Solve the Equation: Finding the Number that Makes 0.1 × ? = 1

Q: Why does dividing by 0.1 give me 10 instead of a smaller number?

When you divide by a number less than 1, the result gets bigger! Think of it this way: if you have 1 whole pizza and cut it into 0.1 (one-tenth) sized pieces, you get 10 pieces total.

Q: Can I just move the decimal point to solve this?

Yes! Dividing by 0.1 is the same as multiplying by 10, which moves the decimal point one place to the right. So 1.0 ÷ 0.1 = 10.0

Q: What if the equation was 0.01 × ? = 1 instead?

The same method works! You'd calculate $ \frac{1}{0.01} = 1 \times 100 = 100 $ because 0.01 = 1/100, so its reciprocal is 100.

Q: How do I remember which operation to use?

Look for the structure: when you see coefficient × unknown = result, always divide both sides by the coefficient to isolate the unknown variable.

Q: Is there a way to check my answer without a calculator?

Absolutely! Just think: 10 × 0.1 means "10 groups of one-tenth" which equals 10/10 = 1. This mental math confirms your answer is correct!

Division by Decimals with Reciprocal Method

$0.1\times?=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Divide by the factor to find the unknown

00:08 Move the point, determine the number of zeros based on the number of shifts

00:15 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

$0.1\times?=1$

Step-by-step solution

To solve this problem, we need to find out what number, when multiplied by $0.1$ , equals $1$ . This means setting up the equation $0.1 \times x = 1$ .

To isolate $x$ , rearrange the equation:
$x = \frac{1}{0.1}$

Next, perform the division $1 \div 0.1$ . Dividing by a decimal is equivalent to multiplying by its reciprocal, thus:
$\frac{1}{0.1} = 1 \times 10 = 10$

Therefore, the solution to the equation is $x = 10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: To solve $0.1 \times ? = 1$ , divide both sides by the coefficient
Technique: Dividing by 0.1 equals multiplying by 10: $\frac{1}{0.1} = 1 \times 10 = 10$
Check: Substitute back into original equation: $0.1 \times 10 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Converting decimal to fraction incorrectly
Don't think 0.1 = 1/100 and get x = 100! This confuses 0.1 with 0.01 and gives the wrong reciprocal. Always remember 0.1 = 1/10, so dividing by 0.1 means multiplying by 10.

Practice Quiz

Test your knowledge with interactive questions

$0.26\times10=$

FAQ

Everything you need to know about this question

Why does dividing by 0.1 give me 10 instead of a smaller number?

When you divide by a number less than 1, the result gets bigger! Think of it this way: if you have 1 whole pizza and cut it into 0.1 (one-tenth) sized pieces, you get 10 pieces total.

Can I just move the decimal point to solve this?

Yes! Dividing by 0.1 is the same as multiplying by 10, which moves the decimal point one place to the right. So 1.0 ÷ 0.1 = 10.0

What if the equation was 0.01 × ? = 1 instead?

The same method works! You'd calculate $\frac{1}{0.01} = 1 \times 100 = 100$ because 0.01 = 1/100, so its reciprocal is 100.

How do I remember which operation to use?

Look for the structure: when you see coefficient × unknown = result, always divide both sides by the coefficient to isolate the unknown variable.

Is there a way to check my answer without a calculator?

Absolutely! Just think: 10 × 0.1 means "10 groups of one-tenth" which equals 10/10 = 1. This mental math confirms your answer is correct!

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