ISEE Upper Level

Conversions

Converting between fractions, decimals, and percents

Generate Unlimited Practice Questions

Learn This Topic

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

3 practice questions for ISEE Upper Level

Q1 Hard

Which value is NOT equal to

\frac{5}{6}

0.8 \overline{3}

\frac{15}{18}

C 0.833

\frac{2.5}{3}

Show Solution

To determine which value is not equal, evaluate each option against $\frac{5}{6}$ . As a decimal, $5 \div 6 = 0.8333...$ , which is exactly represented by $0.8 \overline{3}$ (Choice A). The fraction $\frac{15}{18}$ simplifies to $\frac{5}{6}$ when dividing both numerator and denominator by 3 (Choice B). Multiplying the numerator and denominator of $\frac{2.5}{3}$ by 2 yields $\frac{5}{6}$ (Choice D). However, 0.833 is a terminating decimal exactly equal to $\frac{833}{1000}$ . This is only an approximation of $\frac{5}{6}$ , making C the correct answer.

Answer: C

Q2 Hard

Which of the following values is the greatest?

\frac{5}{8}

62%

0. \overline{6}

\frac{3}{5}

Show Solution

To compare these values, convert all of them to decimals. $\frac{5}{8} = 5 \div 8 = 0.625$ . $62%$ means 62 per 100, which is $0.62$ . $0. \overline{6}$ is a repeating decimal equivalent to $0.666...$ . $\frac{3}{5} = 3 \div 5 = 0.60$ . Comparing the decimals (0.625, 0.62, 0.666..., 0.60), the largest value is $0. \overline{6}$ .

Answer: C

Q3 Hard

Which value is NOT equal to

12.5%

\frac{1}{8}

B 0.125

\frac{12.5}{100}

\frac{1}{80}

Show Solution

Convert $12.5%$ to different formats to check equivalency. A percentage is a part out of 100, so $12.5%$ is exactly equal to $\frac{12.5}{100}$ (Choice C). Dividing 12.5 by 100 gives the decimal equivalent, 0.125 (Choice B). As a fraction, 0.125 is equal to $\frac{125}{1000}$ , which simplifies to $\frac{1}{8}$ (Choice A). However, $\frac{1}{80}$ as a decimal is 0.0125, which is equal to $1.25%$ . Therefore, $\frac{1}{80}$ is NOT equal to $12.5%$ .

Answer: D

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 $0.333 = \frac{333}{1000}$ ).

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Fractions, Decimals, Ratios & Percents

Other Levels

Browse

Generate Unlimited Practice Questions