Convert between a decimal and an equivalent fraction. - ISEE Lower Level Mathematics Achievement

SECTION 1

Where Do Decimals and Fractions Come From?

People have been splitting things into parts for thousands of years. Imagine sharing a pizza with a friend. You each get one half of the pizza. Ancient people needed a way to write down parts like this!

Over time, mathematicians invented two different ways to write parts of a whole: fractions and decimals. Both say the same thing, just in different ways. Let's see how they developed!

1800 BC • Ancient Egypt

Egyptians used fractions to share bread and land fairly. They mostly used fractions with 1 on top, like ½ and ¼.

300 BC • Ancient Greece

Greek mathematicians used fractions to study music and measure buildings. Fractions helped them build amazing temples!

1200 AD • Fraction Bar Invented

Mathematicians in the Middle East started writing fractions with a line between two numbers, like ³⁄₄. This is the style we use today!

1585 AD • Decimals Arrive

A Dutch mathematician named Simon Stevin showed people how to use a decimal point. This made math with parts much easier!

Today we use both fractions and decimals all the time. On the ISEE, you need to be able to switch between them quickly. Let's learn how!

SECTION 2

Core Ideas You Need to Know

Before we start converting, let's learn a few important ideas. Think of these as your building blocks!

Place Value Matters

The digit's position after the decimal point tells you the denominator. The first spot is tenths, the second is hundredths.

Same Value, Different Look

0.5 and ½ are the same amount. They look different, but they both mean "half." Think of them as twins in different outfits!

Read It, Write It

If you can read a decimal out loud, you can write the fraction. "Zero point five" is "five tenths," which is 5/10.

Always Simplify

After you write your fraction, check if you can make it simpler. 5/10 becomes ½ when you divide the top and bottom by 5.

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KEY TAKEAWAY

Think of decimals and fractions like two languages that say the same thing. Just like "hello" in English and "hola" in Spanish mean the same greeting, 0.25 and ¼ mean the same amount. Learning to translate between them is like being bilingual in math!

SECTION 3

See It! Decimals and Fractions Side by Side

Let's look at a picture that shows how decimals and fractions match up. This diagram shows a bar split into 10 equal parts.

The top bar shows tenths. Each section is 1/10 or 0.1. The shaded purple area shows 5/10, which equals 0.5. The bottom grid shows hundredths, where 25 shaded squares out of 100 equals 25/100, or 0.25.

See how the purple shading covers exactly half the bar? That's why 5/10 equals 0.5. In the grid below, 25 out of 100 tiny squares are shaded in blue. That's 25 hundredths, or 0.25. Pretty cool, right?

SECTION 4

The Steps: How to Convert

Decimal → Fraction

Here is the simple trick. Just say the decimal out loud! The last word you say becomes the denominator (the bottom number).

DECIMAL TO FRACTION

0.7 → "seven tenths" → 7/10

The digit 7 is in the tenths place, so the denominator is 10.

TWO DECIMAL PLACES

0.35 → "thirty-five hundredths" → 35/100

The last digit is in the hundredths place, so the denominator is 100. Then simplify: 35/100 = 7/20.

Fraction → Decimal

To go the other way, divide the top number by the bottom number. Or, if the denominator is 10 or 100, just place the digits!

FRACTION TO DECIMAL

3/10 → 0.3

The denominator is 10, so put the 3 in the tenths place. Easy!

DENOMINATOR OF 100

47/100 → 0.47

The denominator is 100, so put 47 in the tenths and hundredths places.

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ISEE Test Tip!

On the ISEE, always check your answer choices. If one choice is a fraction and you found a decimal, convert to see if they match. Memorize the common ones: ½ = 0.5, ¼ = 0.25, ¾ = 0.75. This saves you time!

SECTION 5

Place Value: Your Secret Weapon

The key to converting is understanding place value. Each spot after the decimal point has a name. That name tells you the denominator of your fraction!

This chart shows the number 0.75. The 7 is in the tenths place and the 5 is in the hundredths place. Since the last digit reaches the hundredths place, the denominator is 100. So 0.75 = 75/100, which simplifies to 3/4.

Decimal	Say It Out Loud	Fraction	Simplified
0.1	one tenth	1/10	1/10
0.25	twenty-five hundredths	25/100	1/4
0.5	five tenths	5/10	1/2
0.75	seventy-five hundredths	75/100	3/4
0.8	eight tenths	8/10	4/5

Common Decimal-to-Fraction Conversions

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REMEMBER THIS!

Count the digits after the decimal point. One digit means tenths (denominator 10). Two digits means hundredths (denominator 100). It's like a code: the number of decimal places tells you how many zeros go in the denominator!

SECTION 6

Worked Example: Step by Step

Let's work through two examples together. Follow each step carefully!

Example 1: Convert 0.6 to a fraction

1
Step 1 — Read the decimal out loud

Say "zero point six" or "six tenths." The word "tenths" tells us the denominator is 10.
2
Step 2 — Write the fraction

Put 6 on top and 10 on the bottom.

6/10
3
Step 3 — Simplify

Both 6 and 10 can be divided by 2. So 6 ÷ 2 = 3 and 10 ÷ 2 = 5.

0.6 = 3/5

Example 2: Convert 3/4 to a decimal

1
Step 1 — Try to make the denominator 10 or 100

Can we turn 4 into 10? No, because 4 does not go into 10 evenly. Can we turn 4 into 100? Yes! 4 × 25 = 100.
2
Step 2 — Multiply top and bottom by the same number

Multiply both the numerator and denominator by 25. So 3 × 25 = 75 and 4 × 25 = 100.

