Where Did These Three Forms Come From?
People have been splitting things into parts for thousands of years. Ancient Egyptians needed to divide bread fairly among workers. They invented some of the earliest fractions (numbers that show a part of a whole) to do it. Over time, mathematicians found other ways to write parts of a whole, giving us decimals and percents.
Today, fractions, decimals, and percents are three different ways to write the same value. On the ISEE, you will need to switch between them quickly. Let's learn how!
Core Principles: Three Names, One Number
Think of fractions, decimals, and percents as three languages for the same idea. The number ½ can also be written as 0.5 or 50%. They all mean half of something. Learning to translate between them is like being fluent in all three languages.
Fraction
Decimal
Percent
Seeing the Connection
The diagram below shows how the same value looks in all three forms. Study the arrows to see how you convert from one form to another.
Notice that every conversion follows a simple rule. The triangle is your roadmap. If you ever get stuck, just think: "Where am I, and where do I need to go?" Then follow the arrow.
The Conversion Formulas
Here are the key formulas you need. Each one is a simple rule that works every time.
Must-Know Equivalents for the ISEE
Some conversions show up so often on the ISEE that you should memorize them. The table below lists the most common ones. Knowing these by heart will save you valuable time.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/3 | 0.333... | 33⅓% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Worked Example: Converting 3/8
Let's walk through a full conversion, step by step. We'll convert the fraction 3/8 into a decimal and then into a percent.
When to Use Each Form
On the ISEE, different question types favor different forms. Knowing when to use each one helps you solve problems faster.
| Form | Best For | Watch Out For |
|---|---|---|
| Fraction | Exact answers, multiplying parts of a number, comparing with common denominators | Hard to compare fractions with different denominators without converting |
| Decimal | Ordering numbers, adding and subtracting, comparing sizes quickly | Repeating decimals (like 0.333...) can be tricky to work with |
| Percent | Discounts, tips, tax problems, data interpretation, comparing ratios | Must convert to a decimal or fraction before doing most calculations |
Connecting to Ratios and Proportions
Converting between fractions, decimals, and percents is the foundation for harder ISEE topics like ratios, proportions, and probability. Once you're comfortable switching forms, those topics become much easier.
| This Lesson | What Comes Next |
|---|---|
| Convert 1/4 to 25% | Find 25% of a number (e.g., 25% of 60) |
| Know that 0.5 = 1/2 | Probability: a 0.5 chance means "equally likely" |
| Write 3/5 as 60% | Use proportions: if 3 out of 5 students play sports, how many out of 30? |
Think of this skill as a building block. Every time you see a ratio or probability question on the ISEE, there's a good chance you'll need to convert at some point. Mastering conversions now makes everything else smoother later.
Practice Problems
Try these five problems. They mix standard multiple-choice questions with quantitative comparisons, just like the real ISEE. Remember: there's no penalty for guessing, so always pick an answer!
Summary: Fractions, Decimals, and Percents
Fractions, decimals, and percents are three ways to write the same value. To go from a fraction to a decimal, divide the numerator by the denominator. To go from a decimal to a percent, multiply by 100. To go from a percent to a fraction, place the number over 100 and simplify.
Memorize the common equivalents (like 1/4 = 0.25 = 25%) to save time on the ISEE. Always match the form of your answer to the answer choices. On quantitative comparisons, convert both columns to the same form before comparing. And remember — never leave a question blank!