Quick answer: the missing number depends on the symbol hiding between 20 and 0.1. Here are the four most common cases.
- 20 ÷ ? = 0.1 → the missing number is 200.
- 20 × ? = 0.1 → the missing number is 0.005.
- 20 − ? = 0.1 → the missing number is 19.9.
- 20 + ? = 0.1 → the missing number is −19.9.
Why the Missing Number 20 0.1 Puzzle Confuses People
The puzzle shows only two numbers, 20 and 0.1, with no operation sign. That gap is the whole problem.
Searchers usually see it as a worksheet line with a blank box. Without the sign, more than one answer fits.
- The blank can sit before or after 20.
- The sign can be +, −, ×, or ÷.
- Decimals like 0.1 make mental maths feel harder than it is.
Good news: one method solves every version. Let's walk through it.
The One Method That Solves Every Missing Number
Teachers call it the inverse operation. You undo the operation to reveal the hidden number.
England's Oak National Academy teaches this with multiplication and division fact families and arrays, as its lesson on finding missing numbers shows.
Classroom Secrets also covers it. Its video tutorial uses the inverse to check calculations and solve missing-number problems, and it maps to an England National Curriculum objective.
Inverse pairs at a glance
- Addition is undone by subtraction.
- Subtraction is undone by addition.
- Multiplication is undone by division.
- Division is undone by multiplication.
Step-by-Step Answers for Each Operation
1. Division: 20 ÷ ? = 0.1
- Ask: what do I divide 20 by to get 0.1?
- Swap to the inverse: ? = 20 ÷ 0.1.
- Dividing by 0.1 is the same as multiplying by 10.
- So ? = 200.
- Check: 20 ÷ 200 = 0.1. ✔
This is the most popular reading of the puzzle. It is also the one that feels most surprising, because dividing by a small number makes a big one.
2. Multiplication: 20 × ? = 0.1
- Use the inverse: ? = 0.1 ÷ 20.
- 0.1 is one tenth, so one tenth split into 20 parts is 0.005.
- Check: 20 × 0.005 = 0.1. ✔
3. Subtraction: 20 − ? = 0.1
- Use the inverse: ? = 20 − 0.1.
- That gives 19.9.
- Check: 20 − 19.9 = 0.1. ✔
4. Addition: 20 + ? = 0.1
- Use the inverse: ? = 0.1 − 20.
- That gives −19.9, a negative number.
- Check: 20 + (−19.9) = 0.1. ✔
Primary worksheets rarely expect negatives. If your task says "whole numbers only," this version has no valid answer.
5. Blank first: ? ÷ 20 = 0.1
- Use the inverse: ? = 0.1 × 20.
- That gives 2.
- Check: 2 ÷ 20 = 0.1. ✔
All Answers in One Table
| Number sentence | Inverse step | Missing number | Check |
|---|---|---|---|
| 20 + ? = 0.1 | 0.1 − 20 | −19.9 | 20 + (−19.9) = 0.1 |
| 20 − ? = 0.1 | 20 − 0.1 | 19.9 | 20 − 19.9 = 0.1 |
| 20 × ? = 0.1 | 0.1 ÷ 20 | 0.005 | 20 × 0.005 = 0.1 |
| 20 ÷ ? = 0.1 | 20 ÷ 0.1 | 200 | 20 ÷ 200 = 0.1 |
| ? ÷ 20 = 0.1 | 0.1 × 20 | 2 | 2 ÷ 20 = 0.1 |
| ? − 20 = 0.1 | 0.1 + 20 | 20.1 | 20.1 − 20 = 0.1 |
Every figure above comes from basic arithmetic, and each row includes its own check.
See the Scale: 20 vs 0.1
A picture helps here. The two numbers sit 200 times apart, which explains why the division answer is so large.
Common Mistakes (and How to Dodge Them)
- Mixing up ÷ 0.1 and × 0.1. 20 ÷ 0.1 = 200, but 20 × 0.1 = 2.
- Moving the decimal the wrong way. Dividing by 0.1 grows a number; it never shrinks it.
