maths.free › Arithmetic › 6. Percents › Understand Percent

Understand Percent

Use the definition of percent

Use the Definition of Percent

How many cents are in one dollar? There are \(100\) cents in a dollar. How many years are in a century? There are \(100\) years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent is a ratio whose denominator is \(100.\) We use the percent symbol \(\text{\%,}\) to show percent.

According to data from the American Association of Community Colleges \((2015)\text{,}\) about \(\text{57\%}\) of community college students are female. This means \(57\) out of every \(100\) community college students are female, as shows. Out of the \(100\) squares on the grid, \(57\) are shaded, which we write as the ratio \(\frac{57}{100}.\)

Similarly, \(\text{25\%}\) means a ratio of \(\frac{25}{100},\text{3\%}\) means a ratio of \(\frac{3}{100}\) and \(\text{100\%}\) means a ratio of \(\frac{100}{100}.\) In words, "one hundred percent" means the total \(\text{100\%}\) is \(\frac{100}{100},\) and since \(\frac{100}{100}=1,\) we see that \(\text{100\%}\) means \(1\) whole.

Example

Try it.

According to the Public Policy Institute of California \((2010)\text{,}\ \text{44\%}\) of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.

Solution

The amount we want to convert is 44%.	\(44\%\)
Write the percent as a ratio. Remember that percent means per 100.	\(\frac{44}{100}\)

Example

Try it.

In \(2007,\) according to a U.S. Department of Education report, \(21\) out of every \(100\) first-time freshmen college students at \(\text{4-year}\) public institutions took at least one remedial course. Write this as a ratio and then as a percent.

Solution

The amount we want to convert is \(21\) out of \(100\).	\(21\) out of \(100\)
Write as a ratio.	\(\frac{21}{100}\)
Convert the 21 per 100 to percent.	\(21\%\)

Convert Percents to Fractions and Decimals

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per \(100,\) so the denominator of the fraction is \(100.\)

Example

Try it.

Convert each percent to a fraction:

ⓐ \(\ \text{36\%}\ \\)
ⓑ \(\ \text{125\%}\)

Solution

ⓐ
	\(36\%\)
Write as a ratio with denominator 100.	\(\frac{36}{100}\)
Simplify.	\(\frac{9}{25}\)

ⓑ
	\(125\%\)
Write as a ratio with denominator 100.	\(\frac{125}{100}\)
Simplify.	\(\frac{5}{4}\)

The previous example shows that a percent can be greater than \(1.\) We saw that \(\text{125\%}\) means \(\frac{125}{100},\) or \(\frac{5}{4}.\) These are improper fractions, and their values are greater than one.

Example

Try it.

Convert each percent to a fraction:

ⓐ \(\ \text{24.5\%}\ \\)
ⓑ \(\ 33\frac{1}{3}\%\)

Solution

ⓐ
	\(24.5\%\)
Write as a ratio with denominator 100.	\(\frac{24.5}{100}\)
Clear the decimal by multiplying numerator and denominator by 10.	\(\frac{24.5(10)}{100(10)}\)
Multiply.	\(\frac{245}{1000}\)
Rewrite showing common factors.	\(\frac{5\cdot 49}{5\cdot 200}\)
Simplify.	\(\frac{49}{200}\)

ⓑ
	\(33\frac{1}{3}\%\)
Write as a ratio with denominator 100.	\(\frac{33\frac{1}{3}}{100}\)
Write the numerator as an improper fraction.	\(\frac{\ \ \frac{100}{3}\ \ }{100}\)
Rewrite as fraction division, replacing 100 with \(\frac{100}{1}\).	\(\frac{100}{3}\div \frac{100}{1}\)
Multiply by the reciprocal.	\(\frac{100}{3}⋅\frac{1}{100}\)
Simplify.	\(\frac{1}{3}\)

In Decimals, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.

Do you see the pattern?

Condensed — the full section is in OpenStax Prealgebra 2e.

Convert Decimals and Fractions to Percents

To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is \(100,\) it is easy to change that fraction to a percent.

Example

Try it.

