Solve the Decimal Equation: Finding the Number in 0.1 × ? = 10

Q: Why do I divide by 0.1 instead of multiplying?

Because division is the opposite of multiplication! When you have $ 0.1 \times ? = 10 $, you need to 'undo' the multiplication by 0.1 to isolate the unknown.

Q: How do I divide by a decimal like 0.1?

Think of it this way: dividing by 0.1 is the same as multiplying by 10! So $ \frac{10}{0.1} = 10 \times 10 = 100 $.

Q: Can I solve this by moving the decimal point?

Yes! Since $ 0.1 = \frac{1}{10} $, dividing by 0.1 means multiplying by 10. Just move the decimal point one place right: 10.0 becomes 100.

Q: What if I get a different answer when I check?

If your check doesn't work, go back and recalculate the division. Make sure you're dividing 10 by 0.1, not the other way around!

Q: Is there another way to solve this equation?

You could also think: 'What number times 0.1 equals 10?' Since $ 0.1 = \frac{1}{10} $, you need a number that when divided by 10 gives 10, which is 100!

Decimal Division with Multiplication Equations

$0.1\times?=10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 Divide by the factor to find the unknown

00:17 Move the point, determine the number of zeros based on the number of shifts

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$0.1\times?=10$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Write down the given equation $0.1 \times ? = 10$ .
Step 2: Solve the equation by isolating $'?'$ using division. We divide both sides of the equation by $0.1$ .

Let's work through these steps in detail:
Step 1: We have $0.1 \times ? = 10$ .
Step 2: To isolate $'?'$ , divide both sides of the equation by $0.1$ . This gives us $? = \frac{10}{0.1}$ .
Calculating this division: $? = \frac{10}{0.1} = 100$ .

Therefore, the solution to this problem is $\boxdot 100$ , confirming the equivalence $0.1 \times 100 = 10$ .

Final Answer

$100$

Key Points to Remember

Essential concepts to master this topic

Inverse Operations: Division undoes multiplication to isolate unknown values
Technique: Divide both sides by 0.1: $\frac{10}{0.1} = 100$
Check: Substitute back into original equation: $0.1 \times 100 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Converting decimals incorrectly when dividing
Don't try to convert 0.1 to a fraction like 1/10 and then flip-multiply = confusing steps! This makes the problem harder and leads to calculation errors. Always divide directly: 10 ÷ 0.1 = 100.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why do I divide by 0.1 instead of multiplying?

Because division is the opposite of multiplication! When you have $0.1 \times ? = 10$ , you need to 'undo' the multiplication by 0.1 to isolate the unknown.

How do I divide by a decimal like 0.1?

Think of it this way: dividing by 0.1 is the same as multiplying by 10! So $\frac{10}{0.1} = 10 \times 10 = 100$ .

Can I solve this by moving the decimal point?

Yes! Since $0.1 = \frac{1}{10}$ , dividing by 0.1 means multiplying by 10. Just move the decimal point one place right: 10.0 becomes 100.

What if I get a different answer when I check?

If your check doesn't work, go back and recalculate the division. Make sure you're dividing 10 by 0.1, not the other way around!

Is there another way to solve this equation?

You could also think: 'What number times 0.1 equals 10?' Since $0.1 = \frac{1}{10}$ , you need a number that when divided by 10 gives 10, which is 100!

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