- Skipping the check. Multiplication verifies a division answer in seconds.
- Forgetting the order. 20 − ? and ? − 20 give different answers.
- Assuming the answer is always positive. Addition here produces −19.9.
Vedantu's decimal worksheets give the same advice. They say to use multiplication as the inverse and check your answer with it.
A Fast Mental-Maths Trick for Decimals
Treat 0.1 as "one tenth." Then the whole puzzle becomes friendlier.
- Dividing by one tenth multiplies by 10.
- Multiplying by one tenth divides by 10.
- 20 ÷ 0.1 → 20 × 10 = 200.
- 20 × 0.1 → 20 ÷ 10 = 2.
Yes, it sounds backwards the first time. Your brain will forgive you.
Why Missing Number Problems Matter
They train you to work backwards. That skill leads straight to algebra.
A Year 6 lesson on working backwards through multi-step problems ends with an algebra-style question: 4x + 9 = 29. The method is identical to the puzzle above.
- Spot the operation.
- Undo it.
- Check by substituting back.
Related Reading on Big Write Hook
Percentages use the same decimal thinking. Our guide What is 20 Percent of 1300? shows how 0.20 turns a discount into a simple multiplication.
Frequently Asked Questions
What is the missing number in 20 ÷ ? = 0.1?
It is 200. Divide 20 by 0.1, then check with 20 ÷ 200 = 0.1.
What is the missing number in 20 × ? = 0.1?
It is 0.005. Divide 0.1 by 20 to find it.
Can the missing number be negative?
Yes, in the addition version. 20 + ? = 0.1 gives −19.9.
How do I check my answer?
- Put your number back into the original sentence.
- Do the calculation.
- Confirm you land on 0.1.
What if my worksheet shows a different layout?
Copy the exact line, including the sign and the blank's position. Then apply the same inverse method from the table above.
Final Takeaway
The missing number between 20 and 0.1 changes with the operation. Division gives 200, multiplication gives 0.005, and subtraction gives 19.9.
Find the sign, flip it, and check your work. That is the whole trick.
Sources
Quick answer: the missing number depends on the symbol hiding between 20 and 0.1. Here are the four most common cases.
- 20 ÷ ? = 0.1 → the missing number is 200.
- 20 × ? = 0.1 → the missing number is 0.005.
- 20 − ? = 0.1 → the missing number is 19.9.
- 20 + ? = 0.1 → the missing number is −19.9.
Why the Missing Number 20 0.1 Puzzle Confuses People
The puzzle shows only two numbers, 20 and 0.1, with no operation sign. That gap is the whole problem.
Searchers usually see it as a worksheet line with a blank box. Without the sign, more than one answer fits.
- The blank can sit before or after 20.
- The sign can be +, −, ×, or ÷.
- Decimals like 0.1 make mental maths feel harder than it is.
Good news: one method solves every version. Let's walk through it.
The One Method That Solves Every Missing Number
Teachers call it the inverse operation. You undo the operation to reveal the hidden number.
England's Oak National Academy teaches this with multiplication and division fact families and arrays, as its lesson on finding missing numbers shows.
Classroom Secrets also covers it. Its video tutorial uses the inverse to check calculations and solve missing-number problems, and it maps to an England National Curriculum objective.
Inverse pairs at a glance
- Addition is undone by subtraction.
- Subtraction is undone by addition.
- Multiplication is undone by division.
- Division is undone by multiplication.
Step-by-Step Answers for Each Operation
1. Division: 20 ÷ ? = 0.1
- Ask: what do I divide 20 by to get 0.1?
- Swap to the inverse: ? = 20 ÷ 0.1.
- Dividing by 0.1 is the same as multiplying by 10.
- So ? = 200.
- Check: 20 ÷ 200 = 0.1. ✔
This is the most popular reading of the puzzle. It is also the one that feels most surprising, because dividing by a small number makes a big one.
2. Multiplication: 20 × ? = 0.1
- Use the inverse: ? = 0.1 ÷ 20.
- 0.1 is one tenth, so one tenth split into 20 parts is 0.005.