Convert each decimal to a percent: ⓐ \(\ 0.05\\) ⓑ \(\ 0.83\)

Solution

ⓐ
	\(0.05\)
Write as a fraction. The denominator is 100.	\(\frac{5}{100}\)
Write this ratio as a percent.	\(5\%\)

ⓑ
	\(0.83\)
The denominator is 100.	\(\frac{83}{100}\)
Write this ratio as a percent.	\(83\%\)

To convert a mixed number to a percent, we first write it as an improper fraction.

Example

Try it.

Convert each decimal to a percent: ⓐ \(\ 1.05\\) ⓑ \(\ 0.075\)

Solution

ⓐ
	\(1.05\)
Write as a fraction.	\(1\frac{5}{100}\)
Write as an improper fraction. The denominator is 100.	\(\frac{105}{100}\)
Write this ratio as a percent.	\(105\%\)

Notice that since \(1.05>1,\) the result is more than \(\text{100\%.}\)

ⓑ
	\(0.075\)
Write as a fraction. The denominator is 1,000.	\(\frac{75}{1,000}\)
Divide the numerator and denominator by 10, so that the denominator is 100.	\(\frac{7.5}{100}\)
Write this ratio as a percent.	\(7.5\%\)

Let's summarize the results from the previous examples in so we can look for a pattern.

Decimal	Percent
\(0.05\)	\(\text{5\%}\)
\(0.83\)	\(\text{83\%}\)
\(1.05\)	\(\text{105\%}\)
\(0.075\)	\(\text{7.5\%}\)

Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.

uses the decimal numbers in and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the \(\%\) sign.

In Decimals, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.

Condensed — the full section is in OpenStax Prealgebra 2e.

Key Concepts

Convert a percent to a fraction.
1. Write the percent as a ratio with the denominator 100.
2. Simplify the fraction if possible.
Convert a percent to a decimal.
1. Write the percent as a ratio with the denominator 100.
2. Convert the fraction to a decimal by dividing the numerator by the denominator.
Convert a decimal to a percent.
1. Write the decimal as a fraction.
2. If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
3. Write this ratio as a percent.
Convert a fraction to a percent.
1. Convert the fraction to a decimal.
2. Convert the decimal to a percent.

Understand Percent

Use the Definition of Percents

In the following exercises, write each percent as a ratio.

Try it.

In \(2014,\) the unemployment rate for those with only a high school degree was \(\text{6.0\%}.\)

Solution

\(\frac{6}{100}\)

Try it.

In \(2015,\) among the unemployed, \(\text{29\%}\) were long-term unemployed.

Try it.

The unemployment rate for those with Bachelor's degrees was \(\text{3.2\%}\) in \(2014.\)

Solution

\(\frac{32}{1000}\)

Try it.

The unemployment rate in Michigan in \(2014\) was \(\text{7.3\%}.\)

In the following exercises, write as

ⓐ a ratio and
ⓑ a percent

Try it.

\(57\) out of \(100\) nursing candidates received their degree at a community college.

Solution

ⓐ \(\ \frac{57}{100}\\)
ⓑ \(\ \text{57\%}\)

Try it.

\(80\) out of \(100\) firefighters and law enforcement officers were educated at a community college.

Try it.

\(42\) out of \(100\) first-time freshmen students attend a community college.

Solution

ⓐ \(\ \frac{42}{100}\\)
ⓑ \(\ \text{42\%}\)

Try it.

\(71\) out of \(100\) full-time community college faculty have a master's degree.

Convert Percents to Fractions and Decimals

In the following exercises, convert each percent to a fraction and simplify all fractions.

Try it.

\(\text{4\%}\)

Solution

\(\frac{1}{25}\)

Try it.

\(\text{8\%}\)

Try it.

\(\text{17\%}\)

Solution

\(\frac{17}{100}\)

Try it.

\(\text{19\%}\)

Try it.

\(\text{52\%}\)

Solution

\(\frac{13}{25}\)

Try it.

\(\text{78\%}\)

Try it.

\(\text{125\%}\)

Solution

\(\frac{5}{4}\)

Try it.

\(\text{135\%}\)

Try it.

\(\text{37.5\%}\)

Solution

\(\frac{3}{8}\)

Try it.

\(\text{42.5\%}\)

Try it.

\(\text{18.4\%}\)

Solution

\(\frac{23}{125}\)

Try it.

\(\text{46.4\%}\)

Try it.

