You will learn
- Read decimals to thousandths.
- Write as fractions.
- Write in words.
- Link to place value.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Thousandths are 1/1000.
- A decimal can be written as a fraction.
- Simplify fractions to lowest terms.
- Say decimals using place value.
Words to know
1/1000.
Number with a point.
Part of a whole.
Equal in value.
1. Discover: a tiny amount
A scientist measures 0.007 m. How do you say and write that number as a fraction?
2. Understand: thousandths
- 0.007 = 7/1000 = seven thousandths.
- 0.125 = 125/1000 = 1/8.
- 2.304 = two and three hundred four thousandths.
- 0.05 = 5/100 = 50/1000.
Idea 1: To fraction
0.009 = 9/1000. 0.25 = 25/100 = 1/4.
Idea 2: To decimal
3/1000 = 0.003. 0.5 = 0.500 = 500/1000.
Idea 3: Say it
1.045 is “one and forty-five thousandths”.
Why thousandths? They let us measure very small quantities.
3. Worked examples
Example 1 (I show you): Fraction
0.009
- Three decimal places.
Answer: 9/1000
Example 2 (We do it together): Lowest terms
0.25
- 25/100 ÷ 25.
Answer: 1/4
Example 3 (You try): Decimal
3/1000
Show the steps and answer
- Thousandths place.
Answer: 0.003
Did you know?
0.125 is the same as 1/8.
Why this matters
Thousandths are used in science, sport and engineering.
4. Explore: say it
You need paper.
- Write 0.007.
- Say it.
- Write as a fraction.
- Simplify 0.125.
Think about it: what did you notice?
7/1000; 1/8.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The decimal has ___ places.
- The denominator is ___.
- In lowest terms it is ___.
- I read it as ___.
Guided practice
Question 1. 0.007 as a fraction?
7/1000.
Question 2. 0.125 in lowest terms?
1/8.
Question 3. 2.304 in words?
Two and three hundred four thousandths.
Independent practice
Level 1: Start
- 0.009 as a fraction
- 0.25 in lowest terms
- Write 3/1000 as a decimal
- 0.5 in thousandths
- Say 1.045
Level 2: Grow
- 0.013 as a fraction
- 0.2 in lowest terms
- 9/1000 as a decimal
Level 3: Stretch
- 0.125 in lowest terms
- 0.64 in lowest terms
- Ana says 0.45 = 45/1000. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A coin is 0.002 m thick. Write as a fraction of a metre.
Show a sample answer
2/1000.
Another one. A coin weighs 0.025 kg. Write this as a fraction in lowest terms.
Show a sample answer
25/1000 = 1/40
7. Common mistakes
Fix: Three decimal places.
Fix: Count the decimal places.
Fix: Divide top and bottom by the common factor.
8. Lesson summary and revision card
- I can read decimals to thousandths.
- I can write decimals as fractions.
- I can write them in words.
- I can link them to place value.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Three places: thousandths.
- Convert and simplify.
- Zeros hold places.
11. Next lesson
Next lesson: Comparing decimals. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Write 0.009 as a fraction. [2 marks]
- Write 0.25 in lowest terms. [3 marks]
- Write 3/1000 as a decimal. [2 marks]
- Write 0.5 in thousandths. [2 marks]
- Ali says 0.07 = 7/1000. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 9 thousandths [1]; 9/1000 [1]
- 25/100 [1]; divide by 25 [1]; 1/4 [1]
- Thousandths place [1]; 0.003 [1]
- 0.500 [1]; 500/1000 [1]
- No [1]. 0.07 has two decimal places [1]. It is 7/100 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 0.009 as a fraction
- 0.25 in lowest terms
- 3/1000 as a decimal
- 0.5 in thousandths
- 0.125 in lowest terms
- 0.007 as a fraction is…
- 0.125 in lowest terms is…
- 3/1000 as a decimal is…
- 0.5 in thousandths is…
- 0.25 in lowest terms is…
Homework
Write 10 decimals to thousandths as fractions.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 0.009 as a fraction | 9/1000 | 2 |
| 0.25 in lowest terms | 1/4 | 2 |
| 3/1000 as a decimal | 0.003 | 2 |
| 0.5 in thousandths | 500/1000 | 2 |
| 0.125 in lowest terms | 1/8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 9/1000; 2 1/4; 3 0.003; 4 500/1000; 5 1/8.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 7/1000; 7 1/8; 8 0.003; 9 500/1000; 10 1/4.
Independent practice answers. Level 1: 1 9/1000; 2 1/4; 3 0.003; 4 500/1000; 5 one and forty-five thousandths. Level 2: 1 13/1000; 2 1/5; 3 0.009. Level 3: 1 1/8; 2 16/25; 3 0.45 has two decimal places, so it is 45/100 = 9/20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read decimals to thousandths | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Write as fractions | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Write in words | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Link to place value | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Writing 7/1000 as 0.07. Three decimal places.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Hundredths as fractions.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child connects decimals to fractions and words. You do not need to be good at mathematics to help.
- Read food label weights aloud.
- Ask: how many decimal places?
- Compare 0.5 and 0.500.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: read decimals to thousandths; write as fractions; write in words; link to place value.
Prerequisite knowledge. Lesson 1.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. How many decimal places? What is the denominator?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Writing 7/1000 as 0.07. Three decimal places.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Hundredths as fractions. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 5 » Number & Operations—Fractions; Grade 5 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.NBT.A.3 and 4.NF.C.6; Cambridge Primary Mathematics Stage 5 (decimals and fractions). These sources informed the lesson.