--- title: "Place value for decimals, measures and integers" description: "Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line" canonical: https://lightmysky.com/learn/mathematics/place-value-for-decimals-measures-and-integers-mt_PsylzZ9lHW source: https://lightmysky.com/learn/mathematics/place-value-for-decimals-measures-and-integers-mt_PsylzZ9lHW.md retrieved: 2026-09-02 --- > **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`. # Place value for decimals, measures and integers Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line Subject: Mathematics · Area: Number Representation & Place Value · Ages 11 to 12 Page: https://lightmysky.com/learn/mathematics/place-value-for-decimals-measures-and-integers-mt_PsylzZ9lHW ## Ready when they can - Identify the value of any digit in numbers of any size including decimals - Place positive and negative integers, decimals, and fractions on a number line - Use place value to compare and order numbers across the full number system ## Lesson: One number line, every kind of number A number line is not just for counting whole numbers. It can hold every kind of number you know: whole numbers, negative numbers, decimals, and fractions, all placed in order from smallest to largest. *(drawing: Zero sits in the middle. This jump starts at 0 and lands on -2.)* Every number has one exact spot on this line, and the order runs from left to right. Numbers to the left of zero are negative, and the further left you go, the smaller the number. That is why -8 is less than -2, even though 8 is bigger than 2. Reading left to right always gives you smallest to largest. After the decimal point, each place is ten times smaller than the one before: tenths, then hundredths, then thousandths. In 5.417 the 4 is 4 tenths, the 1 is 1 hundredth, and the 7 is 7 thousandths. To compare two decimals, line up the same places and read left to right. Tenths decide first, so 0.4 beats 0.35 even though 35 looks like the bigger number. *(drawing: 1/4 means one piece out of four equal pieces.)* A fraction fits between whole numbers too. The bottom number says how many equal pieces the space from 0 to 1 is cut into, and the top number says how many of those pieces you take. So 1/4 sits a quarter of the way along, closer to 0 than to 1. A fraction past the half way mark, like 5/8, sits closer to 1. **Tip.** Turn both numbers into the same form before you compare. A fraction like 1/2 is 0.5 as a decimal, and once both are decimals the place values line up. **Recap.** Every number, negative or positive, whole or fraction, has one exact spot on the number line, and place value tells you where it goes. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Reading and writing numbers to 10,000,000](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-10-000-000-mt_Gag_h98jWP) ## Opens up - [Fractions on a number line (age 11+)](https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-age-11-mt_uDJY0X0hgo)