Greater than less than checker, with the reason.

A greater than less than calculator tells you which of two numbers is bigger and which symbol to write between them. The symbol > means greater than, < means less than, and = means equal. 7 > 3 reads "seven is greater than three". The open side of the symbol always faces the bigger number, and the point faces the smaller one. This checker works with whole numbers, negatives, decimals, fractions, mixed numbers and percents, shows why the answer is right, and can also check a statement or sort a list.

How to use the checker

1. Type a number in First number and another in Second number. The answer updates as you type.
2. Read the big card for the symbol and the sentence, then the steps under Why and the number line.
3. To check a homework line such as 3/4 ≥ 0.75, pick the symbol under Check a statement. The checker says whether it is true, and if not, which symbol is right.
4. Click A list to put many numbers in order. Type them one per line, or with a comma and a space between them.
5. Swap them flips the two numbers, Copy result copies the line, and the symbol buttons copy a single sign to paste anywhere.

The six symbols

On a Mac with a US keyboard, Option and comma types ≤, Option and full stop types ≥, and Option and the equals key types ≠. In HTML, write &lt; &gt; &le; &ge; and &ne;.

Worked examples

• Whole numbers. 1234 and 1243 both have 4 digits, so compare from the left. The first two digits match, and at the tens place 3 is less than 4. So 1234 < 1243. A number with more digits is bigger: 99 < 100.
• Decimals. Is 0.5 or 0.45 bigger? Write both with 2 decimal places: 0.50 and 0.45. Now compare 50 and 45. 50 is greater, so 0.5 > 0.45. A longer decimal is not a bigger one.
• Negatives. −2 and −5 are both below zero. The one closer to zero is greater, so −2 > −5. Any positive number is greater than any negative number, and zero is greater than every negative.
• Fractions. To compare 3/4 and 5/8, use a common denominator. 4 and 8 both divide into 8. 3/4 = 6/8, and 6/8 > 5/8, so 3/4 > 5/8.
• Fraction against decimal. 1/3 and 0.33: 1/3 = 100/300 and 0.33 = 33/100 = 99/300. So 1/3 > 0.33. Both are about a third, but only one is exact.
• Mixed numbers. 2 1/2 is 5/2, so 2 1/2 = 5/2 and the answer is equal.
• Percents. 45% is 45/100 = 0.45, and 1/2 is 0.5, so 45% < 1/2.

Putting a list in order

In list mode the checker sorts the numbers and writes the symbols between them. Take 3/4, 0.7, 5/8, −2 and 45%. As decimals they are 0.75, 0.7, 0.625, −2 and 0.45. From smallest to greatest that gives −2 < 45% < 5/8 < 0.7 < 3/4. Two numbers with the same value get an equals sign between them. The table under the answer shows each number as a decimal so you can see why it sits where it does.

Exact or approximate

Whole numbers, decimals, fractions, mixed numbers, percents and scientific numbers are compared exactly. A sum with a root or pi, such as sqrt(2), cannot be written as an exact fraction, so it is compared as a decimal and the page says so. Two such results that agree to 12 digits count as equal.

Common problems

• A space in the middle of a number. Write a mixed number as 2 1/2, with one space. Two plain numbers side by side, such as 3 4, are refused.
• A comma inside a list. A comma followed by exactly three digits, as in 1,250, is read as a thousands comma. Use a comma and a space between list items, or a new line.
• A fraction with 0 underneath. Dividing by zero has no value, so the checker asks for a different number.

To work with fractions step by step use the fraction calculator, to turn a ratio into a percent use the percentage calculator, and for an average of a list try the average calculator.