U.3 Write decimals as fractions and mixed numbers
What is a decimal?
A decimal is a way to write a number that is less than one whole, or a number that includes a part of a whole. Decimals use a decimal point (.) to separate the whole number part from the fractional part.
- 0.5 (five tenths) is a decimal less than one whole.
- 3.25 (three and twenty-five hundredths) is a decimal greater than one whole.
- 0.7 (seven tenths) means seven parts out of ten equal parts.
The decimal point is like a border. Digits to the left of the decimal point are whole numbers. Digits to the right of the decimal point are fractional parts (tenths, hundredths, thousandths).
Place value with decimals: tenths and hundredths
In fourth grade, you focus on decimals to the tenths and hundredths place. The first digit to the right of the decimal point is the tenths place. The second digit to the right is the hundredths place.
- 0.3 → 3 is in the tenths place (3 tenths).
- 0.47 → 4 is in the tenths place, 7 is in the hundredths place (47 hundredths).
- 2.05 → 2 is the whole number, 0 is in the tenths place, 5 is in the hundredths place (two and five hundredths).
Think of a dollar: one dime is 0.1 (one tenth of a dollar). One penny is 0.01 (one hundredth of a dollar). Ten dimes make one dollar; one hundred pennies make one dollar.
Writing decimals as fractions (decimals less than 1)
To write a decimal less than 1 as a fraction, read the decimal aloud using place value. The denominator (bottom number) is 10 for tenths, 100 for hundredths. The numerator (top number) is the digits after the decimal point.
- 0.3 (three tenths) → 310
- 0.45 (forty-five hundredths) → 45100
- 0.07 (seven hundredths) → 7100
Always check if the fraction can be simplified (reduced). For example, 0.5 = 510 = 12. However, fourth grade often focuses on writing the fraction with denominator 10 or 100 first.
Writing decimals as mixed numbers (decimals greater than 1)
A mixed number has a whole number part and a fraction part. To write a decimal greater than 1 as a mixed number, keep the whole number part the same. Then write the decimal part as a fraction (tenths or hundredths).
- 2.3 (two and three tenths) → 2310
- 5.67 (five and sixty-seven hundredths) → 567100
- 1.09 (one and nine hundredths) → 19100
When the decimal part has zeros, like 0.09, the zero in the tenths place means there are no tenths. Write the fraction as 9100, not 09100.
Writing decimals as fractions: tenths and hundredths forms
Any decimal can be written as a fraction with denominator 10 (tenths) or denominator 100 (hundredths). Sometimes you must convert between tenths and hundredths to write the fraction correctly.
- 0.7 (seven tenths) = 710 = 70100 (equivalent fractions)
- 0.50 (fifty hundredths) = 50100 = 510
- 3.2 = 3210 = 320100
When you see a decimal like 0.4, you can write it as 410 or 40100. Both are correct, but the problem will tell you which denominator to use.
Writing fractions as decimals (the reverse process)
To write a fraction with denominator 10 or 100 as a decimal, read the fraction as tenths or hundredths. Then write the decimal point and the digits. If the fraction is a mixed number, keep the whole number.
- 710 = 0.7 (seven tenths)
- 23100 = 0.23 (twenty-three hundredths)
- 49100 = 4.09 (four and nine hundredths)
- 8510 = 8.5 (eight and five tenths)
If the fraction has denominator 10 but you want a hundredths decimal, add a zero in the hundredths place. Example: 310 = 0.30.
Using a number line with decimals and fractions
A number line helps you see that decimals and fractions are two ways to name the same point. Between 0 and 1, you can mark tenths and hundredths. Both 110 and 0.1 are the same location.
- 0.5 and 510 are the same point halfway between 0 and 1.
- 0.75 and 75100 are the same point three-quarters of the way from 0 to 1.
- 1.3 and 1310 are the same point on the number line after 1.
When you place decimals on a number line, always look at the place value. 0.3 is three tenths, which is less than 0.5 (five tenths).
Equivalent fractions and decimals
Equivalent fractions are fractions that name the same amount, even though they have different numerators and denominators. Decimals can also be equivalent. For example, 0.4 and 0.40 name the same amount.
