U.2 Write fractions and mixed numbers as decimals
What are fractions and decimals?
Fractions and decimals are two different ways to show the same idea: a part of a whole. A fraction uses a numerator (top number) and a denominator (bottom number). A decimal uses a decimal point to separate the whole number part from the fractional part.
- The fraction 12 of a pizza is the same as 0.5 of a pizza.
- The fraction 34 of a dollar is the same as $0.75.
- The mixed number 212 is the same as 2.5 in decimal form.
Decimals are based on the number ten. That is why fractions with denominators of 10, 100, or 1000 are the easiest to convert into decimals.
Converting fractions with denominators of 10 or 100
When a fraction has a denominator of 10 or 100, you can write it as a decimal by looking at the numerator. The denominator tells you how many decimal places to use. Denominator 10 means one decimal place. Denominator 100 means two decimal places.
- 710 = 0.7 (seven tenths)
- 310 = 0.3 (three tenths)
- 25100 = 0.25 (twenty-five hundredths)
- 9100 = 0.09 (nine hundredths – remember to write the zero in the tenths place)
If the numerator is a single digit and the denominator is 100, always write a zero in the tenths place. For example, 4100 = 0.04, not 0.4.
Converting fractions with denominators of 1000
A fraction with denominator 1000 converts to a decimal with three decimal places. The numerator becomes the digits after the decimal point. If the numerator has fewer than three digits, add zeros to the left to make three digits.
- 71000 = 0.007 (seven thousandths)
- 421000 = 0.042 (forty-two thousandths)
- 3501000 = 0.350 (three hundred fifty thousandths)
- 51000 = 0.005 (five thousandths)
The decimal 0.350 is equal to 0.35, but when we convert from a fraction with denominator 1000, we keep all three decimal places to show the thousandths.
Converting fractions by finding an equivalent denominator
If a fraction does not have a denominator of 10, 100, or 1000, you can sometimes multiply or divide to get one of those denominators. Then convert as before. This works when the denominator is a factor of 10, 100, or 1000.
- 15 → Multiply numerator and denominator by 2: 210 = 0.2
- 34 → Multiply numerator and denominator by 25: 75100 = 0.75
- 720 → Multiply numerator and denominator by 5: 35100 = 0.35
- 1350 → Multiply numerator and denominator by 2: 26100 = 0.26
Not all fractions can be converted this way. For example, 13 does not have an equivalent fraction with denominator 10, 100, or 1000 using whole numbers. In fourth grade, we focus on fractions that do work, like halves, fourths, fifths, and twentieths.
Converting mixed numbers to decimals
A mixed number has a whole number part and a fraction part. To convert a mixed number to a decimal, keep the whole number the same, then convert the fraction part into a decimal. Write the whole number, then the decimal point, then the decimal part.
- 212 = 2.5 (because 12 = 0.5)
- 434 = 4.75 (because 34 = 0.75)
- 1710 = 1.7
- 59100 = 5.09 (the whole number is 5, and the fraction is nine hundredths)
- 358 → First convert 58 to 6251000 = 0.625, so 358 = 3.625
Be careful with mixed numbers like 37100. The decimal is 3.07, not 3.7. The fraction 7100 means zero tenths and seven hundredths.
Using place value to understand the conversion
Place value helps explain why fractions convert to decimals the way they do. The first place after the decimal is the tenths place (like denominator 10). The second place is the hundredths place (like denominator 100). The third place is the thousandths place (like denominator 1000).
- 0.8 = eight tenths = 810
- 0.45 = forty-five hundredths = 45100
- 0.207 = two hundred seven thousandths = 2071000
- 6.3 = 6310 (six and three tenths)
- 2.09 = 29100 (two and nine hundredths)
Reading decimals correctly helps with conversion. The decimal 0.3 is "three tenths," which directly points to the fraction 310. The decimal 0.03 is "three hundredths," which points to 3100.
Simplifying decimals after conversion
After converting a fraction to a decimal, you may have extra zeros at the end of the decimal. These zeros are called trailing zeros. They do not change the value of the decimal. You can remove them to write the decimal in simplest form.
- 310 = 0.30 = 0.3 (the zero after 3 is not needed)
- 410 = 0.40 = 0.4
- 1510 = 1.50 = 1.5
- 71000 = 0.007 (here the zeros are not trailing; they are placeholders and cannot be removed)
You can only remove zeros that come after all non-zero digits at the end of a decimal. For example, 0.500 = 0.5, but 0.05 cannot be simplified to 0.5 because that would change the value.
Common mistakes and how to avoid them
When converting fractions to decimals, fourth graders often make a few common mistakes. Learning about these mistakes helps you avoid them.
- Mistake: 5100 = 0.5 → Fix: Remember denominator 100 needs two decimal places: 0.05
- Mistake: 312 = 3.1 → Fix: Convert the fraction first: 12 = 0.5, so 3.5
- Mistake: 25 = 0.2 → Fix: Find an equivalent denominator: 25 = 410 = 0.4, not 0.2
- Mistake: 0.6 = 6100 → Fix: 0.6 is six tenths, so 610. Six hundredths would be 0.06
Always check: Does your decimal have the correct number of places? Does your mixed number keep the whole number correctly? Asking these questions will catch most errors.
Common Core alignment: CCSS.MATH.CONTENT.4.NF.C.6 – Use decimal notation for fractions with denominators 10 or 100. CCSS.MATH.CONTENT.4.NF.C.5 – Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with denominators 10 and 100.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.C.6 and CCSS.MATH.CONTENT.4.NF.C.5. All content is 100% free. Use it for whole-class instruction, independent study and practice, or homework. Students should already understand basic fraction concepts and place value through the thousandths place before beginning this lesson.