You will learn
- Say a hundredth is one of 100 equal parts.
- Write hundredths as fractions and decimals.
- Read two-decimal numbers.
- Link tenths to hundredths.
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
- A hundredth is one of 100 equal parts.
- Write hundredths as fractions and decimals.
- Two decimal places show tenths and hundredths.
- 10 hundredths make 1 tenth.
Words to know
One of 100 equal parts.
Separates ones from tenths.
Digits in tenths and hundredths.
Equal in value.
1. Discover: a hundred grid
A square is cut into 100 equal small squares. If 45 are shaded, what fraction and decimal is that?
2. Understand: hundredths
- 1/100 = 0.01.
- 7/100 = 0.07.
- 45/100 = 0.45 (4 tenths and 5 hundredths).
- 0.3 = 0.30 = 30/100.
10 hundredths make 1 tenth.
Idea 1: Hundredths
23/100 = 0.23. 7/100 = 0.07. 100/100 = 1.
Idea 2: Decimal to fraction
0.09 = 9/100. 0.45 = 45/100.
Idea 3: Link to tenths
0.6 = 6 tenths = 60 hundredths = 60/100. In 0.45 the tenths digit is 4.
Why two places? The first place is tenths and the second is hundredths.
3. Worked examples
Example 1 (I show you): To decimal
23/100
- 23 hundredths.
Answer: 0.23
Example 2 (We do it together): To fraction
0.09
- 9 hundredths.
Answer: 9/100
Example 3 (You try): Link
0.6 in hundredths
Show the steps and answer
- 6 tenths = 60 hundredths.
Answer: 60/100
Did you know?
Cents are hundredths of a dollar.
Why this matters
Hundredths allow precise measurements and money.
4. Explore: hundred grid
You need a 10 × 10 grid.
- Shade 45 squares.
- Write 45/100.
- Write 0.45.
- Shade 30 and write 0.30.
Think about it: what did you notice?
0.45 and 0.3.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The tenths digit is ___.
- The hundredths digit is ___.
- ___/100 = ___.
- ___ tenths = ___ hundredths.
Guided practice
Question 1. 7/100 as a decimal?
0.07.
Question 2. 45/100 as a decimal?
0.45.
Question 3. 0.3 as hundredths?
30/100.
Independent practice
Level 1: Start
- 23/100 as a decimal
- 0.09 as a fraction
- 0.6 as hundredths
- 100/100 as a decimal
- Tenths in 0.45
Level 2: Grow
- 17/100 as a decimal
- 0.71 as a fraction
- 0.2 as hundredths
Level 3: Stretch
- 0.05 + 0.04
- 0.3 as hundredths and in simplest form
- Ben writes 7/100 as 0.7. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
45 of 100 squares are shaded. Write this as a decimal.
Show a sample answer
0.45.
Another one. 45 of the 100 squares on a grid are shaded. Write this as a fraction and a decimal.
Show a sample answer
45/100 = 0.45
7. Common mistakes
Fix: Hundredths are the second place.
Fix: Two places: 0.07.
Fix: The first place is tenths.
8. Lesson summary and revision card
- I can say a hundredth is one of 100 equal parts.
- I can write hundredths as fractions and decimals.
- I can read two-decimal numbers.
- I can link tenths to hundredths.
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
- Hundredths: second place.
- 0.1 = 0.10.
- 100 hundredths = 1.
11. Next lesson
Next lesson: Decimal place value. 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 23/100 as a decimal. [1 mark]
- Write 0.09 as a fraction. [1 mark]
- Write 0.6 as hundredths. [2 marks]
- Write 100/100 as a whole number. [1 mark]
- Ana says 0.45 has 5 tenths. Is she right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- 0.23 [1]
- 9/100 [1]
- 6 tenths = 60 hundredths [1]; 60/100 [1]
- 1 [1]
- No [1]. 4 is in the tenths place [1]. 5 is in the hundredths place [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- 23/100 as a decimal
- 0.09 as a fraction
- 0.6 as hundredths
- 100/100 as a decimal
- Tenths in 0.45
- 7/100 as a decimal is
- 45/100 as a decimal is
- 0.3 equals
- 0.09 as a fraction is
- 100/100 as a decimal is
Homework
Shade a hundred grid to show 0.25, 0.5 and 0.75.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 23/100 as a decimal | 0.23 | 2 |
| 0.09 as a fraction | 9/100 | 2 |
| 0.6 as hundredths | 60/100 | 2 |
| 100/100 as a decimal | 1 | 2 |
| Tenths in 0.45 | 4 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.23; 2 9/100; 3 60/100; 4 1; 5 4.
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 0.07; 7 0.45; 8 30/100; 9 9/100; 10 1.
Independent practice answers. Level 1: 1 0.23; 2 9/100; 3 60/100; 4 1; 5 4. Level 2: 1 0.17; 2 71/100; 3 20/100. Level 3: 1 0.09; 2 30/100 = 3/10; 3 0.7 = 70/100. 7/100 = 0.07..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say a hundredth is one of 100 equal parts | 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 hundredths as fractions and 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 Read two-decimal numbers | 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 to hundredths | 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 7/100 as 0.7. Hundredths are the second place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Count hundredths on a grid.
- 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 hundredths as fractions and decimals. You do not need to be good at mathematics to help.
- Use a hundred grid to colour hundredths.
- Ask: tenths or hundredths?
- Use cents and dollars.
- 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: say a hundredth is one of 100 equal parts; write hundredths as fractions and decimals; read two-decimal numbers; link tenths to hundredths.
Prerequisite knowledge. Lesson 1.
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 10 × 10 grid. 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 digit is tenths? Which is hundredths?
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 7/100 as 0.7. Hundredths are the second place.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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. Count hundredths on a grid. 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.5 and 4.NF.C.6 (hundredths); Cambridge Primary Mathematics Stage 4 (hundredths). These sources informed the lesson; no official alignment is claimed.