- 0.2 = 210 = 20100
- 0.6 = 610 = 60100
- 1.50 = 1510 = 150100
When you add a zero to the right of the last digit after a decimal point, you do not change the value. 0.8 = 0.80 = 0.800. This is called using equivalent decimals.
Common mistakes when writing decimals as fractions
Many fourth-grade students make similar mistakes. Knowing these errors will help you write decimals as fractions correctly every time.
- Mistake: Writing 0.3 as 3100. Correction: 0.3 is three tenths, so denominator is 10: 310.
- Mistake: Writing 0.45 as 4510. Correction: 0.45 has two digits after the decimal, so denominator is 100: 45100.
- Mistake: Writing 1.5 as 15100. Correction: 1.5 = 1 and five tenths = 1510.
Always count the digits after the decimal point. One digit = tenths (denominator 10). Two digits = hundredths (denominator 100). Never use denominator 100 for a decimal like 0.4 unless you are writing an equivalent fraction.
Real-world examples of decimals as fractions
Decimals and fractions appear everywhere in daily life. Understanding how to convert between them helps you measure, shop, cook, and tell time.
- Money: $0.25 = 25100 of a dollar = one quarter.
- Measurement: 0.5 meters = 510 meter = half a meter.
- Sports: A basketball player makes 0.8 of their free throws = 810 = eight out of ten.
- Cooking: 0.75 cup of sugar = 75100 cup = three-fourths cup.
When you see a decimal in the real world, practice saying it as a fraction. For example, at the grocery store, $0.99 is “ninety-nine hundredths of a dollar.”
Step-by-step: writing any decimal as a fraction or mixed number
Follow these steps every time you need to write a decimal as a fraction or mixed number. This process works for all decimals to the tenths and hundredths place.
- Step 1: Identify the whole number part (the digits to the left of the decimal point). If there are no digits, the whole number is 0.
- Step 2: Count the digits to the right of the decimal point. One digit = tenths, two digits = hundredths, and so on.
- Step 3: Write the digits after the decimal point as the numerator (top number).
- Step 4: Write the denominator (bottom number) as 10 for tenths or 100 for hundredths.
- Step 5: If the whole number part is greater than 0, write it as a mixed number: whole number + fraction.
Example using steps: 4.07 → whole number is 4; digits after decimal are 07 (but write as 7); two digits = hundredths; fraction = 7100; mixed number = 4 7100.
Key rules to remember
These are the most important rules for writing decimals as fractions and mixed numbers. Keep them in mind for all your math work.
- Rule 1: Tenths → denominator 10. Hundredths → denominator 100.
- Rule 2: The decimal point separates whole numbers from fractions.
- Rule 3: A decimal less than 1 becomes a proper fraction (numerator smaller than denominator).
- Rule 4: A decimal greater than 1 becomes a mixed number.
- Rule 5: Always read the decimal aloud to check your fraction.
- Rule 6: 0.0, 0.00, and 0 are all the same: zero.
If you ever feel unsure, draw a picture. Shade 0.4 of a 10-by-10 grid. You will see 40 out of 100 squares shaded, which equals 40100 or 410.
Looking ahead: decimals to the thousandths place
In fifth grade, you will work with decimals to the thousandths place. A digit in the thousandths place means you write a fraction with denominator 1000.
- 0.125 (one hundred twenty-five thousandths) → 1251000
- 2.007 (two and seven thousandths) → 2 71000
For now, master tenths and hundredths. The same rules apply for thousandths: count the digits after the decimal. Three digits = thousandths.
Check your understanding
Ask yourself these questions to make sure you understand the lesson. Answer each one in your head or on paper.
- What denominator do you use for a decimal with one digit after the decimal point?
- What denominator do you use for a decimal with two digits after the decimal point?
- How do you write 0.9 as a fraction?
- How do you write 3.04 as a mixed number?
- Is 0.5 equal to 510 or 5100?
1. 10 (tenths). 2. 100 (hundredths). 3. 910. 4. 3 4100. 5. 510.
Common Core alignment: CCSS.MATH.CONTENT.4.NF.C.6 – Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.C.6 (Use decimal notation for fractions with denominators 10 or 100).
All content is 100% free. Use it for whole-class instruction, independent study and practice, or homework. Encourage students to read decimals aloud to reinforce place value understanding.