You will learn
- Write a decimal as a percent.
- Write a percent as a decimal.
- Multiply or divide by 100.
- Link tenths and hundredths to percent.
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
- Percent means per hundred.
- Multiply a decimal by 100 to get a percent.
- Divide a percent by 100 to get a decimal.
- 0.01 equals 1%.
Words to know
Number with a point.
Per hundred.
0.01 = 1%.
Change form.
1. Discover: 0.45
0.45 means 45 hundredths. What percent is that?
2. Understand: decimals and percents
- 0.45 = 45/100 = 45%.
- 0.07 = 7%.
- 0.3 = 0.30 = 30%.
- 62% = 0.62; 5% = 0.05.
Percent to decimal: divide by 100 (move the point two places left).
Idea 1: To percent
0.07 × 100 = 7%. 0.3 × 100 = 30%. 0.8 = 80%.
Idea 2: To decimal
90% ÷ 100 = 0.9. 12% ÷ 100 = 0.12.
Idea 3: Link
Tenths are 10%: 0.1 = 10%. Hundredths are 1%: 0.01 = 1%.
Why × 100? Percent is out of 100.
3. Worked examples
Example 1 (I show you): To percent
0.07
- × 100.
Answer: 7%
Example 2 (We do it together): To percent
0.3
- × 100.
Answer: 30%
Example 3 (You try): To decimal
12%
Show the steps and answer
- ÷ 100.
Answer: 0.12
Did you know?
Moving the decimal point two places converts between decimals and percents.
Why this matters
Calculators, discounts and interest all switch between decimals and percents.
4. Explore: convert
You need paper.
- Write 0.45.
- Move the point 2 right.
- Add %.
- Convert 62% back.
Think about it: what did you notice?
45%; 0.62.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply / divide by ___.
- The point moves ___ places.
- So the answer is ___.
- Check: ___% = ___.
Guided practice
Question 1. 0.45 as a percent?
45%.
Question 2. 62% as a decimal?
0.62.
Question 3. 5% as a decimal?
0.05.
Independent practice
Level 1: Start
- 0.07
- 0.3
- 0.8
- 90%
- 12%
Level 2: Grow
- 0.45
- 23%
- 0.9
Level 3: Stretch
- 0.005
- 125%
- Ben says 5% = 0.5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tax is 0.15. What percent?
Show a sample answer
15%.
Another one. A phone battery is 0.85 charged. What percent is that?
Show a sample answer
0.85 × 100 = 85%
7. Common mistakes
Fix: 5% = 0.05.
Fix: Move it two places.
Fix: × 100 to get a percent; ÷ 100 to get a decimal.
8. Lesson summary and revision card
- I can write a decimal as a percent.
- I can write a percent as a decimal.
- I can multiply or divide by 100.
- I can link tenths and hundredths to percent.
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
- ×100 for percent.
- ÷100 for decimal.
- Two places.
11. Next lesson
Next lesson: Representing percentages visually. 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 0.07 as a percent. [2 marks]
- Write 0.3 as a percent. [2 marks]
- Write 0.8 as a percent. [2 marks]
- Write 90% as a decimal. [2 marks]
- Ali says 12% = 1.2. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- × 100 [1]; 7% [1]
- × 100 [1]; 30% [1]
- × 100 [1]; 80% [1]
- ÷ 100 [1]; 0.9 [1]
- No [1]. 12 ÷ 100 [1]. It is 0.12 [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
- 0.07
- 0.3
- 0.8
- 90%
- 12%
- 0.45 =
- 0.07 =
- 62% =
- 5% =
- 0.3 =
Homework
Convert ten decimals and percents.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 0.07 | 7% | 2 |
| 0.3 | 30% | 2 |
| 0.8 | 80% | 2 |
| 90% | 0.9 | 2 |
| 12% | 0.12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 7%; 2 30%; 3 80%; 4 0.9; 5 0.12.
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 45%; 7 7%; 8 0.62; 9 0.05; 10 30%.
Independent practice answers. Level 1: 1 7%; 2 30%; 3 80%; 4 0.9; 5 0.12. Level 2: 1 45%; 2 0.23; 3 90%. Level 3: 1 0.5%; 2 1.25; 3 5 ÷ 100 = 0.05..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write a decimal as a percent | 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 a percent as a decimal | 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 Multiply or divide by 100 | 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 tenths and hundredths to percent | 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: Writing 5% as 0.5. 5% = 0.05.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: 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 converts between decimals and percents. You do not need to be good at mathematics to help.
- Read battery or discount percents together.
- Ask: which way does the point move?
- Link money: 0.25 is 25 cents.
- 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: write a decimal as a percent; write a percent as a decimal; multiply or divide by 100; link tenths and hundredths to percent.
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. Multiply or divide by 100? How far does the point move?
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 5% as 0.5. 5% = 0.05.
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. 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
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 6.RP.A.3c; Cambridge Primary Mathematics Stage 6 (decimals and percents). These sources informed the lesson; no official alignment is claimed.