1.7 Percent

Basic mathematics review Page 1 / 1

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.

Overview

The Meaning of Percent
Converting A Fraction To A Percent
Converting A Decimal To A Percent
Converting A Percent To A Decimal

The meaning of percent

The word percent comes from the Latin word “per centum,” “per” meaning “for each,” and “centum” meaning “hundred.”

Percent (%)

Percent means “for each hundred” or “for every hundred.” The symbol % is used to represent the word percent.

Thus, $\begin{array}{r} 1 % = \frac{1}{100} & or & 1 % = 0.01. \end{array}$

Converting a fraction to a percent

We can see how a fraction can be converted to a percent by analyzing the method that $\frac{3}{5}$ is converted to a percent. In order to convert $\frac{3}{5}$ to a percent, we need to introduce $\frac{1}{100}$ (since percent means for each hundred).

$\begin{array}{r} \frac{3}{5} & = & \frac{3}{5} \cdot \frac{100}{100} & Multiply the fraction by 1 . \\ = & \frac{3}{5} \cdot 100 \cdot \frac{1}{100} & Since \frac{100}{100} = 100 \cdot \frac{1}{100} . \\ = & \frac{300}{5} \cdot \frac{1}{100} & Divide 300 by 5 . \\ = & 60 \cdot \frac{1}{100} & Multiply the fractions . \\ = & 60 % & Replace \frac{1}{100} with the % symbol . \end{array}$

Fraction to percent

To convert a fraction to a percent, multiply the fraction by 1 in the form

100 \cdot \frac{1}{100}

, then replace

\frac{1}{100}

with the % symbol.

Sample set a

Convert each fraction to a percent.

$\begin{array}{l} \frac{1}{4} & = & \frac{1}{4} \cdot 100 \cdot \frac{1}{100} \\ = & \frac{100}{4} \cdot \frac{1}{100} \\ = & 25 \cdot \frac{1}{100} \\ = & 25 % \end{array}$

$\begin{array}{l} \frac{8}{5} & = & \frac{8}{5} \cdot 100 \cdot \frac{1}{100} \\ = & \frac{800}{5} \cdot \frac{1}{100} \\ = & 160 % \end{array}$

$\begin{array}{l} \frac{4}{9} & = & \frac{4}{9} \cdot 100 \cdot \frac{1}{100} \\ = & \frac{400}{9} \cdot \frac{1}{100} \\ = & (44.4...) \cdot \frac{1}{100} \\ = & (44. \bar{4}) \cdot \frac{1}{100} \\ = & 44. \bar{4} % \end{array}$

Converting a decimal to a percent

We can see how a decimal is converted to a percent by analyzing the method that $0.75$ is converted to a percent. We need to introduce $\frac{1}{100} .$

$\begin{array}{l} 0.75 & = & 0.75 \cdot 100 \cdot \frac{1}{100} & Multiply the decimal by 1 . \\ = & 75 \cdot \frac{1}{100} \\ = & 75 % & Replace \frac{1}{100} with the % symbol . \end{array}$

Decimal to percent

To convert a fraction to a percent, multiply the decimal by 1 in the form

100 \cdot \frac{1}{100}

, then replace

\frac{1}{100}

with the % symbol. This amounts to moving the decimal point 2 places to the right.

Sample set b

Convert each decimal to a percent.

$\begin{array}{l} 0.62 & = & 0.62 \cdot 100 \cdot \frac{1}{100} \\ = & 62 \cdot \frac{1}{100} \\ = & 62 % \end{array}$

Notice that the decimal point in the original number has been moved to the right 2 places.

$\begin{array}{l} 8.4 & = & 8.4 \cdot 100 \cdot \frac{1}{100} \\ = & 840 \cdot \frac{1}{100} \\ = & 840 % \end{array}$

Notice that the decimal point in the original number has been moved to the right 2 places.

$\begin{array}{l} 0.47623 & = & 0.47623 \cdot 100 \cdot \frac{1}{100} \\ = & 0.47623 \cdot \frac{1}{100} \\ = & 47.623 % \end{array}$

Notice that the decimal point in the original number has been moved to the right 2 places.

Converting a percent to a decimal

We can see how a percent is converted to a decimal by analyzing the method that 12% is converted to a decimal. We need to introduce $\frac{1}{100} .$

$\begin{array}{l} 12 % & = & 12 \cdot \frac{1}{100} & Replace % with \frac{1}{100} . \\ = & \frac{12}{100} & Multiply the fractions . \\ = & 0.12 & Divide 12 by 1 00. \end{array}$

Percent to decimal

To convert a percent to a decimal, replace the % symbol with

\frac{1}{100},

then divide the number by 100. This amounts to moving the decimal point 2 places to the left.

Sample set c

Convert each percent to a decimal.

$\begin{array}{l} 48 % & = & 48 \cdot \frac{1}{100} \\ = & \frac{48}{100} \\ = & 0.48 \end{array}$

Notice that the decimal point in the original number has been moved to the left 2 places.

$\begin{array}{l} 659 % & = & 659 \cdot \frac{1}{100} \\ = & \frac{659}{100} \\ = & 6.59 \end{array}$

Notice that the decimal point in the original number has been moved to the left 2 places.

$\begin{array}{l} 0.4113 % & = & 0.4113 \cdot \frac{1}{100} \\ = & \frac{0.4113}{100} \\ = & 0.004113 \end{array}$

Notice that the decimal point in the original number has been moved to the left 2 places.

Exercises

For the following problems, convert each fraction to a percent.

$\frac{2}{5}$

$40 %$

$\frac{7}{8}$

$\frac{1}{8}$

$12.5 %$

$\frac{5}{16}$

$15 \div 22$

$68.18 %$

$\frac{2}{11}$

$\frac{2}{9}$

$22.22 %$

$\frac{16}{45}$

$\frac{27}{55}$

$49.09 %$

$\frac{7}{27}$

$1500 %$

For the following problems, convert each decimal to a percent.

$0.36$

$36 %$

$0.42$

$0.446$

$44.6 %$

$0.1298$

$4.25$

$425 %$

$5.875$

$86.98$

$8698 %$

$21.26$

$1400 %$

For the following problems, convert each percent to a decimal.

$35 %$

$0.35$

$76 %$

$18.6 %$

$0.186$

$67.2 %$

$9.0145 %$

$0.090145$

$3.00156 %$

$0.00005 %$

$0.0000005$

$0.00034 %$

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Basic mathematics review. OpenStax CNX. Jun 06, 2012 Download for free at http://cnx.org/content/col11427/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Basic mathematics review' conversation and receive update notifications?

Ask

	Anthropology Biology Culture By Richley Crapo Start Assignment
	6 AP 06 Skeletal System Essay By OpenStax Start Flashcards
	Power Enigeering types of bearing lubrication By Sam Luong Start Quiz
©flickr: Abraham	Biology Exam 3 By Vanessa Soledad Start Exam
©flickr: Miguel	Gram Positive Infections and Clostridium By Cath Yu Start Quiz
	1 AP 01 Human Body Anatomy Physiology MCQ By OpenStax Start Quiz
	NCE Ch 08 Appraisal By Anh Dao Start Quiz
	12 Neuroanatomy 12 The Basal Ganglia By Stephen Voron Start Quiz
	Computer Skills Literacy MCQ By LaToya Trowers Start Quiz
	Society and Culture By Mahee Boo Start Flashcards