You will learn
- Name the decimal places.
- Say the value of each digit.
- Compare values of the same digit.
- Write a number in expanded form.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Name the places: ones, tenths, hundredths.
- Each digit has a value from its place.
- Moving right makes a place ten times smaller.
- Write a decimal in expanded form.
Words to know
Value by position.
Whole units.
First place after the point.
Second place after the point.
1. Discover: 3.47
In 3.47, what is the value of the 4? What is the value of the 7?
2. Understand: decimal place value
In 3.47: 3 is ones, 4 is tenths, 7 is hundredths.
- The 4 is worth 0.4 (4 tenths).
- The 7 is worth 0.07 (7 hundredths).
- Expanded: 3 + 0.4 + 0.07 = 3.47.
In 5.74 the 7 is worth 0.7. Same digit, different value.
Idea 1: Tenths
In 6.82 the 8 is in the tenths place, so its value is 0.8. The tenths digit of 9.31 is 3.
Idea 2: Hundredths
In 6.82 the 2 is in the hundredths place, so its value is 0.02. The 5 in 0.05 is 5 hundredths.
Idea 3: Expanded form
4.25 = 4 + 0.2 + 0.05.
Why add the values? Each digit is worth its place value.
3. Worked examples
Example 1 (I show you): Tenths
Value of 8 in 6.82
- First place after the point.
Answer: 0.8
Example 2 (We do it together): Hundredths
Value of 2 in 6.82
- Second place after the point.
Answer: 0.02
Example 3 (You try): Expand
4.25
Show the steps and answer
- Ones, tenths, hundredths.
Answer: 4 + 0.2 + 0.05
Did you know?
Each place to the right is ten times smaller than the one before.
Why this matters
Place value makes sure we read every decimal correctly.
4. Explore: chart
You need paper.
- Draw a chart: ones, tenths, hundredths.
- Write 3.47 in it.
- State each value.
- Write expanded form.
Think about it: what did you notice?
3 + 0.4 + 0.07.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digit ___ is in the ___ place.
- Its value is ___.
- Expanded form is ___ + ___ + ___.
- The tenths digit is ___.
Guided practice
Question 1. Value of 4 in 3.47?
0.4.
Question 2. Value of 7 in 3.47?
0.07.
Question 3. Value of 7 in 5.74?
0.7.
Independent practice
Level 1: Start
- Value of 8 in 6.82
- Value of 2 in 6.82
- Value of 5 in 0.05
- Expand 4.25
- Digit in the tenths place of 9.31
Level 2: Grow
- Value of 5 in 8.35
- Tenths digit of 4.72
- Expand 6.39
Level 3: Stretch
- Value of 9 in 12.90
- Write 7 + 0.4 + 0.02 as a decimal
- Ben says the 5 in 3.05 is worth 0.5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A book costs 12.65. What is the value of the digit 6?
Show a sample answer
0.6.
Another one. In 36.48, give the value of every digit.
Show a sample answer
3 is 30, 6 is 6, 4 is 0.4 and 8 is 0.08.
7. Common mistakes
Fix: Use the place.
Fix: The value is the digit times its place.
Fix: The first place is tenths.
8. Lesson summary and revision card
- I can name the decimal places.
- I can say the value of each digit.
- I can compare values of the same digit.
- I can write a number in expanded form.
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
- Ones, tenths, hundredths.
- Place changes value.
- Expand to check.
11. Next lesson
Next lesson: Writing 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.
- What is the value of 8 in 6.82? [2 marks]
- What is the value of 2 in 6.82? [2 marks]
- What is the value of 5 in 0.05? [1 mark]
- Write 4.25 in expanded form. [3 marks]
- Ali says the tenths digit of 9.31 is 9. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 8 is in the tenths place [1]; 0.8 [1]
- 2 is in the hundredths place [1]; 0.02 [1]
- 5 hundredths [1]
- 4 [1]; 0.2 [1]; 0.05 [1]
- No [1]. 9 is in the ones place [1]. The tenths digit is 3 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Value of 8 in 6.82
- Value of 2 in 6.82
- Value of 5 in 0.05
- Expand 4.25
- Tenths digit of 9.31
- Value of 4 in 3.47
- Value of 7 in 3.47
- Value of 8 in 6.82
- Expanded 4.25
- Tenths digit of 9.31
Homework
Make a place value chart for five decimals.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Value of 8 in 6.82 | 0.8 | 2 |
| Value of 2 in 6.82 | 0.02 | 2 |
| Value of 5 in 0.05 | 0.05 | 2 |
| Expand 4.25 | 4 + 0.2 + 0.05 | 2 |
| Tenths digit of 9.31 | 3 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.8; 2 0.02; 3 0.05; 4 4 + 0.2 + 0.05; 5 3.
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 0.07; 8 0.8; 9 4 + 0.2 + 0.05; 10 3.
Independent practice answers. Level 1: 1 0.8; 2 0.02; 3 0.05; 4 4 + 0.2 + 0.05; 5 3. Level 2: 1 0.05; 2 7; 3 6 + 0.3 + 0.09. Level 3: 1 0.9; 2 7.42; 3 5 is in the hundredths place, so its value is 0.05..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name the 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 Say the value of each digit | 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 Compare values of the same digit | 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 Write a number in 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Giving the value of 7 in 3.47 as 7. Use the place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use base-10 blocks.
- 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 says what each digit is worth. You do not need to be good at mathematics to help.
- Read prices and say the value of each digit.
- Ask: which place is the digit in?
- Use 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 the decimal places; say the value of each digit; compare values of the same digit; write a number in expanded form.
Prerequisite knowledge. Lessons 1 and 2.
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 is the digit in? 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. Giving the value of 7 in 3.47 as 7. Use the place.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Use base-10 blocks. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.NF.C.6 and 5.NBT.A.3; Cambridge Primary Mathematics Stage 4 and 5 (decimal place value). These sources informed the lesson; no official alignment is claimed.