Fractions and Decimals — How They Connect
A parent- and student-friendly walkthrough of the 8 core ideas that link fractions and decimals, with 20 practice questions and hidden step-by-step answers. Best for grades 3–6 (or any older student who never felt sure about this topic).
Class plan (about 45 minutes):
- Read the 8 core ideas below — pause after each one to try an example on paper.
- Try the 20 questions on your own without clicking to reveal the answer first.
- Only click "Show answer" after you have a written answer to compare.
- If your answer is wrong, look at the strategy tag on the answer and re-read that section.
Table of contents
- 1. One number, two costumes
- 2. Decimals are place value pushed to the right
- 3. The fraction bar means divide
- 4. Fractions with denominators of 10, 100, 1000 are the easiest
- 5. Turn any fraction into a /10, /100, or /1000
- 6. Both live on the same number line
- 7. To compare, put them in the same clothes
- 8. Decimal → fraction: read it, write it, reduce it
- Strategy cheat sheet
- 20 practice questions
- Answer key summary
- Common questions from parents
Why fractions and decimals are the same idea
Most children learn fractions in one grade and decimals in a different grade — and no one ever tells them they are talking about the same numbers. Here is the whole idea in one sentence:
A fraction is a division problem waiting to happen. A decimal is the answer to that division.
Once a student really believes that, everything else in this post is just practice.
1. One number, two costumes
A fraction and a decimal can be the same number — just written differently.
The most important idea to teach first is that fractions and decimals are two ways to write the same number. There is no "converting" happening — you're just changing the outfit.
1/2 = 0.5 = 0.50 = 50/100 2/4 = 1/2 = 0.5 3/10 = 0.3 7/100 = 0.07The fraction bar says "divide the top by the bottom." A decimal is just what pops out of that division.
2. Decimals are place value pushed to the right
Everything to the right of the decimal point is a fraction with a denominator of 10, 100, 1000...
Kids already know place value going left: ones, tens, hundreds, thousands. Decimals just keep the same pattern going right, but each step divides by 10 instead of multiplying.
Tens Ones . Tenths Hundredths Thousandths 10 1 . 1/10 1/100 1/1000 0.1 0.01 0.001So 0.347 means:
0.3 = 3/10 0.04 = 4/100 0.007 = 7/1000 Total = 347/1000Once a child sees the "1/10, 1/100, 1/1000" columns, decimal numbers stop being scary.
3. The fraction bar means divide
3/4 literally means 3 ÷ 4. Do the division and you get the decimal.
This one rule turns every fraction into a decimal instantly — as long as the child can divide.
3/4 → 3 ÷ 4 = 0.75 1/8 → 1 ÷ 8 = 0.125 7/10 → 7 ÷ 10 = 0.7 1/3 → 1 ÷ 3 = 0.333... (repeats)Some divisions end cleanly (called terminating decimals), and some go on forever with a repeating pattern (called repeating decimals). Both are valid decimals.
4. Fractions with denominators of 10, 100, 1000 are the easiest
If the denominator is already a power of 10, no division needed — just read the place value.
The fastest fraction→decimal conversion happens when the bottom number is already 10, 100, or 1000.
3/10 = 0.3 (three tenths) 27/100 = 0.27 (twenty-seven hundredths) 9/100 = 0.09 (nine hundredths — the 0 holds the tenths place) 143/1000 = 0.143 (one hundred forty-three thousandths)The rule: count the zeros in the denominator. That's how many digits go after the decimal point. If the top number is shorter, pad with zeros just to the right of the decimal point.
5. Turn any fraction into a /10, /100, or /1000
If the denominator divides evenly into 10, 100, or 1000, scale the fraction up.
Some fractions look hard but are secretly friendly. Ask: can I multiply the denominator by something to get 10, 100, or 1000?
1/2 → ×5/5 → 5/10 = 0.5 3/4 → ×25/25 → 75/100 = 0.75 7/20 → ×5/5 → 35/100 = 0.35 9/25 → ×4/4 → 36/100 = 0.36Denominators that scale to a power of 10: 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. These all give terminating decimals.
Denominators that don't scale: 3, 6, 7, 9, 11, 12, 13, ... These give repeating decimals.
6. Both live on the same number line
Sliding a fraction and its decimal onto the number line proves they're the same point.
Draw a number line from 0 to 1. Mark thirds. Mark halves. Mark tenths. Mark hundredths. Kids see with their own eyes that 1/2 and 0.5 land on the exact same tick.
0 ────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬──── 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/2 also lives here ↑Number-line practice is the single best cure for the "decimals are bigger than fractions because they have more digits" misconception.
7. To compare, put them in the same clothes
Convert both to decimals — or convert both to fractions with the same denominator.
