Compare Numbers
The calculator compares whole numbers and decimals, positive and negative, and explains step by step which number is greater.
First number:
x
Second number:
x
The number comparison calculator compares whole numbers and decimals, positive and negative, and explains why one number is greater than the other: by the number of digits, by the first different digit or by the sign.
Comparison signs
| Sign | Read as | Example |
|---|---|---|
| > | greater than | 7 > 3 |
| < | less than | 3 < 7 |
| = | equal to | 2.50 = 2.5 |
Tip: the open side of the sign always faces the greater number.
How to compare whole numbers
- The number with more digits is greater: 1000 > 999.
- If the numbers have the same number of digits, compare them place by place from left to right. The number with the greater first different digit is greater: 5721 > 5699.
How to compare decimals
- First compare the whole parts.
- If the whole parts are equal, make the number of decimal places equal by adding zeros on the right, then compare the decimal parts place by place.
Example. Compare 3.45 and 3.405.
The whole parts are equal. Add a zero: 3.450 and 3.405.
The first different digit is in the hundredths place: 5 > 0.
Answer: 3.45 > 3.405
A common mistake is to think that 3.405 is greater because "it has more digits". For the decimal part the number of digits does not matter; only the digit in each place does.
How to compare negative numbers
- Any positive number is greater than zero, and zero is greater than any negative number: 0.1 > 0 > −100.
- Of two negative numbers, the one with the smaller absolute value is greater, that is, the one closer to zero on the number line: −5.19 > −5.2, −3 > −12.