Chapter 9.5, Problem 47HP

(a)

To determine

To find: the number better describes the population of Miami, $3.8\times {10}^4$ or $3.8\times {10}^6$ .

Answer to Problem 47HP

  $3.8\times {10}^6$ .

Explanation of Solution

Given information:

Miami is the second most populous city in Florida.

Calculation:

Let the two numbers are $3.8\times {10}^4$ and $3.8\times {10}^6$ . Here $3.8\times {10}^4$ in standard form is equals to 38000. The number $3.8\times {10}^6$ in standard form is equals to 3800000.

Of the two values $3.8\times {10}^6$ represents the population of most populous city. Because the value $3.8\times {10}^4$ is very small to represent most populous city in Florida.

Thus, the correct value is $3.8\times {10}^6$ .

(b)

To determine

To express: Miami’s population in another form.

Answer to Problem 47HP

3800000

Explanation of Solution

Calculation:

Consider Miami;s population $3.8\times {10}^6$ .

In conversion of scientific notation to standard form, If the exponent of 10 is negative the decimal point moves to the left and if the exponent of 10 is positive the decimal point moves to the right according to its exponent.

Take the number $3.8\times {10}^6$ .

Simplify the multiplication as shown:

3800000

(c)

To determine

To find: the notation is best to use when describing population.

Answer to Problem 47HP

3800000

Explanation of Solution

Calculation:

For the number $3.8\times {10}^6$ the exponent of 10 is positive. So the decimal point 6 places to the right.

  $3.8\times {10}^6=3800000$

Thus, the value of the number $3.8\times {10}^6$ in the standard form is equals to 3800000.

Therefore, the answer is 3800000.

It is best notation to calculate in the form to describe the population.