Is 3/8 bigger than 0.4? You can't tell by looking. But convert both:
3/8 = 0.375 0.4 = 0.400 So 0.4 > 3/8Or keep everything in fraction form:
3/8 = 15/40 0.4 = 4/10 = 16/40 So 0.4 > 3/8Whichever form your child is more comfortable in, use that. The trick is same clothes: same denominator, or same decimal-place count.
8. Decimal → fraction: read it, write it, reduce it
Say the decimal out loud. What you hear is the fraction.
To go from decimal back to fraction, say the number out loud using place-value words.
0.7 = "seven tenths" = 7/10 0.25 = "twenty-five hundredths" = 25/100 = 1/4 0.125 = "one hundred twenty-five thousandths" = 125/1000 = 1/8 0.6 = "six tenths" = 6/10 = 3/5Then reduce the fraction to lowest terms by dividing top and bottom by the same number. Kids should learn to spot 2, 5, and 10 as the most common divisors.
Strategy cheat sheet
Use this table to pick the fastest strategy in 2 seconds.
| Situation | Strategy | Example |
|---|---|---|
| Denominator is 10, 100, or 1000 | Read place value directly | 17/100 → 0.17 |
| Denominator is 2, 4, 5, 8, 20, 25, 50 | Scale up to /10, /100, or /1000 | 3/4 = 75/100 = 0.75 |
| Denominator is 3, 6, 7, 9, 11, 12 | Divide top ÷ bottom (long division) | 1/3 = 0.333... |
| Decimal → Fraction | Say it out loud, then reduce | 0.6 = 6/10 = 3/5 |
| Compare a fraction and a decimal | Turn both into decimals | 3/8 = 0.375 vs 0.4 |
| Adding a fraction and a decimal | Convert one so both match | 1/2 + 0.3 = 0.5 + 0.3 = 0.8 |
20 practice questions
Try each one on paper first. Then click "Show answer" to check.
Question 1
Write 7/10 as a decimal.
Answer: 0.7 Denominator = 10
Seven tenths. The 7 sits in the tenths place, right after the decimal point. 7/10 = 0.7
Question 2
Write 23/100 as a decimal.
Answer: 0.23 Denominator = 100
Twenty-three hundredths. Two digits after the decimal point (because 100 has 2 zeros). 23/100 = 0.23
Question 3
Write 0.9 as a fraction.
Answer: 9/10 Read the decimal
Say it out loud: "nine tenths." That's the fraction. 0.9 = 9/10
Question 4
Write 0.41 as a fraction.
Answer: 41/100 Read the decimal
Say it out loud: "forty-one hundredths." Two decimal digits = /100. 0.41 = 41/100
Question 5
Write 3/100 as a decimal.
Answer: 0.03 Denominator = 100
Because 100 has two zeros, we need two decimal digits. The 3 goes in the hundredths place; pad with a zero in the tenths place. 3/100 = 0.03
Question 6
Write 1/2 as a decimal.
Answer: 0.5 Scale to /10
Multiply top and bottom by 5 to get a friendly denominator of 10. 1/2 = (1×5)/(2×5) = 5/10 = 0.5
Question 7
Write 0.6 as a fraction in simplest form.
Answer: 3/5 Read + reduce
Say it: "six tenths" = 6/10. Now divide top and bottom by 2 to reduce. 0.6 = 6/10 = (6÷2)/(10÷2) = 3/5
Question 8
Write 3/4 as a decimal.
Answer: 0.75 Scale to /100
Multiply top and bottom by 25 so the denominator becomes 100. 3/4 = (3×25)/(4×25) = 75/100 = 0.75 Or use the division rule: 3 ÷ 4 = 0.75.
Question 9
Write 7/20 as a decimal.
Answer: 0.35 Scale to /100
Multiply top and bottom by 5 to get a denominator of 100. 7/20 = (7×5)/(20×5) = 35/100 = 0.35
Question 10
Write 9/25 as a decimal.
Answer: 0.36 Scale to /100
Multiply top and bottom by 4 to reach /100. 9/25 = (9×4)/(25×4) = 36/100 = 0.36
Question 11
Write 0.25 as a fraction in simplest form.
Answer: 1/4 Read + reduce
Say it: "twenty-five hundredths" = 25/100. Divide top and bottom by 25. 0.25 = 25/100 = 1/4
Question 12
Which is larger: 2/5 or 0.35?
Answer: 2/5 Compare — same clothes
Convert 2/5 to a decimal: 2/5 = 4/10 = 0.40. 0.40 vs 0.35 0.40 > 0.35, so 2/5 is larger.
Question 13
Which is larger: 3/8 or 0.4?
Answer: 0.4 Compare — same clothes
3/8 = 3 ÷ 8 = 0.375. Now compare in decimal form. 0.375 vs 0.400 0.400 > 0.375, so 0.4 is larger.
Question 14
Place 1/4, 0.3, and 2/5 in order from smallest to largest.
