Chapter C, Problem 1P

Write each number in scientific notation.

a. $760,000$

b. $0.00035$

To determine

(a)

To write:

The number $\mathrm{760,\; 000}$ in scientific notation

Answer to Problem 1P

Solution:

$\mathrm{760,\; 000}=7.6\times {10}^5$

Explanation of Solution

Approach:

To write a number in scientific notation:

1. Move the decimal point in the original number so that the new number has a value between $1$ and $10$.

2. Count the number of decimal places the decimal point is moved in the step-1. If the original number is $10$ or greater, the count is positive. If the original number is less than $1$, the count is negative.

3. Multiply the new number in step-1 by $10$ raised to an exponent equal to the count found in step-2.

Calculation:

Given number: $\mathrm{760,\; 000}$

The original number is greater than $10$. So, move the decimal point until the number is between $1$ and $10$. Since we move $5$ decimal places, $5$ becomes the exponent of $10$.

$\mathrm{760,\; 000}=7.6\times {10}^5$

Thus, $\mathrm{760,\; 000}=7.6\times {10}^5$.

Final statement:

Therefore, the scientific notation of $\mathrm{760,\; 000}=7.6\times {10}^5$.

To determine

(b)

To write:

The number $0.00035$ in scientific notation

Answer to Problem 1P

Solution:

$0.00035=3.5\times {10}^{-4}$

Explanation of Solution

Approach:

To write a number in scientific notation:

1. Move the decimal point in the original number so that the new number has a value between $1$ and $10$.

2. Count the number of decimal places the decimal point is moved in the step-1. If the original number is $10$ or greater, the count is positive. If the original number is less than $1$, the count is negative.

Multiply the new number in step-1 by $10$ raised to an exponent equal to the count found in step-2.

Calculation:

Given number: $0.00035$

The original number is less than $10$. So, move the decimal point until the number is between $1$ and $10$. Since we move $4$ decimal places, $-4$ becomes the exponent of $10$.

$0.00035=3.5\times {10}^{-4}$

Thus, $0.00035=3.5\times {10}^{-4}$.

Final statement:

Therefore, the scientific notation of $0.00035=3.5\times {10}^{-4}$.