---
title: "Decimals and fractions (age 11+)"
description: "Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms"
canonical: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ
source: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ.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 11+)

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms

Subject: Mathematics · Area: Fractions · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ

## Ready when they can

- Convert any terminating decimal to a fraction in simplest form
- Convert any fraction with a denominator whose prime factors are only 2 and 5 to a terminating decimal
- Explain why some fractions produce terminating decimals and others do not

## Lesson: Decimals and fractions, fluently both ways

You already know decimals and fractions can name the same number. Now you'll convert between them for any terminating decimal, simplify the fraction all the way, and understand why some fractions stop while others repeat forever.

**Example.** To convert 0.375 to a fraction, write it over the matching power of ten: 0.375 = 375/1000. Both numbers share a factor of 125, so divide top and bottom by 125 to get 3/8.

*(drawing: 3 shaded parts out of 8 is the same amount as 0.375.)*

**Example.** To go the other way, look at the denominator. 8 = 2 x 2 x 2, so it only has 2s as prime factors. That means you can multiply top and bottom to reach a power of ten: 3/8 = 375/1000 = 0.375.

**Tip.** A fraction only becomes a terminating decimal when its simplest-form denominator is built from 2s and 5s alone. A denominator like 6 or 7 always leaves something over, so the decimal repeats no matter how far you divide.

**Recap.** If a fraction's simplest denominator has only 2s and 5s as prime factors, it terminates; convert by matching a power of ten, then simplify all the way.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Decimals and fractions (age 10+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi)
- [Calculations with fractions, decimals and negatives](https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk)

## Opens up

- [Number Sets & Infinity](https://lightmysky.com/learn/mathematics/number-sets-and-infinity-mt_b4lbTOJYwI)
- [Recurring Decimals as Exact Fractions](https://lightmysky.com/learn/mathematics/recurring-decimals-as-exact-fractions-mt_Mb-sXIZDWd)