# 5.16: Solve Percent Problems Involving Scientific Notation

**At Grade**Created by: CK-12

**Practice**Operations with Numbers in Scientific Notation

On certain dates, Mars is about

In this concept, you will learn to solve percent problems involving scientific notation.

### Scientific Notation

**Scientific notation** is a useful mathematical tool that allows you to work with very large or very small numbers. **Scientific notation** is when a number is written as a rational number and a power of 10. This means that you are using exponents to represent the power of 10. Scientific notation has the general form:

where ‘

When you conduct operations involving percent with numbers in scientific notation, you can use any operation with the ‘

Let’s look at an example.

Find 25% of

First, multiply the 25% by 3.

Next, since the ‘

The answer is

Very large and very small numbers are not always written in scientific notation. Some numbers remain expanded or in **standard notation**. You can still work with numbers that are very large but again must be most careful of decimal places.

Let’s look at an example.

In the year 2000, the United States had a population of about 280,000,000 people. By 2010, the population was about 308,000,000. What will the percent increase have been in those 10 years?

First, find the difference in the populations.

Next, use the percent increase formula to find the answer.

The answer is 10%.

The population increased 10% in 10 years.

### Examples

#### Example 1

Earlier, you were given a problem about the trip to Mars.

You want to find the number of miles a spacecraft has gone if it is 30% of the way to Mars, which at its nearest is about

First, change 30% into a decimal.

Next, multiply 0.30 by

The answer is

The spacecraft has traveled

#### Example 2

Find 32% of 0.00000054.

First, change 32% into a decimal. Remember that percent means that the denominator is 100.

Next, multiply 0.32 by 0.00000054

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent

The answer is

#### Example 3

Find 30% of .000567

First, change 30% into a decimal. Remember that percent means that the denominator is 100.

Next, multiply 0.30 by 0.000567

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent

The answer is

#### Example 4

Find 10% of 123,000,000

First, change 10% into a decimal.

Next, multiply 0.10 by 123,000,000

Then, change to scientific notation. Notice that the number is larger than 1 so the exponent

The answer is

#### Example 5

Find 25% of 0.0000987.

First, change 25% into a decimal.

Next, multiply 0.25 by 0.0000987

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent

The answer is

### Review

Round the ‘

1. Find 62% of

2. Find 5% of

3. Find 180% of

4. Find 12% of

5. Find 22% of \begin{align*}56.4 \times 10^{-2}\end{align*}.

6. Find 14% of \begin{align*}56.4 \times 10^{-2}\end{align*}.

7. Find 30% of \begin{align*}.999 \times 10^{12}\end{align*}.

Answer each question and leave your answers in standard form.

8. What percent of 8,570,000 is 152?

9. Find 230% of .00000488.

10. The number .00036 is 45% of what number?

11. Find 23% of 98.78.

12. Find 150% of .0000866.

13. Find 210% of .002368.

14. Find 30% of .000009.

15. A light year is about 5,880,000,000,000 miles. In one month, it travels about 8.2% of that distance. About how far does it travel in one month?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 5.16.

### Resources

Percent of Change

The percent of change is the percent that a value has increased or decreased by.Standard Notation

As opposed to scientific notation, standard notation means writing numbers in the usual way with all of the zeros accounted for in the value.Statistics

Statistics is a branch of mathematics that involves collecting, analyzing and displaying data.### Image Attributions

In this concept, you will learn to solve percent problems involving scientific notation.

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