\(9\frac{1}{2}\%\)

Solution

\(\frac{19}{200}\)

Try it.

\(8\frac{1}{2}\%\)

Try it.

\(5\frac{1}{3}\%\)

Solution

\(\frac{4}{75}\)

Try it.

\(6\frac{2}{3}\%\)

In the following exercises, convert each percent to a decimal.

Try it.

\(\text{5\%}\)

Solution

0.05

Try it.

\(\text{9\%}\)

Try it.

\(\text{1\%}\)

Solution

0.01

Try it.

\(\text{2\%}\)

Try it.

\(\text{63\%}\)

Solution

0.63

Try it.

\(\text{71\%}\)

Try it.

\(\text{40\%}\)

Solution

0.4

Try it.

\(\text{50\%}\)

Try it.

\(\text{115\%}\)

Solution

1.15

Try it.

\(\text{125\%}\)

Try it.

\(\text{150\%}\)

Solution

1.5

Try it.

\(\text{250\%}\)

Try it.

\(\text{21.4\%}\)

Solution

0.214

Try it.

\(\text{39.3\%}\)

Try it.

\(\text{7.8\%}\)

Solution

0.078

Try it.

\(\text{6.4\%}\)

In the following exercises, convert each percent to

ⓐ a simplified fraction and
ⓑ a decimal

Try it.

In \(2010,\text{1.5\%}\) of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011)

Solution

ⓐ \(\ \frac{3}{200}\\)
ⓑ \(\ 0.015\)

Try it.

In \(2000,\text{4.2\%}\) of the United States population was of Asian descent. (Source: www.census.gov)

Try it.

According to government data, in \(2013\) the number of cell phones in India was \(\text{70.23\%}\) of the population.

Solution

ⓐ \(\ \frac{7023}{10,000}\\)
ⓑ \(\ 0.7023\)

Try it.

According to the U.S. Census Bureau, among Americans age \(25\) or older who had doctorate degrees in \(2014,\text{37.1\%}\) are women.

Try it.

A couple plans to have two children. The probability they will have two girls is \(\text{25\%}.\)

Solution

ⓐ \(\ \frac{1}{4}\\)
ⓑ \(\ 0.25\)

Try it.

Javier will choose one digit at random from \(0\) through \(9.\) The probability he will choose \(3\) is \(\text{10\%}.\)

Try it.

According to the local weather report, the probability of thunderstorms in New York City on July \(15\) is \(\text{60\%}.\)

Solution

ⓐ \(\ \frac{3}{5}\\)
ⓑ \(\ 0.6\)

Try it.

A club sells \(50\) tickets to a raffle. Osbaldo bought one ticket. The probability he will win the raffle is \(\text{2\%}.\)

Convert Decimals and Fractions to Percents

In the following exercises, convert each decimal to a percent.

Try it.

\(0.01\)

Solution

Try it.

\(0.03\)

Try it.

\(0.18\)

Solution

18%

Try it.

\(0.15\)

Try it.

\(1.35\)

Solution

135%

Try it.

\(1.56\)

Try it.

\(3\)

Solution

300%

Try it.

\(4\)

Try it.

\(0.009\)

Solution

0.9%

Try it.

\(0.008\)

Try it.

\(0.0875\)

Solution

8.75%

Try it.

\(0.0625\)

Try it.

\(1.5\)

Solution

150%

Try it.

\(2.2\)

Try it.

\(2.254\)

Solution

225.4%

Try it.

\(2.317\)

In the following exercises, convert each fraction to a percent.

Try it.

\(\frac{1}{4}\)

Solution

25%

Try it.

\(\frac{1}{5}\)

Try it.

\(\frac{3}{8}\)

Solution

37.5%

Try it.

\(\frac{5}{8}\)

Try it.

\(\frac{7}{4}\)

Solution

175%

Try it.

\(\frac{9}{8}\)

Try it.

\(6\frac{4}{5}\)

Solution

680%

Try it.

\(5\frac{1}{4}\)

Try it.

\(\frac{5}{12}\)

Solution

\(41\frac{2}{3}\text{\%}\ or\ 41.\overset{-}{6}\text{\%}\)

Try it.

\(\frac{11}{12}\)

Try it.

\(2\frac{2}{3}\)

Solution

\(266.\overset{-}{6}\text{\%}\)

Try it.

