You will learn
- Name decimal places.
- Read decimals.
- Write expanded form.
- Find digit values.
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
- Tenths, hundredths and thousandths follow the point.
- Each place is ten times smaller.
- Expanded form shows each place value.
- A digit value depends on its place.
Words to know
One of ten equal parts.
One of a hundred parts.
One of a thousand parts.
Separates whole and part.
1. Discover: beyond the point
In 3.456, what is the 5 worth?
2. Understand: decimal place value
- 3.456: 3 ones, 4 tenths, 5 hundredths, 6 thousandths.
- The 5 is worth 0.05.
- Expanded: 3 + 0.4 + 0.05 + 0.006.
- 0.007 is seven thousandths.
Idea 1: Places
In 3.456: 4 is tenths (0.4), 5 is hundredths (0.05), 6 is thousandths (0.006).
Idea 2: Expanded
2 + 0.3 + 0.07 = 2.37.
Idea 3: Names
The 9 in 0.209 is in the thousandths place. Nine thousandths is 0.009. The 8 in 12.083 is worth 0.08.
Why zero? Zeros hold places so digits sit in the right spot.
3. Worked examples
Example 1 (I show you): Value
4 in 3.456
- First digit after the point.
Answer: 0.4
Example 2 (We do it together): Expanded
2 + 0.3 + 0.07
- Add the parts.
Answer: 2.37
Example 3 (You try): Place
9 in 0.209
Show the steps and answer
- Third place.
Answer: thousandths
Did you know?
Each place to the right is ten times smaller.
Why this matters
Decimal place value is the key to money, measures and science.
4. Explore: read
You need paper.
- Say the whole part.
- Say “point”.
- Read digits one by one.
- Name the last place.
Think about it: what did you notice?
Three point four five six.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The ___ is in the ___ place.
- Its value is ___.
- In expanded form: ___.
- As a decimal: ___.
Guided practice
Question 1. Value of 5 in 3.456?
0.05.
Question 2. Value of 6?
0.006.
Question 3. 0.007 in words?
seven thousandths.
Independent practice
Level 1: Start
- Value of 4 in 3.456
- Write 2 + 0.3 + 0.07 as a decimal
- Name the place of 9 in 0.209
- Write nine thousandths
- Value of 8 in 12.083
Level 2: Grow
- Value of 3 in 4.36
- 5 + 0.2 + 0.01
- Place of 8 in 0.608
Level 3: Stretch
- Value of 7 in 9.073
- Write 4 tenths and 6 thousandths as a decimal
- Ben says the 8 in 12.083 is worth 8. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A race is won by 0.05 seconds. How many hundredths?
Show a sample answer
5 hundredths.
Another one. A length is 2.375 m. What is the value of each digit?
Show a sample answer
2 m, 0.3 m, 0.07 m, 0.005 m
7. Common mistakes
Fix: 0.05 is five hundredths.
Fix: Count places from the point.
Fix: Zeros keep each digit in its place.
8. Lesson summary and revision card
- I can name decimal places.
- I can read decimals.
- I can write expanded form.
- I can find digit values.
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
- Places shrink by ten.
- Count digits after the point.
- Zero holds a place.
11. Next lesson
Next lesson: Decimal comparison. 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.
- What is the value of the 4 in 3.456? [2 marks]
- Write 2 + 0.3 + 0.07 as a decimal. [2 marks]
- Name the place of the 9 in 0.209. [2 marks]
- Write nine thousandths as a decimal. [1 mark]
- Ali says the 8 in 12.083 is worth 8. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- It is in the tenths place [1]; 0.4 [1]
- Add the place values [1]; 2.37 [1]
- Three digits after the point [1]; thousandths [1]
- 0.009 [1]
- No [1]. 8 is the second digit after the point [1]. It is worth 0.08 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Value of 4 in 3.456
- 2 + 0.3 + 0.07
- Place of 9 in 0.209
- Nine thousandths
- Value of 8 in 12.083
- Value of 4 in 3.456
- 2 + 0.3 + 0.07
- Place of 9 in 0.209
- Nine thousandths
- Value of 8 in 12.083
Homework
Write three decimals and name each digit’s place.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Value of 4 in 3.456 | 0.4 | 2 |
| 2 + 0.3 + 0.07 | 2.37 | 2 |
| Place of 9 in 0.209 | thousandths | 2 |
| Nine thousandths | 0.009 | 2 |
| Value of 8 in 12.083 | 0.08 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.4; 2 2.37; 3 thousandths; 4 0.009; 5 0.08.
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 0.4; 7 2.37; 8 thousandths; 9 0.009; 10 0.08.
Independent practice answers. Level 1: 1 0.4; 2 2.37; 3 thousandths; 4 0.009; 5 0.08. Level 2: 1 0.3; 2 5.21; 3 thousandths. Level 3: 1 0.07; 2 0.406; 3 It is the second place after the point: 0.08..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name decimal places | 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 Read decimals | 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 expanded form | 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 Find digit values | 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: Thinking 0.05 is five tenths. 0.05 is five hundredths.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Tenths and hundredths.
- 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 names decimal places and values. You do not need to be good at mathematics to help.
- Use money to talk about tenths and hundredths.
- Ask: which place is the digit in?
- Write numbers in a place-value chart.
- 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: name decimal places; read decimals; write expanded form; find digit values.
Prerequisite knowledge. Grade 5 decimals.
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. Which place? What is its value?
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. Thinking 0.05 is five tenths. 0.05 is five hundredths.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Tenths and hundredths. 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 6 » Ratios & Proportional Relationships; Grade 6 » The Number System. 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.1 and 5.NBT.A.3; Cambridge Primary Mathematics Stage 6 (decimal place value). These sources informed the lesson.