“0.75 is bigger than 0.8 because 75 is bigger than 8.” If your child gives that answer, ask them what the 8 represents. Their explanation gives you somewhere useful to begin.
Try this short conversation when decimals appear in homework. You will need a pencil and enough space to draw three columns. The examples and parent prompts below are Genie's suggestions for practising at home.
Name what each digit is worth
Write 0.8 and ask, “Eight of what?” The first place to the right of the decimal point is the tenths place, so 0.8 means eight tenths. The next place is the hundredths place. In 0.75, the 7 represents seven tenths and the 5 represents five hundredths.
One tenth equals ten hundredths. That means eight tenths can also be written as eighty hundredths: 0.8 = 0.80. The extra zero records zero additional hundredths.
| Number | Ones | Tenths | Hundredths |
|---|---|---|---|
| 0.80 | 0 | 8 | 0 |
| 0.75 | 0 | 7 | 5 |
Start at the greatest place value and move right. Both numbers have zero ones. In the tenths column, 8 is greater than 7, so 0.8 is greater than 0.75. You can also compare eighty hundredths with seventy-five hundredths.
If your child says “I just added a zero”, follow up with “Why is the value still the same?” Listen for an explanation about tenths and hundredths. Give them time to draw or point to the columns.
Check where the zero goes
Now write 0.08 beside 0.8. Ask your child to place both numbers in the table. In 0.08, there are zero tenths and eight hundredths. In 0.8, there are eight tenths. The 8 has moved into a different place, so the values differ.
Keep this distinction precise. Adding a zero at the end of the decimal part gives an equivalent number, as in 0.8 and 0.80. Inserting a zero before the 8 gives 0.08 and changes its value.
A familiar money example can help: $0.80 is eighty cents, while $0.08 is eight cents. Ask your child to return to the tenths and hundredths explanation after discussing the money, so the reasoning also works for numbers outside a price label.
Use the same columns when adding
Try 0.6 + 0.25. Before working it out, ask whether the answer should be greater or smaller than 0.6. Since you are adding a positive amount, it must be greater.
Write 0.6 as 0.60. Put the decimal points directly beneath each other. This lines up ones with ones, tenths with tenths and hundredths with hundredths.
0.60 + 0.25 ────── 0.85
There are five hundredths altogether and eight tenths altogether. Another explanation is sixty hundredths plus twenty-five hundredths, giving eighty-five hundredths. The answer, 0.85, is greater than 0.6, as expected.
If the written columns drift, draw the place-value headings again. Squared paper can help keep one digit in each column. Ask your child to name the column they are adding before they calculate it.
Try three questions together
Let your child explain one at a time. Offer the table if they need it, then compare their reasoning with the answers.
- Which is greater, 1.2 or 1.08? Explain using place values.
- Work out 0.09 + 0.3. Show where the 3 belongs.
- A friend says 0.4, 0.40 and 0.04 all have the same value. Which two are equal, and why?
Open the answers and explanations
1. 1.2 is greater. Both have one whole, but 1.2 has two tenths and 1.08 has zero tenths. Writing 1.2 as 1.20 also lets you compare twenty hundredths with eight hundredths after the one whole.
2. 0.09 + 0.30 = 0.39. The 3 belongs in the tenths column. Nine hundredths plus thirty hundredths gives thirty-nine hundredths.
3. 0.4 and 0.40 are equal: four tenths is forty hundredths. 0.04 is four hundredths, so it has a different value.
Choose the next step from the explanation
If your child can calculate the sum but cannot explain 0.6 = 0.60, return to one comparison with the table. If they can explain both, put the table aside and try a fresh pair, such as 0.5 and 0.47. Ask which place settles the comparison.
For a later practice session, our read, cover, try routine shows how to revisit a worked example. If your child gets stuck, the one-hint homework guide offers ways to help them take the next step.
Further reading. The Open University's explanation of decimal place value and OpenStax's guides to decimals and decimal addition provide background on the mathematics used here. The practice questions and parent prompts are our own.