\(1\frac{2}{3}\)

Try it.

\(\frac{3}{7}\)

Solution

42.9%

Try it.

\(\frac{6}{7}\)

Try it.

\(\frac{5}{9}\)

Solution

\(55.\overset{-}{5}\text{\%}\)

Try it.

\(\frac{4}{9}\)

In the following exercises, convert each fraction to a percent.

Try it.

\(\frac{1}{4}\) of washing machines needed repair.

Solution

25%

Try it.

\(\frac{1}{5}\) of dishwashers needed repair.

In the following exercises, convert each fraction to a percent.

Try it.

According to the National Center for Health Statistics, in \(2012,\frac{7}{20}\) of American adults were obese.

Solution

35%

Try it.

The U.S. Census Bureau estimated that in \(2013,\text{85\%}\) of Americans lived in the same house as they did \(1\) year before.

In the following exercises, complete the table.

Try it.

Fraction	Decimal	Percent
\(\frac{1}{2}\)
	\(0.45\)
		\(18\text{\%}\)
\(\frac{1}{3}\)
	\(0.008\)
\(2\)

Solution

Fraction	Decimal	Percent
\(\frac{1}{2}\)	\(0.5\)	\(50\text{\%}\)
\(\frac{9}{20}\)	\(0.45\)	\(45\text{\%}\)
\(\frac{9}{50}\)	\(0.18\)	\(18\text{\%}\)
\(\frac{1}{3}\)	\(0.3\)	\(33.3\text{\%}\)
\(\frac{1}{125}\)	\(0.008\)	\(0.8\text{\%}\)
\(2\)	\(2.0\)	\(200\text{\%}\)

Try it.

Fraction	Decimal	Percent
\(\frac{1}{4}\)
	\(0.65\)
		\(22\text{\%}\)
\(\frac{2}{3}\)
	\(0.004\)
\(3\)

Condensed — the full section is in OpenStax Prealgebra 2e.

Practice (40)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

Translate “the ratio of \(33\) to \(\text{5”}\) into an algebraic expression.
If you missed this problem, review .

كشفت الإجابة

\(\frac{33}{5}\)
Write \(\frac{3}{5}\) as a decimal.
If you missed this problem, review .

كشفت الإجابة

\(0.6\)
Write \(0.62\) as a fraction.
If you missed this problem, review .

كشفت الإجابة

\(\frac{31}{50}\)
According to the Public Policy Institute of California \((2010)\text{,}\ \text{44\%}\) of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.

كشفت الإجابة

The amount we want to convert is 44%. \(44\%\)
Write the percent as a ratio. Remember that percent means per 100. \(\frac{44}{100}\)
Write the percent as a ratio.
According to a survey, \(\text{89\%}\) of college students have a smartphone.

كشفت الإجابة

\(\frac{89}{100}\)
Write the percent as a ratio.
A study found that \(\text{72\%}\) of U.S. teens send text messages regularly.

كشفت الإجابة

\(\frac{72}{100}\)
In \(2007,\) according to a U.S. Department of Education report, \(21\) out of every \(100\) first-time freshmen college students at \(\text{4-year}\) public institutions took at least one remedial course. Write this as a ratio and then as a percent.

كشفت الإجابة

The amount we want to convert is \(21\) out of \(100\). \(21\) out of \(100\)
Write as a ratio. \(\frac{21}{100}\)
Convert the 21 per 100 to percent. \(21\%\)
Write as a ratio and then as a percent: The American Association of Community Colleges reported that \(62\) out of \(100\) full-time community college students balance their studies with full-time or part time employment.

كشفت الإجابة

\(\frac{62}{100},\text{62\%}\)
Write as a ratio and then as a percent: In response to a student survey, \(41\) out of \(100\) Santa Ana College students expressed a goal of earning an Associate's degree or transferring to a four-year college.

