You will learn
- Find the rounding place.
- Look at the next digit.
- Round up or stay.
- Round to whole, tenth, hundredth.
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
- Find the rounding place.
- Look at the digit to its right.
- 5 or more rounds up; 4 or less stays.
- Keep or drop the following digits.
Words to know
Change to a nearby number.
Closest.
Digit rounded to.
About.
1. Discover: rounding a measurement
A length is 3.456 m. Round it to the nearest tenth, hundredth and whole number.
2. Understand: rounding decimals
- 3.456 to the nearest tenth: 3.5.
- To the nearest hundredth: 3.46.
- To the nearest whole number: 3.
- 2.949 to the nearest hundredth: 2.95.
- 0.995 to the nearest tenth: 1.0.
Idea 1: Tenth
6.78 to the nearest tenth: hundredths digit 8 rounds up, so 6.8. 0.995 to the nearest tenth is 1.0.
Idea 2: Hundredth
2.949 to the nearest hundredth: thousandths digit 9 rounds up, so 2.95. 4.304: digit 4 stays, so 4.30.
Idea 3: Whole
12.5 to the nearest whole number: tenths digit 5 rounds up, so 13.
Why keep 4.30? It shows we rounded to hundredths.
3. Worked examples
Example 1 (I show you): Tenth
6.78
- Hundredths digit 8.
Answer: 6.8
Example 2 (We do it together): Hundredth
2.949
- Thousandths digit 9.
Answer: 2.95
Example 3 (You try): Whole
12.5
Show the steps and answer
- Tenths digit 5.
Answer: 13
Did you know?
Rounding 0.995 to the nearest tenth carries all the way to 1.0.
Why this matters
Rounding makes measurements and money easier to use.
4. Explore: round
You need paper.
- Underline the rounding place.
- Look right.
- Round.
- Check on a number line.
Think about it: what did you notice?
3.5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The rounding place is ___.
- The next digit is ___.
- So I round ___.
- The answer is ___.
Guided practice
Question 1. 3.456 to the nearest tenth?
3.5.
Question 2. 3.456 to the nearest hundredth?
3.46.
Question 3. 3.456 to the nearest whole?
3.
Independent practice
Level 1: Start
- 6.78 to the nearest tenth
- 2.949 to the nearest hundredth
- 0.995 to the nearest tenth
- 12.5 to the nearest whole
- 4.304 to the nearest hundredth
Level 2: Grow
- 3.67 to the nearest whole
- 0.826 to the nearest hundredth
- 5.04 to the nearest tenth
Level 3: Stretch
- 99.95 to the nearest tenth
- 0.0449 to the nearest thousandth
- Ben says 2.45 to the nearest whole is 3 because 4 rounds the 5 up. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A rope is 3.456 m. Round to the nearest centimetre (hundredth).
Show a sample answer
3.46 m.
Another one. A bottle holds 1.746 L. Round to the nearest tenth and explain.
Show a sample answer
The hundredths digit is 4, so 1.7 L.
7. Common mistakes
Fix: 5 or more rounds up.
Fix: Look just right of the rounding place.
Fix: Keep it to show the rounding place.
8. Lesson summary and revision card
- I can find the rounding place.
- I can look at the next digit.
- I can round up or stay.
- I can round to whole, tenth and hundredth.
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
- Find the place.
- Look right.
- 5 or more: up.
11. Next lesson
Next lesson: Adding 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.
- Round 6.78 to the nearest tenth. [2 marks]
- Round 2.949 to the nearest hundredth. [2 marks]
- Round 0.995 to the nearest tenth. [3 marks]
- Round 12.5 to the nearest whole number. [2 marks]
- Ali says 4.304 to the nearest hundredth is 4.31. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Hundredths digit 8 rounds up [1]; 6.8 [1]
- Thousandths digit 9 rounds up [1]; 2.95 [1]
- Hundredths digit 9 rounds up [1]; carries [1]; 1.0 [1]
- Tenths digit 5 rounds up [1]; 13 [1]
- No [1]. Thousandths digit 4 stays [1]. The answer is 4.30 [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
- 6.78 to nearest tenth
- 2.949 to nearest hundredth
- 0.995 to nearest tenth
- 12.5 to nearest whole
- 4.304 to nearest hundredth
- 3.456 to the nearest tenth
- 3.456 to the nearest hundredth
- 3.456 to the nearest whole
- 2.949 to the nearest hundredth
- 0.995 to the nearest tenth
Homework
Round five decimals to three different places.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 6.78 to nearest tenth | 6.8 | 2 |
| 2.949 to nearest hundredth | 2.95 | 2 |
| 0.995 to nearest tenth | 1.0 | 2 |
| 12.5 to nearest whole | 13 | 2 |
| 4.304 to nearest hundredth | 4.30 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6.8; 2 2.95; 3 1.0; 4 13; 5 4.30.
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 3.5; 7 3.46; 8 3; 9 2.95; 10 1.0.
Independent practice answers. Level 1: 1 6.8; 2 2.95; 3 1.0; 4 13; 5 4.30. Level 2: 1 4; 2 0.83; 3 5.0. Level 3: 1 100.0; 2 0.045; 3 The tenths digit is 4, so it rounds down to 2..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find the rounding place | 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 Look at the next 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 Round up or stay | 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 Round to whole, tenth, hundredth | 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: Rounding down 5. 5 or more rounds up.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Round whole numbers.
- 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 rounds decimals to whole, tenth and hundredth. You do not need to be good at mathematics to help.
- Round prices to the nearest whole.
- Ask: which digit do we look at?
- Use number lines.
- 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: find the rounding place; look at the next digit; round up or stay; round to whole, tenth, hundredth.
Prerequisite knowledge. Lessons 1 to 3.
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. What is the rounding place? What is the next digit?
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. Rounding down 5. 5 or more rounds up.
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. Round whole numbers. 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.4; Cambridge Primary Mathematics Stage 5 (rounding decimals). These sources informed the lesson.