You will learn
- Name decimal places.
- Say the value of each digit.
- Compare values of the same digit.
- Write in expanded form.
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 are decimal places.
- Each place is 1/10 of the one to its left.
- The value of a digit depends on its place.
- Expanded form adds the values.
Words to know
First decimal place.
Second.
Third.
Separates whole and fraction.
1. Discover: 3.456
In 3.456, what does each digit stand for?
2. Understand: decimal place value
In 3.456: 3 ones, 4 tenths, 5 hundredths, 6 thousandths.
- The 4 is worth 0.4; the 5 is 0.05; the 6 is 0.006.
- Expanded: 3 + 0.4 + 0.05 + 0.006.
- Each place is 10 times the place to its right.
Idea 1: Places
In 6.287: 2 is in the tenths place, 8 is 0.08 (hundredths) and 7 is 0.007 (thousandths).
Idea 2: Digits
In 4.912 the thousandths digit is 2. In 9.081 the tenths digit is 0.
Idea 3: Expanded
2.35 = 2 + 0.3 + 0.05.
Why a decimal point? It separates the whole part from the parts.
3. Worked examples
Example 1 (I show you): Value
8 in 6.287
- Second decimal place.
Answer: 0.08
Example 2 (We do it together): Digit
Thousandths digit of 4.912
- Third decimal place.
Answer: 2
Example 3 (You try): Expand
2.35
Show the steps and answer
- Add the values.
Answer: 2 + 0.3 + 0.05
Did you know?
Each decimal place is ten times smaller than the one before.
Why this matters
Decimal place value is the key to money, measures and science.
4. Explore: chart
You need a place value chart.
- Write 3.456.
- Name each place.
- State each value.
- Write expanded form.
Think about it: what did you notice?
3 + 0.4 + 0.05 + 0.006.
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 it is ___ + ___.
- It is ten times ___ than the next place.
Guided practice
Question 1. Value of 5 in 3.456?
0.05.
Question 2. Value of 6?
0.006.
Question 3. Value of 4?
0.4.
Independent practice
Level 1: Start
- Value of 8 in 6.287
- Value of 7 in 6.287
- Thousandths digit of 4.912
- Expand 2.35
- Tenths digit of 9.081
Level 2: Grow
- Value of 4 in 3.842
- Expand 5.019
- Write 6 + 0.4 + 0.02 as a decimal
Level 3: Stretch
- Value of 3 in 12.034
- Write 9 + 0.007 as a decimal
- Ben says the value of 5 in 3.456 is 5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A runner’s time is 12.347 s. What is the value of 4?
Show a sample answer
0.04.
Another one. A seed is 2.345 cm long. Write 2.345 in expanded form.
Show a sample answer
2 + 0.3 + 0.04 + 0.005
7. Common mistakes
Fix: Count the places.
Fix: The value of 5 in 3.456 is 0.05.
Fix: They are equal.
8. Lesson summary and revision card
- I can name decimal places.
- I can say the value of each digit.
- I can compare values of the same digit.
- I can write decimals 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, thousandths.
- ÷10 each step right.
- Expand to check.
11. Next lesson
Next lesson: Decimals to thousandths. 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.
- Find the value of 8 in 6.287. [2 marks]
- Find the value of 7 in 6.287. [2 marks]
- Write the thousandths digit of 4.912. [2 marks]
- Write 2.35 in expanded form. [3 marks]
- Ali says the tenths digit of 9.081 is 8. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 8 is in the hundredths place [1]; 0.08 [1]
- 7 is in the thousandths place [1]; 0.007 [1]
- Third decimal place [1]; 2 [1]
- 2 [1]; 0.3 [1]; 0.05 [1]
- No [1]. Tenths is the first decimal place [1]. It is 0 [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
- Value of 8 in 6.287
- Value of 7 in 6.287
- Thousandths digit of 4.912
- Expand 2.35
- Tenths digit of 9.081
- Value of 5 in 3.456
- Value of 6 in 3.456
- Value of 4 in 3.456
- Thousandths digit of 4.912
- Expand 2.35
Homework
Make a place value chart for five decimals.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Value of 8 in 6.287 | 0.08 | 2 |
| Value of 7 in 6.287 | 0.007 | 2 |
| Thousandths digit of 4.912 | 2 | 2 |
| Expand 2.35 | 2 + 0.3 + 0.05 | 2 |
| Tenths digit of 9.081 | 0 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.08; 2 0.007; 3 2; 4 2 + 0.3 + 0.05; 5 0.
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 0.05; 7 0.006; 8 0.4; 9 2; 10 2 + 0.3 + 0.05.
Independent practice answers. Level 1: 1 0.08; 2 0.007; 3 2; 4 2 + 0.3 + 0.05; 5 0. Level 2: 1 0.04; 2 5 + 0.01 + 0.009; 3 6.42. Level 3: 1 0.03; 2 9.007; 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 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 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 |
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: Treating 0.05 as 0.5. Count the places.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Review 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 learns decimal place value to thousandths. You do not need to be good at mathematics to help.
- Look at prices and measures.
- Ask: which place is this 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 decimal places; say the value of each digit; compare values of the same digit; write in expanded form.
Prerequisite knowledge. Grade 4 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 a place value chart. 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. Treating 0.05 as 0.5. Count the 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. Review 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 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.3a; Cambridge Primary Mathematics Stage 5 (decimal place value). These sources informed the lesson.