Comparing Decimals
Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
What a learner can do afterwards
- Compare 0.45 and 0.405 and explain which is greater
- Order 3.142, 3.14, 3.2 from smallest to largest
- Justify that 0.7 = 0.70 = 0.700 using place-value reasoning
The lesson
To compare two decimals, look at the digits in the same place-value column, starting from the left. Compare the ones first, then the tenths, then the hundredths, and so on. The first column where the digits differ tells you which decimal is bigger.
Compare 0.45 and 0.405. Both have 0 ones, so that's a tie. Both have 4 tenths, another tie. Now check the hundredths: 0.45 has 5 hundredths, but 0.405 has 0 hundredths. Since 5 is more than 0, 0.45 is greater. We write it as 0.45 > 0.405.
Zeros at the end of a decimal don't change its value. 0.7, 0.70, and 0.700 are all the same amount, just written with extra placeholder zeros. Adding zeros at the end can help you line up columns fairly before you compare.
Order 3.142, 3.14, and 3.2 from smallest to largest. Write them with the same number of decimal places: 3.142, 3.140, 3.200. The ones match at 3. The tenths are 1, 1, and 2, so 3.2 is the largest. Between 3.142 and 3.140, the hundredths match at 4, so check the thousandths: 2 beats 0. The order is 3.14, 3.142, 3.2.
Compare decimals column by column from the left, and remember that extra end zeros never change the value.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.