كشفت الإجابة

\(\frac{41}{100},\text{41\%}\)
Convert each percent to a fraction:
1. ⓐ \(\ \text{36\%}\ \\)
2. ⓑ \(\ \text{125\%}\)
كشفت الإجابة

ⓐ
\(36\%\)
Write as a ratio with denominator 100. \(\frac{36}{100}\)
Simplify. \(\frac{9}{25}\)
ⓑ
\(125\%\)
Write as a ratio with denominator 100. \(\frac{125}{100}\)
Simplify. \(\frac{5}{4}\)
Convert each percent to a fraction:
1. ⓐ \(\ \text{48\%}\\)
2. ⓑ \(\ \text{110\%}\)
كشفت الإجابة
1. ⓐ \(\ \frac{12}{25}\\)
2. ⓑ \(\ \frac{11}{10}\)
Convert each percent to a fraction:
1. ⓐ \(\ \text{64\%}\\)
2. ⓑ \(\ \text{150\%}\)
كشفت الإجابة
1. ⓐ \(\ \frac{16}{25}\\)
2. ⓑ \(\ \frac{3}{2}\)

Convert each percent to a fraction:

ⓐ \(\ \text{24.5\%}\ \\)
ⓑ \(\ 33\frac{1}{3}\%\)

كشفت الإجابة

ⓐ
	\(24.5\%\)
Write as a ratio with denominator 100.	\(\frac{24.5}{100}\)
Clear the decimal by multiplying numerator and denominator by 10.	\(\frac{24.5(10)}{100(10)}\)
Multiply.	\(\frac{245}{1000}\)
Rewrite showing common factors.	\(\frac{5\cdot 49}{5\cdot 200}\)
Simplify.	\(\frac{49}{200}\)

ⓑ
	\(33\frac{1}{3}\%\)
Write as a ratio with denominator 100.	\(\frac{33\frac{1}{3}}{100}\)
Write the numerator as an improper fraction.	\(\frac{\ \ \frac{100}{3}\ \ }{100}\)
Rewrite as fraction division, replacing 100 with \(\frac{100}{1}\).	\(\frac{100}{3}\div \frac{100}{1}\)
Multiply by the reciprocal.	\(\frac{100}{3}⋅\frac{1}{100}\)
Simplify.	\(\frac{1}{3}\)

Convert each percent to a fraction:
1. ⓐ \(\ \text{64.4\%}\\)
2. ⓑ \(\ 66\frac{2}{3}\%\)
كشفت الإجابة
1. ⓐ \(\ \frac{161}{250}\\)
2. ⓑ \(\ \frac{2}{3}\)
Convert each percent to a fraction:
1. ⓐ \(\ \text{42.5\%}\\)
2. ⓑ \(\ 8\frac{3}{4}\%\)
كشفت الإجابة
1. ⓐ \(\ \frac{17}{40}\\)
2. ⓑ \(\ \frac{7}{80}\)
Convert each percent to a decimal:
1. ⓐ \(\ \text{6\%}\\)
2. ⓑ \(\ \text{78\%}\)
كشفت الإجابة

Because we want to change to a decimal, we will leave the fractions with denominator \(100\) instead of removing common factors.
ⓐ
\(6\%\)
Write as a ratio with denominator 100. \(\frac{6}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(0.06\)
ⓑ
\(78\%\)
Write as a ratio with denominator 100. \(\frac{78}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(0.78\)
Convert each percent to a decimal:
1. ⓐ \(\ \text{9\%}\\)
2. ⓑ \(\ \text{87\%}\)
كشفت الإجابة
1. ⓐ 0.09
2. ⓑ 0.87
Convert each percent to a decimal:
1. ⓐ \(\ \text{3\%}\\)
2. ⓑ \(\ \text{91\%}\)
كشفت الإجابة
1. ⓐ 0.03
2. ⓑ 0.91
Convert each percent to a decimal:
1. ⓐ \(\ \text{135\%}\\)
2. ⓑ \(\ \text{12.5\%}\)
كشفت الإجابة

ⓐ
\(135\%\)
Write as a ratio with denominator 100. \(\frac{135}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(1.35\)
ⓑ
\(12.5\%\)
Write as a ratio with denominator 100. \(\frac{12.5}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(0.125\)
Convert each percent to a decimal:
1. ⓐ \(\ \text{115\%}\\)
2. ⓑ \(\ \text{23.5\%}\)
كشفت الإجابة
1. ⓐ 1.15
2. ⓑ 0.235
Convert each percent to a decimal:
1. ⓐ \(\ \text{123\%}\\)
2. ⓑ \(\ \text{16.8\%}\)
كشفت الإجابة
1. ⓐ 1.23
2. ⓑ 0.168
Among a group of business leaders, \(\text{77\%}\) believe that poor math and science education in the U.S. will lead to higher unemployment rates.
Convert the percent to: ⓐ a fraction ⓑ a decimal

