# 1.7 Percent

 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, $\begin{array}{rrrrr}\hfill 1%=\frac{1}{100}& \hfill & \hfill \text{or}& \hfill & \hfill 1%=0.01.\end{array}$

## 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).

$\begin{array}{rrrrr}\hfill \frac{3}{5}& \hfill =& \frac{3}{5}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{100}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fraction\hspace{0.17em}by\hspace{0.17em}1}.\hfill \\ \hfill & \hfill =& \frac{3}{5}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Since \hspace{0.17em}}\frac{100}{100}=100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}.\hfill \\ \hfill & \hfill =& \frac{300}{5}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Divide\hspace{0.17em}}300\text{\hspace{0.17em}by\hspace{0.17em}5}.\hfill \\ \hfill & \hfill =& 60\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fractions}.\hfill \\ \hfill & \hfill =& 60%\hfill & \hfill & \text{Replace\hspace{0.17em}}\frac{1}{100}\text{\hspace{0.17em}}\text{with\hspace{0.17em}the\hspace{0.17em}}%\text{\hspace{0.17em}symbol}.\hfill \end{array}$

## Fraction to percent

To convert a fraction to a percent, multiply the fraction by 1 in the form $100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}$ , then replace $\frac{1}{100}$ with the % symbol.

## Sample set a

Convert each fraction to a percent.

$\begin{array}{lll}\frac{1}{4}\hfill & =\hfill & \frac{1}{4}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{100}{4}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 25\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 25%\hfill \end{array}$

$\begin{array}{lll}\frac{8}{5}\hfill & =\hfill & \frac{8}{5}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{800}{5}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 160%\hfill \end{array}$

$\begin{array}{lll}\frac{4}{9}\hfill & =\hfill & \frac{4}{9}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{400}{9}\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \left(44.4...\right)\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \left(44.\overline{4}\right)\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 44.\overline{4}%\hfill \end{array}$

## 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 $\frac{1}{100}.$

$\begin{array}{lllll}0.75\hfill & =\hfill & 0.75\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}decimal\hspace{0.17em}by\hspace{0.17em}1}\text{.}\hfill \\ \hfill & =\hfill & 75\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \hfill \\ \hfill & =\hfill & 75%\hfill & \hfill & \text{Replace\hspace{0.17em}}\frac{1}{100}\text{\hspace{0.17em}with\hspace{0.17em}the\hspace{0.17em}%\hspace{0.17em}symbol}.\hfill \end{array}$

## Decimal to percent

To convert a fraction to a percent, multiply the decimal by 1 in the form $100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}$ , 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.

$\begin{array}{lll}0.62\hfill & =\hfill & 0.62\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 62\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 62%\hfill \end{array}$

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

$\begin{array}{lll}8.4\hfill & =\hfill & 8.4\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 840\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 840%\hfill \end{array}$

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

$\begin{array}{lll}0.47623\hfill & =\hfill & 0.47623\text{\hspace{0.17em}}·\text{\hspace{0.17em}}100\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 0.47623\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 47.623%\hfill \end{array}$

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 $\frac{1}{100}.$

$\begin{array}{lllll}12%\hfill & =\hfill & 12\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Replace}\text{\hspace{0.17em}}%\text{\hspace{0.17em}}\text{with}\text{\hspace{0.17em}}\frac{1}{100}.\hfill \\ \hfill & =\hfill & \frac{12}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fractions}.\hfill \\ \hfill & =\hfill & 0.12\hfill & \hfill & \text{Divide\hspace{0.17em}12\hspace{0.17em}by\hspace{0.17em}1}00.\hfill \end{array}$

## 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.

$\begin{array}{lll}48%\hfill & =\hfill & 48\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{48}{100}\hfill \\ \hfill & =\hfill & 0.48\hfill \end{array}$

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

$\begin{array}{lll}659%\hfill & =\hfill & 659\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{659}{100}\hfill \\ \hfill & =\hfill & 6.59\hfill \end{array}$

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

$\begin{array}{lll}0.4113%\hfill & =\hfill & 0.4113\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{0.4113}{100}\hfill \\ \hfill & =\hfill & 0.004113\hfill \end{array}$

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.

$\frac{2}{5}$

$40%$

$\frac{7}{8}$

$\frac{1}{8}$

$12.5%$

$\frac{5}{16}$

$15÷22$

$68.18%$

$\frac{2}{11}$

$\frac{2}{9}$

$22.22%$

$\frac{16}{45}$

$\frac{27}{55}$

$49.09%$

$\frac{7}{27}$

15

$1500%$

8

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

$0.36$

$36%$

$0.42$

$0.446$

$44.6%$

$0.1298$

$4.25$

$425%$

$5.875$

$86.98$

$8698%$

$21.26$

14

$1400%$

12

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

$35%$

$0.35$

$76%$

$18.6%$

$0.186$

$67.2%$

$9.0145%$

$0.090145$

$3.00156%$

$0.00005%$

$0.0000005$

$0.00034%$

#### Questions & Answers

the art of managing the production, distribution and consumption.
what is economics
what is Open Market Operation
dominating middlemen men activities circumstances
what Equilibrium price
what is gap
mirwais
who is good with the indifference curve
Dexter
What is diseconomic
what are the types of goods
WARIDI
how can price determination be the central problem of micro economics
marginal cost formula
you should differentiate the total cost function in order to get marginal cost function then you can get marginal cost from it
boniphace
What about total cost
Foday
ok
Foday
how can price determination be the central problem if micro economics
simon
formula of cross elasticity of demand
what is ceteris paribus
what is ceteris parabus
Priyanka
Ceteris paribus - Literally, "other things being equal"; usually used in economics to indicate that all variables except the ones specified are assumed not to change.
Abdullah
What is broker
scor
land is natural resources that is made by nature
scor
What is broker
scor
what is land
kafui
What is broker
scor
land is natural resources that is made by nature
scor
whats poppina nigga turn it up for a minute get it
what is this?
Philo
am from nigeria@ pilo
Frank
am from nigeria@ pilo
Frank
so
owusu
what is production possibility frontier
owusu
it's a summary of opportunity cost depicted on a curve.
okhiria
please help me solve this question with the aid of appropriate diagrams explain how each of the following changes will affect the market price and quantity of bread 1. A
please l need past question about economics
ok let me know some of the questions please.
Effah
ok am not wit some if den nw buh by tommorow I shall get Dem
Hi guys can I get Adam Smith's WEALTH OF NATIONS fo sale?
Ukpen
hello I'm Babaisa alhaji Mustapha. I'm studying Economics in the university of Maiduguri
Babaisa
okay
Humaira
my name is faisal Yahaya. i studied economics at Kaduna state university before proceeding to West African union university benin republic for masters
Faisal
Hi guys..I am from Bangladesh..
Mannan
Wat d meaning of management
disaster management cycle
cooperate social responsibility
igwe
Fedric Wilson Taylor also define management as the act of knowing what to do and seeing that it is done in the best and cheapest way
OLANIYI
Difference between extinct and extici spicies
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.