- Check: 20 × 0.005 = 0.1. ✔
3. Subtraction: 20 − ? = 0.1
- Use the inverse: ? = 20 − 0.1.
- That gives 19.9.
- Check: 20 − 19.9 = 0.1. ✔
4. Addition: 20 + ? = 0.1
- Use the inverse: ? = 0.1 − 20.
- That gives −19.9, a negative number.
- Check: 20 + (−19.9) = 0.1. ✔
Primary worksheets rarely expect negatives. If your task says "whole numbers only," this version has no valid answer.
5. Blank first: ? ÷ 20 = 0.1
- Use the inverse: ? = 0.1 × 20.
- That gives 2.
- Check: 2 ÷ 20 = 0.1. ✔
All Answers in One Table
| Number sentence | Inverse step | Missing number | Check |
|---|---|---|---|
| 20 + ? = 0.1 | 0.1 − 20 | −19.9 | 20 + (−19.9) = 0.1 |
| 20 − ? = 0.1 | 20 − 0.1 | 19.9 | 20 − 19.9 = 0.1 |
| 20 × ? = 0.1 | 0.1 ÷ 20 | 0.005 | 20 × 0.005 = 0.1 |
| 20 ÷ ? = 0.1 | 20 ÷ 0.1 | 200 | 20 ÷ 200 = 0.1 |
| ? ÷ 20 = 0.1 | 0.1 × 20 | 2 | 2 ÷ 20 = 0.1 |
| ? − 20 = 0.1 | 0.1 + 20 | 20.1 | 20.1 − 20 = 0.1 |
Every figure above comes from basic arithmetic, and each row includes its own check.
See the Scale: 20 vs 0.1
A picture helps here. The two numbers sit 200 times apart, which explains why the division answer is so large.
Common Mistakes (and How to Dodge Them)
- Mixing up ÷ 0.1 and × 0.1. 20 ÷ 0.1 = 200, but 20 × 0.1 = 2.
- Moving the decimal the wrong way. Dividing by 0.1 grows a number; it never shrinks it.
- Skipping the check. Multiplication verifies a division answer in seconds.
- Forgetting the order. 20 − ? and ? − 20 give different answers.
- Assuming the answer is always positive. Addition here produces −19.9.
Vedantu's decimal worksheets give the same advice. They say to use multiplication as the inverse and check your answer with it.
A Fast Mental-Maths Trick for Decimals
Treat 0.1 as "one tenth." Then the whole puzzle becomes friendlier.
- Dividing by one tenth multiplies by 10.
- Multiplying by one tenth divides by 10.
- 20 ÷ 0.1 → 20 × 10 = 200.
- 20 × 0.1 → 20 ÷ 10 = 2.
Yes, it sounds backwards the first time. Your brain will forgive you.
Why Missing Number Problems Matter
They train you to work backwards. That skill leads straight to algebra.
A Year 6 lesson on working backwards through multi-step problems ends with an algebra-style question: 4x + 9 = 29. The method is identical to the puzzle above.
- Spot the operation.
- Undo it.
- Check by substituting back.
Related Reading on Big Write Hook
Percentages use the same decimal thinking. Our guide What is 20 Percent of 1300? shows how 0.20 turns a discount into a simple multiplication.
Frequently Asked Questions
What is the missing number in 20 ÷ ? = 0.1?
It is 200. Divide 20 by 0.1, then check with 20 ÷ 200 = 0.1.
What is the missing number in 20 × ? = 0.1?
It is 0.005. Divide 0.1 by 20 to find it.
Can the missing number be negative?
Yes, in the addition version. 20 + ? = 0.1 gives −19.9.
How do I check my answer?
- Put your number back into the original sentence.
- Do the calculation.
- Confirm you land on 0.1.
What if my worksheet shows a different layout?
Copy the exact line, including the sign and the blank's position. Then apply the same inverse method from the table above.
Final Takeaway
The missing number between 20 and 0.1 changes with the operation. Division gives 200, multiplication gives 0.005, and subtraction gives 19.9.
Find the sign, flip it, and check your work. That is the whole trick.
