--- title: "Decimals and fractions (age 10+)" description: "Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages i" canonical: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi source: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi.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`. # Decimals and fractions (age 10+) Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts Subject: Mathematics · Area: Fractions · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi ## Ready when they can - Convert between fractions and decimals using division, place value or equivalent fractions, and convert between decimals and percentages (for example, 3/8 = 0.375) - State that 1/5 = 0.2 = 20% from memory - Use equivalences between fractions, decimals and percentages to compare 30%, 1/3, and 0.35 and put them in order ## Lesson: Turning a fraction into a decimal You have used fractions to show division. Divide the top number by the bottom number: 3/8 means 3 ÷ 8. The decimal shows the same amount. Fractions can exceed one whole: 7 ÷ 2 gives 3 remainder 1. The remainder contributes 1/2 = 0.5, so 7/2 = 3.5. Compare whole-number parts first. After the decimal point, the first place is tenths, the second is hundredths and the third is thousandths. *(drawing: The shaded amount is 3/8 of one whole. Dividing 3 by 8 gives the same amount.)* **Example.** Write 3 as 3.000. Since 3 is less than 8, start with 0 and a decimal point. Divide 30 tenths by 8: 3 tenths, remainder 6 tenths. Regroup as 60 hundredths: 7 hundredths, remainder 4 hundredths. Regroup as 40 thousandths: 5 thousandths, no remainder. So 3 ÷ 8 = 0.375 exactly. Rounding gives an estimate if it changes the value. Rounding to three decimal places leaves 0.375 unchanged. Percent means out of 100. Divide a percentage number by 100 to write it as a decimal: 18% = 18/100 = 0.18. To write a decimal as a percentage, multiply by 100 and add %. For example, 0.375 = 37.5%. Remember the common equivalence 1/5 = 0.2 = 20%. Compare fractions, decimals and percentages by writing them as decimals. For 30%, 1/3 and 0.35, compare 0.30, 0.333... and 0.35. The dots mean the 3s keep repeating. Compare digits from left to right. Their hundredths digits are 0, 3 and 5, so 30% < 1/3 < 0.35. Writing 1/3 as 0.333 gives an estimate that leaves out the continuing 3s. To write a decimal as a fraction, read its place value. For example, 0.9 is nine tenths, or 9/10. A decimal with two places can be written over 100: 0.12 = 12/100. For simplest form, divide the top and bottom by the same common factor. Here, divide both by 4 to get 3/25. Stop when no whole-number factor greater than 1 divides both. You can also make an equivalent fraction with a denominator of 10 or 100. Multiply the top and bottom by the same number to keep the value equal. For 9/25, multiply both by 4: 9/25 = 36/100 = 0.36. **Recap.** A fraction is a division: work it out, and you get the matching decimal and percent. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Fractions of a whole (age 10+)](https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-10-mt_4Km38F4L-6) - [Percentage and decimal equivalents](https://lightmysky.com/learn/mathematics/percentage-and-decimal-equivalents-mt_4ubP_RMg9o) - [Decimal & Percent Notation](https://lightmysky.com/learn/mathematics/decimal-and-percent-notation-mt_W17Kbwm0-u) - [Decimals and fractions](https://lightmysky.com/learn/mathematics/decimals-and-fractions-mt_wB-GBDkoNr) - [Understanding Percentages](https://lightmysky.com/learn/mathematics/understanding-percentages-mt_ZM9mhHsyYZ) ## Opens up - [Using structure in shapes and expressions](https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh) - [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ) - [Decimals and fractions (age 11+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ)