Suppose you ask a student to compare 0.508 and 0.58. They point to 0.508: “That one’s larger because 508 is larger than 58.” Try asking, “What’s the value of the five in each number?” Then work through the other places together. You’re listening for how they’re comparing the numbers, rather than just whether they choose the right symbol.
Compare the same places
Try this walkthrough with the pair. Write 0.58 as 0.580; adding a zero at the end of its decimal part leaves its value unchanged. Place the numbers in a table so matching places sit together.
| Number | Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 0.508 | 0 | 5 | 0 | 8 |
| 0.580 | 0 | 5 | 8 | 0 |
The ones match. The tenths match too. At the hundredths, they differ: zero hundredths in 0.508 and eight hundredths in 0.580. So 0.508 < 0.580.
Could the final eight change that result? Ten lots of 0.001 equal 0.01, or one hundredth. After the shared five tenths, the first number has only eight thousandths; the second has eight hundredths. Eight thousandths is still less than eight hundredths, so the later digit can’t change the result.
This applies the base-ten relationships in the Mathematics Hub’s place-value guidance. Comparing beyond two decimal places is part of Year 5 mathematics.
Ask for the reason as well
The two sample pages below come from Decimals to Thousandths – Year 5. Start with Compare Decimals to put the place-by-place explanation to work.
The page has twelve comparisons using <, > or =, then asks students to explain why 2.090 > 2.009 and 0.670 = 0.67. Its footer reminds them to align decimal points and compare from left to right.
For an added spoken prompt, ask students to name the first different place before choosing a symbol. In 2.090 and 2.009, it’s the hundredths. Give them time to explain: the Mathematics Hub’s questioning guidance recommends focused questions and time to respond.
Which zero can go?
In 0.670, there are six tenths, seven hundredths and zero thousandths. Removing the final zero leaves those values unchanged, so 0.670 = 0.67.
Now compare 5.060 and 5.6. The six represents hundredths in the first number and tenths in the second, so 5.060 < 5.6. Removing only the final zero gives 5.06, which preserves the value. Removing the zero between the decimal point and the six moves that six into the tenths place. That zero is holding a place; it can’t simply disappear without changing the number.
Put the zero explanation to work
The page opens with 2.300 in a place-value table. Students complete equivalent decimals, judge true-or-false statements and circle every value equal to 2.3. The correct selections are 2.30 and 2.300.
They then explain why 0.8 = 0.80 and correct Kai’s statement that 5.060 = 5.6. Afterwards, try asking, “Which digit changes place if that zero disappears?” It gives students something specific to examine when a rule such as “zeros don’t matter” stops working.
Return to the opening pair: “Which places match, and where do the values first differ?” If the explanation still compares 508 with 58, revisit the table and name each digit’s value. If that reasoning is clear, move to the printed zero examples. Use the response to choose the next teaching step; one answer won’t tell you everything.