Solve Decimal Division: 0.123 ÷ 10 Step-by-Step

Q: Why does dividing by 10 move the decimal left?

Division by 10 makes numbers smaller, so the decimal point moves toward zero. Think of it this way: 10 ÷ 10 = 1, and 1.0 ÷ 10 = 0.1 - the decimal moves left!

Q: What if I need to add zeros when moving the decimal?

That's normal! When $ 0.123 $ becomes $ 0.0123 $, we add a zero as a placeholder. This keeps all digits in their correct place values.

Q: How is this different from multiplying by 10?

Opposite directions! Multiplying by 10 moves the decimal right (makes bigger), while dividing by 10 moves it left (makes smaller).

Q: What about dividing by 100 or 1000?

Same pattern! Dividing by 100 moves the decimal 2 places left, dividing by 1000 moves it 3 places left. Count the zeros in the divisor!

Q: How can I remember which way to move the decimal?

Remember: Division makes smaller = move left toward zero. Multiplication makes bigger = move right away from zero.

Decimal Division with Powers of Ten

$0.123:10=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the amount of zeros, move the decimal point

00:09 Move the decimal point according to the number of zeros

00:23 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

$0.123:10=$

Step-by-step solution

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

Step 1: Identify the given decimal number, $0.123$ .
Step 2: Apply the rule for dividing a decimal by $10$ , which involves moving the decimal point one place to the left.
Step 3: Perform the movement of the decimal point.

Now, let's work through each step:

Step 1: We have the decimal number $0.123$ .

Step 2: The rule for dividing by $10$ tells us to move the decimal point one place to the left.

Step 3: Moving the decimal point one place to the left, $0.123$ becomes $0.0123$ .

Therefore, the solution to the problem is $0.0123$ .

Checking the answer against the choices, the correct choice is: : $0.0123$ .

Final Answer

$0.0123$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by 10 moves decimal point one place left
Technique: Move 0.123 becomes 0.0123 when dividing by 10
Check: Multiply result by 10: 0.0123 × 10 = 0.123 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction
Don't move the decimal point right when dividing by 10 = 1.23 instead of 0.0123! Division makes numbers smaller, not larger. Always move the decimal point left when dividing by powers of 10.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does dividing by 10 move the decimal left?

Division by 10 makes numbers smaller, so the decimal point moves toward zero. Think of it this way: 10 ÷ 10 = 1, and 1.0 ÷ 10 = 0.1 - the decimal moves left!

What if I need to add zeros when moving the decimal?

That's normal! When $0.123$ becomes $0.0123$ , we add a zero as a placeholder. This keeps all digits in their correct place values.

How is this different from multiplying by 10?

Opposite directions! Multiplying by 10 moves the decimal right (makes bigger), while dividing by 10 moves it left (makes smaller).

What about dividing by 100 or 1000?

Same pattern! Dividing by 100 moves the decimal 2 places left, dividing by 1000 moves it 3 places left. Count the zeros in the divisor!

How can I remember which way to move the decimal?

Remember: Division makes smaller = move left toward zero. Multiplication makes bigger = move right away from zero.

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