كشفت الإجابة

ⓐ
\(77\%\)
Write as a ratio with denominator 100. \(\frac{77}{100}\)
ⓑ
\(\frac{77}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(0.77\)
Convert the percent to: ⓐ a fraction and ⓑ a decimal
Twitter's share of web traffic jumped \(\text{24\%}\) when one celebrity tweeted live on air.
كشفت الإجابة
1. ⓐ \(\ \frac{6}{25}\\)
2. ⓑ \(\ 0.24\)
Convert the percent to: ⓐ a fraction and ⓑ a decimal
The U.S. Census estimated that in \(2013,\text{44\%}\) of the population of Boston age \(25\) or older have a bachelor's or higher degrees.
كشفت الإجابة
1. ⓐ \(\ \frac{11}{25}\\)
2. ⓑ \(\ 0.44\)
There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is \(\text{25\%}.\) Convert the percent to:
1. ⓐ a fraction
2. ⓑ a decimal
كشفت الإجابة

ⓐ
\(25\%\)
Write as a ratio with denominator 100. \(\frac{25}{100}\)
Simplify. \(\frac{1}{4}\)
ⓑ \(\frac{1}{4}\)
Change the fraction to a decimal by dividing the numerator by the denominator. \(0.25\)
Convert the percent to: ⓐ a fraction, and ⓑ a decimal
The probability that it will rain Monday is \(\text{30\%}.\)
كشفت الإجابة
1. ⓐ \(\ \frac{3}{10}\\)
2. ⓑ \(\ 0.3\)
Convert the percent to: ⓐ a fraction, and ⓑ a decimal
The probability of getting heads three times when tossing a coin three times is \(\text{12.5\%}.\)
كشفت الإجابة
1. ⓐ \(\ \frac{1}{8}\\)
2. ⓑ \(\ 0.125\)
Convert each decimal to a percent: ⓐ \(\ 0.05\\) ⓑ \(\ 0.83\)

كشفت الإجابة

ⓐ
\(0.05\)
Write as a fraction. The denominator is 100. \(\frac{5}{100}\)
Write this ratio as a percent. \(5\%\)
ⓑ
\(0.83\)
The denominator is 100. \(\frac{83}{100}\)
Write this ratio as a percent. \(83\%\)
Convert each decimal to a percent: ⓐ \(\ 0.01\\) ⓑ \(\ 0.17.\)
كشفت الإجابة
1. ⓐ 1%
2. ⓑ 17%
Convert each decimal to a percent: ⓐ \(\ 0.04\\) ⓑ \(\ 0.41\)
كشفت الإجابة
1. ⓐ 4%
2. ⓑ 41%

Convert each decimal to a percent: ⓐ \(\ 1.05\\) ⓑ \(\ 0.075\)

كشفت الإجابة

ⓐ
	\(1.05\)
Write as a fraction.	\(1\frac{5}{100}\)
Write as an improper fraction. The denominator is 100.	\(\frac{105}{100}\)
Write this ratio as a percent.	\(105\%\)

Notice that since \(1.05>1,\) the result is more than \(\text{100\%.}\)

ⓑ
	\(0.075\)
Write as a fraction. The denominator is 1,000.	\(\frac{75}{1,000}\)
Divide the numerator and denominator by 10, so that the denominator is 100.	\(\frac{7.5}{100}\)
Write this ratio as a percent.	\(7.5\%\)

Convert each decimal to a percent: ⓐ \(\ 1.75\\) ⓑ \(\ 0.0825\)
كشفت الإجابة
1. ⓐ 175%
2. ⓑ 8.25%
Convert each decimal to a percent: ⓐ \(\ 2.25\\) ⓑ \(\ 0.0925\)
كشفت الإجابة
1. ⓐ 225%
2. ⓑ 9.25%
Convert each fraction or mixed number to a percent: ⓐ \(\ \frac{3}{4}\\) ⓑ \(\ \frac{11}{8}\\) ⓒ \(\ 2\frac{1}{5}\)

