Comparing decimals
Comparing decimals follows the same digit-by-digit-from-the-left rule as whole numbers. The catch is making sure the decimal points line up before you start.
Step 1: line up the points
Write the two decimals so the decimal points are directly above each other. Add trailing zeros to the shorter one so they have the same number of places.
Compare 0.6 and 0.58
| Tenths | Hundredths |
| 6 | 0 |
| 5 | 8 |
We pad 0.6 to 0.60 so both numbers have hundredths.
Step 2: compare from left
Tenths first: 6 > 5. So 0.6 > 0.58.
Even though "58" looks bigger than "6", the tenths place is the more important one. Always start there.
Step 3: only break ties further right
When the tenths match, look at hundredths.
Compare 0.34 and 0.37
Tenths: 3 = 3. Move on.
Hundredths: 4 < 7. So 0.34 < 0.37.
A common trap
Children often think "more digits = bigger number". For whole numbers that's true (1 000 > 999), but for decimals it's not:
0.7 vs. 0.65
0.65 has more digits, but 0.7 is bigger! Add a zero: 0.70 vs. 0.65. Now compare hundredths: 70 > 65 (in the same way you'd compare 70 and 65 as whole numbers).
Ordering a list
Take a list of decimals and put them in order from smallest to largest.
0.4, 0.38, 0.5, 0.408
Pad them all to the same number of decimal places:
| 0.400 | 0.380 | 0.500 | 0.408 |
Now compare like whole numbers (400, 380, 500, 408). Order them:
0.38 < 0.4 < 0.408 < 0.5
Notice that 0.4 = 0.400 and 0.408 differ only in the hundredths place — they're very close on the number line.
Equal decimals in disguise
Two decimals can look different but be equal. Adding zeros at the end doesn't change the value.
0.5 = 0.50 = 0.500
This isn't a comparison error — it's a different way of writing the same number.