How to Convert Between Percent, Fractions, and Decimals?
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Fractions, decimals, and percents are three ways to name the same value. A percent compares a value to \(100\), a decimal uses place value, and a fraction compares a numerator to a denominator.
Percent to Decimal or Fraction
To change a percent to a decimal, divide by \(100\). For example, \(45\% = 45 \div 100 = 0.45\). To write it as a fraction, use \(\frac{45}{100}\) and simplify to \(\frac{9}{20}\).
Decimal to Percent or Fraction
To change a decimal to a percent, multiply by \(100\). For example, \(0.375 \times 100 = 37.5\%\). To write it as a fraction, read the place value: \(0.375=\frac{375}{1000}=\frac{3}{8}\).
Fraction to Decimal or Percent
Converting Between Percent, Fractions, and Decimals
Think of this lesson as more than a rule to memorize. Converting Between Percent, Fractions, and Decimals is about parts, wholes, rates, discounts, tax, and percent change. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.
Percent means ?per 100,? so \(p\%\) is \(\frac{p}{100}\). Most percent problems come from part = percent \(\times\) whole.
Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.
- Read what is given and what is being asked.
- Choose the rule that connects them.
- Substitute carefully and simplify in small steps.
- Check the final answer against the original question.
A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.
Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.
When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.
On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.
Divide the numerator by the denominator to get a decimal, then multiply by \(100\) for a percent. For example, \(\frac{7}{20}=0.35=35\%\).
Exercises for Converting Between Percent, Fractions, and Decimals
1) Convert \(0.37\) to a percent.
2) Convert \(45\%\) to a decimal.
3) Convert \(\frac{3}{4}\) to a percent.
4) Convert \(0.125\) to a fraction in simplest form.
5) Convert \(18\%\) to a fraction in simplest form.
6) Convert \(\frac{7}{20}\) to a decimal and percent.
7) Convert \(2.5\%\) to a decimal.
8) Convert \(1.2\) to a percent.
9) Convert \(\frac{5}{8}\) to a percent.
10) Convert \(0.006\) to a percent.
11) Convert \(135\%\) to a decimal and mixed number.
12) Convert \(\frac{11}{25}\) to a percent.
13) Convert \(0.\overline{3}\) to a fraction and percent.
14) Convert \(62.5\%\) to a fraction in simplest form.
15) Convert \(\frac{9}{16}\) to a decimal and percent.
16) Convert \(0.048\) to a percent and fraction.
17) Convert \(\frac{13}{40}\) to a decimal and percent.
18) Convert \(175\%\) to a decimal and improper fraction.
19) Order from least to greatest: \(0.58\), \(\frac{3}{5}\), \(57\%\).
20) Which is larger: \(\frac{7}{12}\) or \(58.4\%\)?
1) Multiply by \(100\): \(0.37 \times 100 = 37\). Answer: \(37\%\).
2) Divide by \(100\): \(45\% = 45 \div 100 = 0.45\).
3) \(\frac{3}{4}=0.75\), and \(0.75 \times 100 = 75\). Answer: \(75\%\).
4) \(0.125=\frac{125}{1000}\). Simplify by \(125\): \(\frac{125}{1000}=\frac{1}{8}\).
5) \(18\%=\frac{18}{100}\). Simplify by \(2\): \(\frac{18}{100}=\frac{9}{50}\).
6) \(\frac{7}{20}=0.35\). Then \(0.35 \times 100=35\). Answer: \(0.35\) and \(35\%\).
7) \(2.5\% = 2.5 \div 100 = 0.025\).
8) \(1.2 \times 100 = 120\). Answer: \(120\%\).
9) \(\frac{5}{8}=0.625\). Then \(0.625 \times 100=62.5\). Answer: \(62.5\%\).
10) \(0.006 \times 100 = 0.6\). Answer: \(0.6\%\).
11) \(135\% = 135 \div 100 = 1.35\). Also \(\frac{135}{100}=\frac{27}{20}=1\frac{7}{20}\).
12) \(\frac{11}{25}=\frac{44}{100}\). Answer: \(44\%\).
13) \(0.\overline{3}=\frac{1}{3}\). As a percent, \(\frac{1}{3} \times 100 = 33\frac{1}{3}\%\).
14) \(62.5\%=\frac{62.5}{100}=0.625=\frac{625}{1000}=\frac{5}{8}\).
15) \(\frac{9}{16}=0.5625\). Then \(0.5625 \times 100=56.25\). Answer: \(0.5625\), \(56.25\%\).
16) \(0.048 \times 100=4.8\), so \(4.8\%\). Also \(0.048=\frac{48}{1000}=\frac{6}{125}\).
17) \(\frac{13}{40}=0.325\). Then \(0.325 \times 100=32.5\). Answer: \(0.325\), \(32.5\%\).
18) \(175\%=1.75\). Also \(\frac{175}{100}=\frac{7}{4}\).
19) Convert all to percents: \(0.58=58\%\), \(\frac{3}{5}=60\%\), and \(57\%\). Order: \(57\%, 0.58, \frac{3}{5}\).
20) \(\frac{7}{12} \times 100 = 58\frac{1}{3}\%\), which is about \(58.33\%\). Since \(58.4\%\) is larger, answer: \(58.4\%\).
Converting Between Percent, Fractions, and Decimals Quiz