كشفت الإجابة

To convert a fraction to a decimal, divide the numerator by the denominator.
ⓐ
Change to a decimal. \(\frac{3}{4}\)
Write as a percent by moving the decimal two places.
\(75\%\)
ⓑ
Change to a decimal. \(\frac{11}{8}\)
Write as a percent by moving the decimal two places.
\(137.5\%\)
ⓒ
Write as an improper fraction. \(2\frac{1}{5}\)
Change to a decimal. \(\frac{11}{5}\)
Write as a percent.
\(220\%\)
Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.
Convert each fraction or mixed number to a percent: ⓐ \(\frac{5}{8}\\) ⓑ \(\frac{11}{4}\\) ⓒ \(3\frac{2}{5}\)
كشفت الإجابة
1. ⓐ 62.5%
2. ⓑ 275%
3. ⓒ 340%
Convert each fraction or mixed number to a percent: ⓐ \(\ \frac{7}{8}\\) ⓑ \(\ \frac{9}{4}\\) ⓒ \(\ 1\frac{3}{5}\)
كشفت الإجابة
1. ⓐ 87.5%
2. ⓑ 225%
3. ⓒ 160%
Convert \(\frac{5}{7}\) to a percent.

كشفت الإجابة

To change a fraction to a decimal, we divide the numerator by the denominator.
\(\frac{5}{7}\)
Change to a decimal—rounding to the nearest thousandth. \(0.714\)
Write as a percent. \(71.4\%\)
Convert the fraction to a percent: \(\frac{3}{7}\)

كشفت الإجابة

42.9%
Convert the fraction to a percent: \(\frac{4}{7}\)

كشفت الإجابة

57.1%
An article in a medical journal claimed that approximately \(\frac{1}{3}\) of American adults are obese. Convert the fraction \(\frac{1}{3}\) to a percent.

كشفت الإجابة

\(\frac{1}{3}\)
Change to a decimal.
Write as a repeating decimal. \(0.333\ldots\)
Write as a percent. \(33\frac{1}{3}\%\)
We could also write the percent as \(33.\overline{3}\%\).

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Understand Percent

Use the definition of percent
Convert percents to fractions and decimals
Convert decimals and fractions to percents
Write the percent as a ratio with the denominator
Simplify the fraction if possible.

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

جرّب نفسك

Parts of this page are adapted from OpenStax Prealgebra 2e (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

أكثر في Arithmetic

Order of operations Fractions Percentages Powers and roots

ⓐ
	\(6\%\)
Write as a ratio with denominator 100.	\(\frac{6}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(0.06\)

ⓑ
	\(78\%\)
Write as a ratio with denominator 100.	\(\frac{78}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(0.78\)

ⓐ
	\(135\%\)
Write as a ratio with denominator 100.	\(\frac{135}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(1.35\)

ⓑ
	\(12.5\%\)
Write as a ratio with denominator 100.	\(\frac{12.5}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(0.125\)

ⓐ
	\(77\%\)
Write as a ratio with denominator 100.	\(\frac{77}{100}\)

ⓑ
	\(\frac{77}{100}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(0.77\)

ⓐ
	\(25\%\)
Write as a ratio with denominator 100.	\(\frac{25}{100}\)
Simplify.	\(\frac{1}{4}\)

ⓑ	\(\frac{1}{4}\)
Change the fraction to a decimal by dividing the numerator by the denominator.	\(0.25\)

ⓐ
Change to a decimal.	\(\frac{3}{4}\)
Write as a percent by moving the decimal two places.
	\(75\%\)

ⓑ
Change to a decimal.	\(\frac{11}{8}\)
Write as a percent by moving the decimal two places.
	\(137.5\%\)

	\(\frac{5}{7}\)
Change to a decimal—rounding to the nearest thousandth.	\(0.714\)
Write as a percent.	\(71.4\%\)

ⓒ
Write as an improper fraction.	\(2\frac{1}{5}\)
Change to a decimal.	\(\frac{11}{5}\)
Write as a percent.
	\(220\%\)

	\(\frac{1}{3}\)
Change to a decimal.
Write as a repeating decimal.	\(0.333\ldots\)
Write as a percent.	\(33\frac{1}{3}\%\)