1. Anchor decimals to fractions first
Before any money, make sure a child knows that 0.1 is another way to write one tenth. Show the same amount three ways: 1/10, 0.1, and one slice of a strip cut into ten equal parts. The decimal point is just a marker that says 'the whole numbers stop here and the parts of one begin'.
If tenths as fractions are shaky, spend time there first. Decimals are an extension of place value to the right of the ones, and that idea has to be solid.
2. Bring in money as the everyday model
Now use dollars and cents. A dollar divides into 100 cents, so a cent is one hundredth of a dollar and ten cents is one tenth. This makes $0.10 and one tenth the same thing, and $0.01 and one hundredth the same thing. Children who freeze at '0.25' happily read '25 cents', so lean on that.
- 10 cents = $0.10 = one tenth of a dollar.
- 1 cent = $0.01 = one hundredth of a dollar.
- 25 cents = $0.25 = 25 hundredths = one quarter of a dollar.
- 50 cents = $0.50 = 5 tenths = half a dollar.
3. Read the place-value chart rightwards
Extend the place-value chart past the ones: ones, then the decimal point, then tenths, then hundredths. Take $3.45 and name each digit by its place: 3 whole dollars, 4 tenths of a dollar (that is 40 cents), and 5 hundredths of a dollar (5 cents). Together the 45 after the point is 45 cents. Naming the places out loud, not just reading 'three point four five', is what makes place value land.
4. Compare decimals by lining up the point
The classic error is thinking 0.45 is bigger than 0.5 because 45 is bigger than 5. Money kills this misconception fast: is 45 cents more than 50 cents? No. The fix is to line up the decimal points and pad with a zero so both have the same number of places.
- Compare 0.5 and 0.45. Write 0.5 as 0.50.
- Now compare 0.50 and 0.45, or 50 cents against 45 cents.
- 50 cents is more, so 0.5 is greater than 0.45.
5. Add and subtract with the points lined up
Adding and subtracting decimals is exactly like whole-number column arithmetic, with one rule: line up the decimal points, not the last digits, so tenths sit under tenths and hundredths under hundredths. Here is $2.75 plus $1.60:
- Line up the points. Hundredths: 5 plus 0 is 5. Tenths: 7 plus 6 is 13, so write 3 and carry 1 to the ones.
- Ones: 2 plus 1 plus the carried 1 is 4.
- Answer: $4.35. Sense-check it as $2.75 and $1.60 being a bit over four dollars.
6. Making change is decimal subtraction
Change from a note is just subtraction across the point, and it is a great real-world reason to get the method right. Say something costs $3.45 and you pay with a $5 note. Write $5.00 (pad the cents with zeros), then subtract:
- Line up the points and work right to left. Hundredths: 0 minus 5 needs regrouping.
- $5.00 minus $3.45 leaves $1.55, the change.
- Check by adding back: $3.45 plus $1.55 is $5.00.
Common mistakes to watch for
- Longer-is-larger: reading 0.45 as bigger than 0.5. Pad with a zero and compare like money.
- Lining numbers up by the last digit instead of by the decimal point when adding or subtracting.
- Saying 'point four five' without ever naming it as 4 tenths and 5 hundredths, so place value never sticks.
- Assuming multiplying always makes a number bigger. Half of 8 is 4, so 0.5 times 8 is 4.
Free decimals and money practice
SproutSheets makes printable decimals and money worksheets with answer keys computed in code, so they are never wrong. Generate a sheet that matches exactly where a child is, from naming tenths and hundredths to adding money and making change, in seconds.