ISEE Middle Level

Conversions

Converting between fractions, decimals, and percents

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Imagine your favorite video game character. They might have a space suit, a ninja outfit, and a classic look. No matter what they wear, they are still the exact same character underneath! 🎮 Fractions, decimals, and percents work exactly the same way. They are just three different "outfits" for the exact same number.

For example, if you eat $\frac{1}{2}$ of a giant chocolate chip cookie, you could also say you ate $0.5$ of the cookie, or $50%$ of the cookie. 🍪 It’s the exact same amount of chocolatey goodness, just wearing a different math disguise!

On the ISEE, the test makers love to see if you can spot these numbers in their different outfits. You will see this a lot in the Quantitative Reasoning section, where you have to compare Column A and Column B. If Column A is wearing a fraction outfit and Column B is wearing a decimal outfit, you have to change one of them so they match! Once they are wearing the same outfit, it is super easy to see which one is bigger. 🦸‍♂️

The secret trick? Percents literally mean "out of 100." So, $75%$ is just $\frac{75}{100}$ . Decimals are just fractions hiding in plain sight based on their place value (like $0.75$ is 75 hundredths, or $\frac{75}{100}$ ). And to turn any fraction into a decimal, just read the fraction bar as a division sign! Let's practice changing these math outfits!

Key Formula

To change a fraction into a decimal, remember that the fraction bar means DIVIDE! Divide the top (numerator) by the bottom (denominator):

\frac{top}{bottom} = top \div bottom

Practice Questions

4 practice questions for ISEE Middle Level

Q1 Medium

Convert the fraction

\frac{5}{16}

to a percentage.

3.125%

31.25%

51.6%

0.3125%

Show Solution

To convert a fraction to a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator, then multiply the decimal by $100$ .

$\frac{5}{16} = 0.3125$
$0.3125 \times 100 = 31.25$
So, $\frac{5}{16}$ is $31.25%$ .

Answer: B

Q2 Medium

A recipe calls for

0.6

cups of sugar. What is this amount expressed as a simplified fraction?

\frac{3}{5}

\frac{6}{10}

\frac{1}{6}

\frac{2}{3}

Show Solution

To convert a decimal to a fraction, write the decimal as a fraction with a denominator that is a power of $10$ , then simplify the fraction.

$0.6$ can be written as $\frac{6}{10}$ .
To simplify $\frac{6}{10}$ , find the greatest common divisor (GCD) of $6$ and $10$ , which is $2$ .
Divide both the numerator and the denominator by $2$ :
$\frac{6}{2} = 3$
$\frac{10}{2} = 5$
So, $0.6$ as a simplified fraction is $\frac{3}{5}$ .

Answer: A

Q3 Medium

What is

72%

expressed as a simplified fraction?

\frac{72}{100}

\frac{18}{25}

\frac{36}{50}

\frac{7}{25}

Show Solution

To convert a percentage to a fraction, first express the percentage as a fraction with a denominator of $100$ , then simplify the fraction.

$72% = \frac{72}{100}$
To simplify the fraction $\frac{72}{100}$ , find the greatest common divisor (GCD) of $72$ and $100$ . Both $72$ and $100$ are divisible by $4$ .
$\frac{72}{4} = 18$
$\frac{100}{4} = 25$
So, $72%$ as a simplified fraction is $\frac{18}{25}$ .

Answer: B

Q4 Medium

On a test, Maria answered

\frac{7}{8}

of the questions correctly. What percentage of the questions did she answer correctly?

78%

87.5%

7.8%

8.75%

Show Solution

To convert a fraction to a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator, then multiply the decimal by $100$ .

$\frac{7}{8} = 0.875$
$0.875 \times 100 = 87.5$
So, Maria answered $87.5%$ of the questions correctly.

Answer: B

Tips & Strategies

Memorize the 'famous' fractions! Knowing that $\frac{1}{4} = 0.25$ , $\frac{1}{2} = 0.5$ , and $\frac{3}{4} = 0.75$ will save you tons of time.
For Quantitative Comparison questions, always convert both numbers to the same format before comparing. Decimals are usually the easiest format to compare!
When moving from a decimal to a percent, just move the decimal point two spots to the right. $0.45$ becomes $45%$ .

Common Mistakes

Watch out for the 'simplest form' trap! The test makers will often put the unsimplified fraction as an answer choice (like $\frac{4}{100}$ ) to trick you. Always check if you can divide the top and bottom by the same number.
Don't confuse tenths and hundredths! $0.4$ is $\frac{4}{10}$ (or $40%$ ), but $0.04$ is $\frac{4}{100}$ (or $4%$ ). Pay close attention to where the zero is!

Frequently Asked Questions

Do I need to memorize every single fraction-to-decimal conversion?

Nope! But memorizing the common ones (halves, quarters, and fifths like $\frac{1}{5} = 0.2$ ) acts like a math superpower on the ISEE. For the weird ones, just remember you can always use long division!

What if I get totally stuck on a Quantitative Comparison conversion?

Remember, the ISEE does NOT penalize you for guessing! If you spend more than a minute trying to convert a tricky number, pick your best guess, smile, and move on to the next question.

How do I know what place value a decimal has?

Just count the spots after the dot! One spot means tenths (like $0.3 = \frac{3}{10}$ ). Two spots means hundredths (like $0.33 = \frac{33}{100}$ ). Three spots means thousandths (like $0.333 = \frac{333}{1000}$ ).

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