How to Teach Decimals (Connecting Fractions to Place Value)
Decimals confuse children because they look like a new kind of number with unfamiliar rules. But decimals are not new. They are fractions written in place value form. 0.5 is 5/10 is one half. 0.25 is 25/100 is one quarter.
When a child understands both fractions and place value, decimals are just the place where those two concepts meet. Here is how to make that connection visible.
The big idea: extending place value
Your child already knows the place value pattern:
- Hundreds → Tens → Ones
Each place is worth 10 times less than the one to its left:
- 100 ÷ 10 = 10
- 10 ÷ 10 = 1
What is 1 ÷ 10? One tenth. And one-tenth of a tenth? One hundredth.
- Ones → Tenths → Hundredths
The decimal point just marks where the whole-number places end and the fractional places begin.
Key Insight: The decimal point does not create a new system. It continues the same pattern your child has used since learning place value: each place to the right is worth one-tenth as much. Hundreds, tens, ones, tenths, hundredths — same rule, same pattern.
Start with money
Money is the most familiar decimal system:
- $1.00 = 1 dollar
- $0.10 = 1 dime = one-tenth of a dollar
- $0.01 = 1 penny = one-hundredth of a dollar
"$0.50 means 50 cents, which is 50 hundredths, which is also 5 tenths, which is also one half of a dollar."
Use actual coins:
- "How many dimes make a dollar? 10. So one dime is one-tenth of a dollar: 0.1."
- "How many pennies make a dollar? 100. So one penny is one-hundredth: 0.01."
- "How many pennies make a dime? 10. So one penny is one-tenth of a dime."
The money model makes tenths and hundredths tangible.
Connect to fractions
Make the fraction-decimal connection explicit:
| Fraction | Decimal | In words |
|---|---|---|
| 1/10 | 0.1 | one tenth |
| 3/10 | 0.3 | three tenths |
| 1/4 | 0.25 | twenty-five hundredths |
| 1/2 | 0.5 | five tenths |
| 3/4 | 0.75 | seventy-five hundredths |
| 1/100 | 0.01 | one hundredth |
"0.3 and 3/10 are two ways of writing the same number. The fraction uses a denominator to show the piece size. The decimal uses place value."
Use number lines
Place decimals on a number line between whole numbers:
Interactive Demo
Fractions on a Number Line
Where does 0.5 go? Exactly halfway between 0 and 1. Where does 1.7? Between 1 and 2, closer to 2. The number line helps children see that decimals are just more precise positions on the same line they already know.
Comparing decimals
The most common mistake: "0.15 is bigger than 0.3 because 15 is bigger than 3."
This is a place value error. Use the money model:
- 0.15 = 15 cents
- 0.3 = 30 cents
- "Which would you rather have, 15 cents or 30 cents?"
Or use the place value chart:
- 0.15 = 0 ones, 1 tenth, 5 hundredths
- 0.3 = 0 ones, 3 tenths, 0 hundredths
- Compare tenths first: 3 tenths > 1 tenth. Done.
Key Insight: Comparing decimals uses the same strategy as comparing whole numbers: start at the leftmost place and compare. The child who already knows how to compare 300 vs. 150 can compare 0.3 vs. 0.15 — if they understand that each decimal digit has a place value.
Adding and subtracting decimals
The key rule: line up the decimal points, then add or subtract as usual.
2.45
+ 1.30
------
3.75
This works because lining up decimal points means lining up place values — tenths with tenths, hundredths with hundredths. It is the same as aligning ones, tens, and hundreds in whole-number addition.
Common decimal mistakes
Treating decimals like whole numbers (0.15 > 0.3): Place value understanding for decimals is not solid. Go back to the money model.
Ignoring the decimal point when computing: They add 2.4 + 1.35 and get 3.39 instead of 3.75. They forgot to align place values.
Thinking 0.50 is different from 0.5: "0.50 has more digits so it must be bigger." Explain: 0.50 = 50 hundredths = 5 tenths = 0.5. Just like $0.50 is the same as $0.5.
Confusing tenths and hundredths: They write "three hundredths" as 0.3 instead of 0.03. Drill the place names: first decimal place is tenths, second is hundredths, third is thousandths.
Decimals are not a separate topic from fractions or place value. They are the intersection of both. When your child sees that 0.5 = 5/10 = 1/2 and that the tenths place is just one step right of the ones place, decimals become an extension of what they already know — not something new to learn.
If you want a system that connects decimals to fractions and place value automatically — and verifies the connections are solid before moving to decimal operations — that is what Lumastery does.