4.1 Percent Concepts & Conversions

Q: Convert 0.045 to a percent.

4.5%. To convert a decimal to a percent, multiply by 100 (or move the decimal point two places to the right) and append the percent symbol. Multiplying 0.045 by 100 yields 4.5%.

Q: Convert 37.5% to a fraction in simplest form.

3/8. Write 37.5% as 37.5/100. To eliminate the decimal in the numerator, multiply numerator and denominator by 2 to get 75/200. Dividing both numerator and denominator by their greatest common factor, 25, simplifies the fraction to 3/8.

Q: Express the fraction 5/8 as a percent.

62.5%. First convert 5/8 to a decimal by dividing 5 by 8, which equals 0.625. Then multiply by 100% to convert the decimal to a percent, resulting in 62.5%.

Q: What is the decimal representation of 1/4%?

0.0025. First convert the fraction inside the percent: 1/4 = 0.25, so 1/4% is equivalent to 0.25%. To convert a percent to a decimal, divide by 100 by shifting the decimal point two places to the left, which yields 0.0025.

Key Takeaways

Percent literally means 'per hundred' or parts out of 100, represented mathematically as a fraction with a denominator of 100.
To convert a percent to a decimal, divide by 100 (shift the decimal point two places left); to convert a decimal to a percent, multiply by 100 (shift two places right).
To convert a percent to a fraction in lowest terms, write the percent value over 100 and simplify by dividing the numerator and denominator by their greatest common factor.
To convert a fraction to a percent, divide the numerator by the denominator to form a decimal, then multiply the resulting decimal by 100%.
Memorizing core benchmark equivalencies (such as 12.5% = 1/8, 33 1/3% = 1/3, and 75% = 3/4) provides a major speed advantage on the non-calculator ACCUPLACER test.

Last updated: August 2026

4.1 Percent Concepts & Conversions

The word percent comes from the Latin phrase per centum, which translates directly to "by the hundred" or "out of one hundred." In mathematics, a percent is a ratio or fraction whose denominator is always 100. The symbol % is used to represent percent. For example, $45\%$ means 45 out of 100, which can be written as the fraction $\frac{45}{100}$ or the decimal $0.45$ .

Understanding percents as standardized hundredths allows us to compare quantities of different sizes on a uniform scale. On the ACCUPLACER Arithmetic test, fluency in converting between percents, decimals, and fractions is vital because test questions frequently require switching representation forms to perform efficient mental or written calculations.

1. Converting Percents to Decimals

To convert a percent to a decimal, you are converting a quantity expressed "per hundred" into a standard base-10 decimal value.

Standard Rule

Dividing a number by 100 shifts its decimal point two places to the left and removes the percent sign (%).

$\text{Decimal} = \frac{\text{Percent}}{100}$

Converting Whole, Decimal, and Fractional Percents

Whole-number percents:
- $85\% = \frac{85}{100} = 0.85$
- $7\% = \frac{7}{100} = 0.07$ (Notice the zero placeholder added in the tenths place)
- $250\% = \frac{250}{100} = 2.50 = 2.5$ (Percents greater than 100% yield decimals greater than 1)
Decimals containing percents:
- $0.4\% = \frac{0.4}{100} = 0.004$
- $37.5\% = \frac{37.5}{100} = 0.375$
Fractional percents:
- $\frac{1}{2}\% = 0.5\% = \frac{0.5}{100} = 0.005$
- $6\frac{1}{4}\% = 6.25\% = \frac{6.25}{100} = 0.0625$

2. Converting Decimals to Percents

Converting a decimal to a percent is the exact inverse of converting a percent to a decimal.

Standard Rule

Multiplying a decimal by 100% shifts its decimal point two places to the right and attaches the percent sign (%).

$\text{Percent} = \text{Decimal} \times 100\%$

Step-by-Step Conversion Examples

Initial Decimal	Shift Decimal Point 2 Places Right	Resulting Percent
$0.62$	$0.62 \rightarrow 62.$	$62\%$
$0.08$	$0.08 \rightarrow 08.$	$8\%$
$0.0035$	$0.0035 \rightarrow 00.35$	$0.35\%$
$1.75$	$1.75 \rightarrow 175.$	$175\%$
$4.0$	$4.00 \rightarrow 400.$	$400\%$

3. Converting Percents to Fractions in Lowest Terms

To convert a percent to a simplified fraction:

Write the percent as a fraction with a denominator of 100.
If the numerator contains a decimal or fraction, clear it:
- Multiply numerator and denominator by 10 (or 100, etc.) to eliminate decimals.
- Convert mixed-number percents to improper fractions first.
Simplify the fraction to lowest terms by dividing the numerator and denominator by their Greatest Common Factor (GCF).

Step-by-Step Worked Conversion Examples

Example A: Convert $68\%$ to a fraction in simplest form.

Place over 100: $\frac{68}{100}$
Find GCF of 68 and 100: $\text{GCF}(68, 100) = 4$
Divide numerator and denominator by 4: $\frac{68 \div 4}{100 \div 4} = \frac{17}{25}$

Example B: Convert $12.5\%$ to a fraction in simplest form.

Place over 100: $\frac{12.5}{100}$
Multiply numerator and denominator by 10 to clear the decimal: $\frac{125}{1000}$
Simplify by dividing by $\text{GCF}(125, 1000) = 125$ : $\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$

Example C: Convert $33\frac{1}{3}\%$ to a fraction in simplest form.