3/4 = 75/100
3
Step 3 — Write as a decimal

75/100 means 75 hundredths. Place 75 in the tenths and hundredths spots.

3/4 = 0.75

SECTION 7

When to Use Each Method

There are different ways to convert. Knowing which one to use saves you time on the ISEE. Let's compare them!

Method	When to Use It	Example
Read it out loud	Going from a decimal to a fraction	0.9 → "nine tenths" → 9/10
Make denominator 10 or 100	Going from a fraction to a decimal when the denominator can become 10 or 100	1/5 → multiply by 2/2 → 2/10 → 0.2
Memorize the common ones	When you see ½, ¼, ¾, or ⅕ on the test	½ = 0.5 (you just know it!)
Divide top by bottom	When other methods don't work easily	3/4: do 3 ÷ 4 = 0.75

Conversion Methods Compared

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ISEE STRATEGY

On the ISEE, you do NOT have a calculator. So memorizing the common conversions is the fastest strategy. Think of it like knowing your times tables — the more you practice, the faster you get. Always answer every question, even if you have to guess!

SECTION 8

Connecting to Bigger Ideas

Converting between decimals and fractions is a skill you'll use again and again. Let's see how this connects to what you'll learn next!

What You Know Now	What Comes Next
0.5 = 1/2	50% is another way to say the same thing!
Simplifying fractions like 25/100 = 1/4	Finding equivalent fractions to add and subtract
Reading place values (tenths, hundredths)	Comparing and ordering decimals and fractions
Writing 3/4 as 0.75	Using decimals in money problems ($0.75 = three quarters)

Now vs. Next

See how it all connects? Once you master converting, you'll be ready for percents, money problems, and comparing numbers. You're building a strong math foundation right now!

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Fun Fact

When you pay for something that costs $0.50, you're really paying 50/100 of a dollar, or ½ of a dollar. Decimals, fractions, and money are all connected!

SECTION 9

Practice Problems

Now it's your turn! Try these five problems. Remember, on the ISEE you should always pick an answer — never leave a question blank. You've got this!

Question 1: CONCEPTUAL

Which fraction is equal to 0.5?

A. 1/5
B. 1/2
C. 2/3
D. 5/2

Show answer (B)

The correct answer is B. 0.5 means "five tenths," which is 5/10. Simplify by dividing top and bottom by 5 to get 1/2. Choice A (1/5) equals 0.2, not 0.5. Choice C (2/3) is about 0.67. Choice D (5/2) equals 2.5, which is much more than 1.

Question 2: BASIC CALCULATION

What is 0.3 written as a fraction?

A. 1/3
B. 3/10
C. 3/5
D. 3/4

Show answer (B)

The correct answer is B. 0.3 means "three tenths," so the fraction is 3/10. This fraction is already in simplest form because 3 and 10 share no common factor. Choice A (1/3) is about 0.333..., which is close but not the same as 0.3. Choice C (3/5) equals 0.6. Choice D (3/4) equals 0.75.

Question 3: INTERMEDIATE

What decimal is equal to 3/5?

A. 0.35
B. 0.53
C. 0.6
D. 0.8

Show answer (C)

The correct answer is C. To convert 3/5 to a decimal, make the denominator 10. Multiply top and bottom by 2: 3 × 2 = 6 and 5 × 2 = 10. So 3/5 = 6/10 = 0.6. Choice A (0.35) just puts the 3 and 5 together, which is a common mistake. Choice B (0.53) reverses the digits. Choice D (0.8) equals 4/5, not 3/5.

Question 4: APPLIED

Maria ate 0.25 of a pie. What fraction of the pie did she eat?

A. 1/4
B. 1/3
C. 2/5
D. 1/2

Show answer (A)

The correct answer is A. 0.25 means "twenty-five hundredths," which is 25/100. Simplify by dividing both by 25: 25 ÷ 25 = 1 and 100 ÷ 25 = 4. So Maria ate 1/4 of the pie. Choice B (1/3) is about 0.33, not 0.25. Choice C (2/5) equals 0.4. Choice D (1/2) equals 0.5, which would be half the pie.

Question 5: CRITICAL THINKING

Which of the following shows a decimal and fraction that are NOT equal to each other?

A. 0.2 and 1/5
B. 0.4 and 2/5
C. 0.6 and 2/3
D. 0.75 and 3/4

Show answer (C)

The correct answer is C. 0.6 equals 6/10, which simplifies to 3/5, not 2/3. The fraction 2/3 actually equals about 0.666..., which is a repeating decimal, not exactly 0.6. Choice A is correct because 1/5 = 2/10 = 0.2. Choice B is correct because 2/5 = 4/10 = 0.4. Choice D is correct because 3/4 = 75/100 = 0.75. This problem requires you to check each pair carefully!

SUMMARY

Let's Wrap It Up!

Summary

Great work! You learned that decimals and fractions are two ways to show the same amount. To convert a decimal to a fraction, read it out loud and use place value to find the denominator. One decimal place means tenths, and two decimal places means hundredths. Always simplify your fraction by dividing top and bottom by the same number.

To convert a fraction to a decimal, try to make the denominator 10 or 100 by multiplying top and bottom by the same number. For the ISEE, memorize the common pairs: ½ = 0.5, ¼ = 0.25, ¾ = 0.75, ⅕ = 0.2, and ⅗ = 0.6. Remember to always answer every question — you've got this!