<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

5.16: Solve Percent Problems Involving Scientific Notation

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Estimated13 minsto complete
%
Progress
Practice Operations with Numbers in Scientific Notation
Practice
Progress
Estimated13 minsto complete
%
Practice Now

On certain dates, Mars is about 4.9×107 miles from Earth. If a spacecraft is headed toward Mars and has traveled 30% of the distance, how many miles has it gone?

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: a×10b

where ‘a’ is any number between 1 and 10, and ‘b’ is the exponent of 10.

When you conduct operations involving percent with numbers in scientific notation, you can use any operation with the ‘a’ value as you have seen in these sections. Then you will be sure to write your answer in scientific notation. You may need to adjust the ‘a’ and ‘b’ values.

Let’s look at an example.

Find 25% of 3×1012.

First, multiply the 25% by 3.

0.25×(3×1012)==(0.25×3)×10120.75×1012

Next, since the ‘a’ value is not between 1 and 10, you must move the decimal place over one place. In other words, 0.75 must change to 7.5. Since you are moving the decimal one place to the right, your exponent b will go down by 1.

0.75×1012=7.5×1011

The answer is 7.5×1011.

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.

308,000,000280,000,000=28,000,000

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

percent of increasepercent of increasepercent of increasepercent of increase====amount of increaseoriginal amount×10028,000,000280,000,000×1000.10×10010%

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 4.9×107 miles from Earth.

First, change 30% into a decimal.

30%==301000.30

Next, multiply 0.30 by 4.9×107

0.30×(4.9×107)==(0.30×4.9)×1071.47×107

The answer is 1.47×107.

The spacecraft has traveled 1.47×107 miles towards Mars if it is 30% of the way.

Example 2

Find 32% of 0.00000054.

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

32%==321000.32

Next, multiply 0.32 by 0.00000054

0.32×0.00000054=0.0000001728

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent (b) will be negative. Move the decimal place until it is after the 1. This means you are moving the decimal 7 places to the right; your exponent (b) is -7.

0.0000001728=1.728×107

The answer is 1.728×107.

Example 3

Find 30% of .000567

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

30%==301000.30

Next, multiply 0.30 by 0.000567

0.30×0.000567=0.0001701

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent (b) will be negative. Move the decimal place until it is after the 1. This means you are moving the decimal 4 places to the right; your exponent (b) is -4.

0.0001701=1.701×104

The answer is 1.701×104.

Example 4

Find 10% of 123,000,000

First, change 10% into a decimal.

10%==101000.10

Next, multiply 0.10 by 123,000,000

0.10×123,000,000=12,300,000

Then, change to scientific notation. Notice that the number is larger than 1 so the exponent (b) will be positive. Move the decimal place until it is after the 1. This means you are moving the decimal 7 places to the left; your exponent (b) is 7.

12,300,000=1.23×107

The answer is 1.23×107.

Example 5

Find 25% of 0.0000987.

First, change 25% into a decimal.

25%==251000.25

Next, multiply 0.25 by 0.0000987

0.25×0.0000987=0.000024675

Then, change to scientific notation. Notice that the number is smaller than 1 so the exponent (b) will be negative. Move the decimal place until it is after the 1. This means you are moving the decimal 5 places to the right; your exponent (b) is -5.

0.000024675=2.4675×105

The answer is 2.47×105.

Review

Round the ‘a’ values to the nearest hundredth and place your answers in scientific notation.

1. Find 62% of 3.5×109.

2. Find 5% of 9.1×1013.

3. Find 180% of 6.3×1017.

4. Find 12% of .18×103.

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?

Answers for Review Problems

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

Resources

Vocabulary

Percent of Change

Percent of Change

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

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

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

Image Attributions

Show Hide Details
Description
Difficulty Level:
At Grade
Grades:
Date Created:
Jan 23, 2013
Last Modified:
Mar 28, 2016
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the Modality. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.934.3.L.2

Original text