# 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.

$35%$

$0.35$

$76%$

$18.6%$

$0.186$

$67.2%$

$9.0145%$

$0.090145$

$3.00156%$

$0.00005%$

$0.0000005$

$0.00034%$

What is scarcity.
why our wants are limited
nooo want is unlimited but resources are limited
Ruchi
and do to that there occurs scarcity and we have to make choice in order to have what we need if need be I will explain more
our wants are not limited but rather the resources
Moses
as we know that there are two principle of microeconomics scarcity of resources and they have alternative uses...
Ruchi
yes .....
Mathias
what is demand
demand is something wt we called in economic theory of demand it simply means if price of product is increase then demand of product will decrease
Ruchi
inverse relationship between demand and price
Ruchi
in microeconomic
Ruchi
demand is what and how much you want and what's your need...
Shikhar
how can one be so with economics even while you have less knowledge in mathematics.
why is it that some products increases everyday by day
because demand is increase
Ruchi
because demand is increase
Patience
but how demand increases?
Aziz
Because of the Marketing and purchasing power of people.
AmarbirSingh
but how could we know that people's demands have increased everyday by day and how could we know that this is time to produced the products in the market. Is any connection among them
yaqoob
for normal good people demand remain the same if price of product will increase or not
Ruchi
see that some product which increases day by day is comes under normal good which is used by consumer
Ruchi
Seems hot discussing going here
Shamamet
If there are less products demand starts to increase for those products
Shamamet
Economics is really interesting to learn ....
Shamamet
see there is Inferior goods ands normal goods inferior good demand is rarely increase whereas as we talk about normal good demand will absolutely Increase whether price is increase or not
Ruchi
and demand for normal goods increase cause people's income as a while increases time to time
Abhisek
and it might also be that the cost of raw materials are high.
ATTAH
may be
Ruchi
obviously because demand is increasing.....and price is getting low.....
Shikhar
hmmm there is inverse relationship between demand and price
Ruchi
Importance of economics
the nature and significance of economics studies
Deborah
What is demand
deman is amount of goods and services a consumer is willing and able to buy or purchase at a given price.
Sainabou
the willingness and ability of a body to purchase goods nd servicesbis called demand ,so if she/has ability but doesn't have willingness it's not a demand same if she or he has willingness but doesn't has ability it's not a demand too
Gul
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time and demand can also be defined as the desire or willingness and backed by the ability to pay.
Yeah
Mathias
What is Choice
Kofi
Choice refers to the ability of a consumer or producer to decide which good, service or resource to purchase or provide from a range of possible options. Being free to chose is regarded as a fundamental indicator of economic well being and development.
Shonal
choice is a act of selecting or choosing from the numerous or plenty wants.
how does consumer make profit
Compare and contract the function of commercial bank and the central bank of Nigeria
what do think is the difference between overhead costs and prime cost
Abdoulkarim
what is economics
economics is a social science that study's how resources can be used to produce goods and services for society
Nathan
Economic is a science which studies human behavior as a relationship between ends and scares means which have alternatives uses or purposes.
what is economics
what is the basic economic problem
rules
unlimited wants vs limited resources
Nathan
what is a new paradigm shift
Paradigm shift it is the reconcilliation of fedural goods in production
Shyline
fedural? what is that?
Aziz
factors that affecting economic system
crux
Shyline
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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.