A decimal is just another way to write a number that falls between whole numbers, using place value instead of a fraction bar. Once you know what each place is worth, comparing and ordering decimals is easy.
The decimal point separates the whole-number part of a number from its fractional part. Every place to the right of the decimal point is 10 times smaller than the one before it.
In 3.475, the digit 4 is in the tenths place, 7 is in the hundredths place, and 5 is in the thousandths place. You can read this number two ways: digit by digit as "three point four seven five," or by place value as "three and four hundred seventy-five thousandths."
A price tag of $3.47 uses decimals for dollars and cents. A sprinter's time of 9.58 seconds uses decimals for fractions of a second. A recipe calling for 2.5 cups of flour uses decimals for a partial amount.
A helpful trick: adding zeros to the end of a decimal never changes its value. 3.4, 3.40, and 3.400 are all exactly the same amount — they're just written with different numbers of place-value columns filled in.
To compare two decimals, line up the decimal points and compare one place at a time, starting from the left (the ones place). Move right place by place until you find digits that are different — whichever number has the bigger digit in that place is the bigger number.
These don't have the same number of decimal places, so it's hard to compare them directly. Line them up by adding a zero to 3.5 — remember, adding a zero to the end doesn't change its value.
The ones digits match (3 = 3). The tenths digits are different: 4 vs 5. Since 5 is bigger than 4, 3.50 is greater than 3.45 — even though 3.45 looks like it has "more" digits before lining them up.
More digits after the decimal point does not mean a bigger number. 0.9 is greater than 0.15, because in the tenths place, 9 beats 1. Always compare place by place — don't just compare the numbers as if the decimal point wasn't there.
Pick <, =, or > to compare the two decimals.
Ordering a whole list of decimals uses the exact same skill as comparing two — just applied over and over. Line up the decimal points for every number, then find the smallest by comparing place by place. Set that one aside, and repeat with what's left.
Imagine every number written with the same number of decimal places, padding with zeros if needed.
Compare the ones digits across all the numbers first. If there's a tie, move to the tenths, then hundredths.
Pull out the number you just found, then repeat the comparison with the numbers that are left.
Lined up as 2.70, 2.07, 2.71, 2.10 — the ones digits all match (2), so compare tenths: 0.7, 0.0, 0.7, 0.1. The smallest tenths digit is 0, so 2.07 comes first. Next smallest tenths digit is 1, so 2.1 is second. That leaves 2.7 and 2.71 tied on tenths (7) — comparing hundredths, 2.70 comes before 2.71. Least to greatest: 2.07, 2.1, 2.7, 2.71.
Click the smallest remaining number each time. It will drop into the next slot below.