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
1 · Read
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. After hundredths comes a third place, thousandths: 10 thousandths make 1 hundredth. In 0.405 there are 4 tenths, 0 hundredths and 5 thousandths.
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 do not change its value. 0.3 means 3 tenths. 0.30 means 3 tenths and 0 hundredths, and 0.300 adds 0 thousandths. The extra places hold nothing, so 0.3 = 0.30 = 0.300. Adding end zeros helps you line up the columns 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.
Two questions are adapted from Open Middle's 'Comparing Decimals 1' by Robert Kaplinsky, and one from Open Middle's 'Comparing Hundredths and Tenths 1' by Dean Johnstone and the Open Middle elementary team. One reading is adapted from a Khan Academy article, and the videos are Khan Academy videos. Terms for these sources are not recorded. All other questions and the second reading are original to this dataset.
2 · Watch
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