--- title: "Comparing Decimals" description: "Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <" canonical: https://lightmysky.com/learn/mathematics/comparing-decimals-mt_933BohS9BH source: https://lightmysky.com/learn/mathematics/comparing-decimals-mt_933BohS9BH.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Comparing Decimals Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, < Subject: Mathematics · Area: Fractions · Ages 9 to 10 Page: https://lightmysky.com/learn/mathematics/comparing-decimals-mt_933BohS9BH ## Ready when they can - 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 ## Lesson: Comparing Decimals 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. **Example.** 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. *(drawing: 0.45 is 450 thousandths and 0.405 is 405 thousandths, so the bar for 0.45 is taller.)* 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. **Example.** 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. **Recap.** Compare decimals column by column from the left, and remember that extra end zeros never change the value. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Comparing two-decimal numbers](https://lightmysky.com/learn/mathematics/comparing-two-decimal-numbers-mt_IegHBHERVa) - [Thousandths (age 9+)](https://lightmysky.com/learn/mathematics/thousandths-age-9-mt_kdWoAel3Zl) ## Opens up - [Reading and writing numbers (age 10+)](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-age-10-mt_Ac7oMWhyPw) - [Decimals to three places](https://lightmysky.com/learn/mathematics/decimals-to-three-places-mt_sA2OvTiech)