Definition
Decimal comparison
Decimal comparison decides whether one decimal number is greater than, less than, or equal to another.
What it means
Check first whether either number is negative. For non-negative decimals, start with the largest place. If the whole-number parts are equal, compare tenths, then hundredths, then thousandths; the first place that differs decides. Adding trailing zeros can make the places easier to see without changing value. For two negative decimals, the one closer to zero is greater.
Remember it
Check the sign, then the first different place; with two negatives, closer to zero is greater.
Example
Compare 3.405 and 3.450. Both have 3 ones and 4 tenths. At the hundredths place, 0 hundredths is less than 5 hundredths, so 3.405 < 3.450. There is no need to compare the thousandths after that.
Watch for
In a measurement or part-of-a-whole context, first make sure the values use the same unit or refer to the same whole.
Common mix-up
A decimal with more digits is not automatically larger: 0.72 is greater than 0.7 because 0.72 = 0.720 and 72 hundredths is greater than 70 hundredths.
Exact meaning
Decimal comparison determines the order or equality of numbers written in decimal notation. Any non-negative decimal is greater than any negative decimal. For non-negative decimals, compare digits from the greatest place value left to right, treating missing trailing places as zeros. For two negative decimals, the number closer to zero is greater.