Express $33\frac{1}{3}$ as an improper fraction: $\frac{100}{3}\%$
Divide by 100: $\frac{100/3}{100} = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3}$

4. Converting Fractions to Percents

There are two primary methods for converting a fraction to a percent:

Method 1: Decimal Division Method (Universal)

Divide the numerator by the denominator to obtain a decimal, then multiply by 100%.

$\text{Fraction } \frac{a}{b} \longrightarrow a \div b = \text{Decimal} \longrightarrow \text{Decimal} \times 100\% = \text{Percent}$

Worked Example: Convert $\frac{7}{16}$ to a percent.

Long division: $7 \div 16 = 0.4375$
Multiply by 100%: $0.4375 \times 100\% = 43.75\%$ (or $43\frac{3}{4}\%$ )

Method 2: Equivalent Denominator Method (Fast for friendly denominators)

Set up an equivalent fraction with a denominator of 100: $\frac{a}{b} = \frac{p}{100}$ .

Worked Example: Convert $\frac{4}{25}$ to a percent.

Multiply numerator and denominator by 4: $\frac{4 \times 4}{25 \times 4} = \frac{16}{100}$
Therefore, $\frac{4}{25} = 16\%$

5. Benchmark Equivalencies Reference Table

Mastering common benchmark equivalencies allows you to bypass tedious long division on the ACCUPLACER.

Percent	Fraction (Lowest Terms)	Decimal	Mental Calculation Shortcut
$5\%$	$\frac{1}{20}$	$0.05$	Divide by 20 (or half of 10%)
$10\%$	$\frac{1}{10}$	$0.1$	Move decimal 1 place left
$12.5\%$ ( $12\frac{1}{2}\%$ )	$\frac{1}{8}$	$0.125$	Divide by 8
$16\frac{2}{3}\%$	$\frac{1}{6}$	$0.1667\dots$	Divide by 6
$20\%$	$\frac{1}{5}$	$0.2$	Divide by 5
$25\%$	$\frac{1}{4}$	$0.25$	Divide by 4
$33\frac{1}{3}\%$	$\frac{1}{3}$	$0.3333\dots$	Divide by 3
$37.5\%$ ( $37\frac{1}{2}\%$ )	$\frac{3}{8}$	$0.375$	Multiply by 3, divide by 8
$50\%$	$\frac{1}{2}$	$0.5$	Divide by 2
$62.5\%$ ( $62\frac{1}{2}\%$ )	$\frac{5}{8}$	$0.625$	Multiply by 5, divide by 8
$66\frac{2}{3}\%$	$\frac{2}{3}$	$0.6667\dots$	Multiply by 2, divide by 3
$75\%$	$\frac{3}{4}$	$0.75$	Multiply by 3, divide by 4
$80\%$	$\frac{4}{5}$	$0.8$	Multiply by 4, divide by 5
$87.5\%$ ( $87\frac{1}{2}\%$ )	$\frac{7}{8}$	$0.875$	Multiply by 7, divide by 8
$100\%$	$1$	$1.0$	The whole quantity

ACCUPLACER Exam Traps & Common Errors

Warning

Trap 1: Confusing Fractional Percents with Standard Decimals A common ACCUPLACER mistake is treating $\frac{1}{2}\%$ as $0.5$ . Remember that $\frac{1}{2}\% = 0.5\% = 0.005$ . Always apply the percent definition (divide by 100)!

Warning

Trap 2: Moving the Decimal Point in the Wrong Direction When converting $4.5\%$ to a decimal, moving the decimal two places right gives $450$ (incorrect!). Converting from percent to decimal ALWAYS moves left, making the number smaller ( $0.045$ ).

Warning

Trap 3: Forgetting to Multiply by 100 when Converting Fractions When asked to convert $\frac{3}{50}$ to a percent, dividing $3 \div 50 = 0.06$ is only step 1. You must multiply by 100% to arrive at $6\%$ , not $0.06\%$ .

Test Your Knowledge

Convert 0.045 to a percent.

4.5%

0.45%

45%

450%

Test Your Knowledge

Convert 37.5% to a fraction in simplest form.

37/100

3/8

3/4

15/40

Test Your Knowledge

Express the fraction 5/8 as a percent.

58%

60%

62.5%

65%

Test Your Knowledge

What is the decimal representation of 1/4%?

0.25

0.025

2.5

0.0025

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4.2 Percent of a Quantity & Percent Equations

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ACCUPLACER Arithmetic

4.1 Percent Concepts & Conversions

Key Takeaways

4.1 Percent Concepts & Conversions

1. Converting Percents to Decimals

Standard Rule

Converting Whole, Decimal, and Fractional Percents

2. Converting Decimals to Percents

Standard Rule

Step-by-Step Conversion Examples

3. Converting Percents to Fractions in Lowest Terms

Step-by-Step Worked Conversion Examples

Example A: Convert 68%68\%68% to a fraction in simplest form.

Example B: Convert 12.5%12.5\%12.5% to a fraction in simplest form.

Example C: Convert 3313%33\frac{1}{3}\%3331​% to a fraction in simplest form.

4. Converting Fractions to Percents

Method 1: Decimal Division Method (Universal)

Method 2: Equivalent Denominator Method (Fast for friendly denominators)

5. Benchmark Equivalencies Reference Table

ACCUPLACER Exam Traps & Common Errors

Example A: Convert $68\%$ to a fraction in simplest form.

Example B: Convert $12.5\%$ to a fraction in simplest form.

Example C: Convert $33\frac{1}{3}\%$ to a fraction in simplest form.