.64}{2}\times {10}^4$

  $\begin{array}{l}=1.82\times {10}^4\\ =1.82\times 10000\\ =18200\end{array}$

(Simplify)

  $\frac{2\times {10}^4}{2}=\frac{2}{2}\times {10}^4$

  $\begin{array}{l}=1\times {10}^4\\ =1\times 10000\\ =10000\end{array}$

(Simplify)

c.

To determine

To explain: Is the exponent of the power 10 divided by 2 when you divide a number in scientific

notation by 2?

Answer to Problem 68PPE

The required answer is: No

Explanation of Solution

Given information:

The given information: exponent of the power 10 divided by 2

Calculation:

The exponent of the power 10 cannot be divided by 2 when you divide a number in scientific notation by 2 because the properties of exponents are not applicable in this case.