Answer: 1/4, 0.3, 2/5 Convert all to decimals
Turn every number into a decimal so they're comparable. 1/4 = 0.25 0.3 = 0.30 2/5 = 0.40 Order: 0.25 < 0.30 < 0.40
Question 15
Write 1/3 as a decimal.
Answer: 0.333... (repeating) Divide top by bottom
The denominator 3 doesn't scale to a power of 10, so we divide. 1 ÷ 3 = 0.3333... Sometimes written 0.3̄ (bar over the 3) to show it repeats.
Question 16
Write 1/8 as a decimal.
Answer: 0.125 Scale to /1000
Multiply top and bottom by 125 to reach a denominator of 1000. 1/8 = (1×125)/(8×125) = 125/1000 = 0.125 Or divide: 1 ÷ 8 = 0.125.
Question 17
Write 2 3/4 (two and three-fourths) as a decimal.
Answer: 2.75 Whole part + fraction part
Keep the whole number, convert only the fraction part. 2 + 3/4 = 2 + 0.75 = 2.75
Question 18
A pizza is cut into 8 equal slices. Two friends eat 3 slices. What decimal of the pizza did they eat?
Answer: 0.375 Fraction → decimal
Three out of eight slices = 3/8. Convert to a decimal. 3/8 = 3 ÷ 8 = 0.375 So they ate 0.375 of the pizza (a bit more than 1/3).
Question 19
Compute 1/2 + 0.3. Give your answer as a decimal.
Answer: 0.8 Convert, then add
Put them in the same clothes before adding. 1/2 = 0.5 0.5 + 0.3 = 0.8
Question 20
A recipe calls for 3/4 cup of milk. You already poured 0.5 cup. How much more milk do you need? Give the answer as a fraction.
Answer: 1/4 cup Convert, subtract, convert back
Turn both into the same form, subtract, then simplify. 3/4 = 0.75 0.75 − 0.50 = 0.25 0.25 = 25/100 = 1/4 cup
Answer key summary
| # | Answer | Strategy |
|---|---|---|
| 1 | 0.7 | Denominator = 10 |
| 2 | 0.23 | Denominator = 100 |
| 3 | 9/10 | Read the decimal |
| 4 | 41/100 | Read the decimal |
| 5 | 0.03 | Denominator = 100 |
| 6 | 0.5 | Scale to /10 |
| 7 | 3/5 | Read + reduce |
| 8 | 0.75 | Scale to /100 |
| 9 | 0.35 | Scale to /100 |
| 10 | 0.36 | Scale to /100 |
| 11 | 1/4 | Read + reduce |
| 12 | 2/5 | Compare — same clothes |
| 13 | 0.4 | Compare — same clothes |
| 14 | 1/4, 0.3, 2/5 | Convert all to decimals |
| 15 | 0.333... (repeating) | Divide top by bottom |
| 16 | 0.125 | Scale to /1000 |
| 17 | 2.75 | Whole part + fraction part |
| 18 | 0.375 | Fraction → decimal |
| 19 | 0.8 | Convert, then add |
| 20 | 1/4 cup | Convert, subtract, convert back |
Want your child in a Kid Einsteins class at SOMATH?
Grades 3–4 program (ages 8–10). Multiplication mastery, long division, fractions and decimals, geometric reasoning with area and perimeter, and multi-step word problems — the core of upper-elementary math.
Common questions from parents
At what grade should my child learn to switch between fractions and decimals?
Most curricula introduce the fraction–decimal connection in 4th grade (Common Core 4.NF.5–7) and expect students to be fluent by the end of 5th grade. At SOMATH we begin the connection earlier — Kid Einsteins (grades 1–2) already meet halves and tenths on the number line, so the idea feels familiar long before formal conversion appears.
Why does 1/3 give a repeating decimal but 1/4 does not?
Any fraction whose denominator (in lowest terms) has only 2s and 5s as prime factors will terminate — because 2 and 5 are the prime factors of 10. Denominators with other primes (like 3, 7, 9, 11) will repeat. So 1/4 = 0.25 (terminates) but 1/3 = 0.333… (repeats) and 1/7 = 0.142857142857… (repeats).
Which is bigger, 0.5 or 0.50?
They are exactly equal. Adding zeros to the right of a decimal does not change its value — it just changes how you're counting. 0.5 = 0.50 = 0.500 = 0.5000 all name the same point on the number line.
My child says 0.6 is smaller than 0.60 because 6 < 60. What do I do?
This is one of the most common misconceptions. Fix it two ways: (1) draw both on a number line and show they land on the same tick; (2) rewrite them as fractions — 0.6 = 6/10 and 0.60 = 60/100, which reduces to 6/10. Same number.
What is the fastest way to memorize the common fraction-decimal pairs?
Focus on the halves, fourths, fifths, eighths, and tenths — these cover 90% of school and real-world problems. The core dozen: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, and 1/10 = 0.1. Drill these until they are automatic.
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