Solve Decimal Division: 0.7 ÷ 0.1 Step-by-Step

Q: Why can I multiply both numbers by 10?

Multiplying both the dividend and divisor by the same number doesn't change the answer! It's like $ \frac{6}{2} = \frac{60}{20} = 3 $ - the ratio stays the same.

Q: What if the decimals have different decimal places?

Multiply by the highest power of 10 needed! For $ 0.75 \div 0.5 $, multiply both by 100 to get $ 75 \div 50 $.

Q: Can I just count decimal places instead?

Counting works but understanding the multiplication method helps you see why it works. Both methods give the same answer!

Q: How do I check my decimal division answer?

Multiply your answer by the original divisor. If you get the original dividend back, you're correct! $ 7 \times 0.1 = 0.7 $ ✓

Decimal Division with Powers of Ten

$0.7:0.1=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's multiply each factor by 10 to make division easier

00:31 We'll divide between the new numbers and calculate the quotient

00:34 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

$0.7:0.1=$

Step-by-step solution

To solve the problem $0.7 \div 0.1$ , we proceed with the following steps:

Step 1: Convert the decimals to whole numbers. Multiply both $0.7$ and $0.1$ by 10 to remove the decimals. This gives us $7$ and $1$ respectively.
Step 2: Divide the resulting whole numbers. Hence, $7 \div 1 = 7$ .
Step 3: The division is straightforward as the divisor is now a whole number.

Therefore, the solution to the problem is $7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numbers by same power of 10
Technique: Convert $0.7 \div 0.1$ to $7 \div 1 = 7$
Check: $7 \times 0.1 = 0.7$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point without multiplying both numbers equally
Don't just move the decimal in 0.7 to get 7 without doing the same to 0.1 = wrong division setup! This creates an entirely different problem. Always multiply both dividend and divisor by the same power of 10.

Practice Quiz

Test your knowledge with interactive questions

$$ 0.121:0.1= $$

FAQ

Everything you need to know about this question

Why can I multiply both numbers by 10?

Multiplying both the dividend and divisor by the same number doesn't change the answer! It's like $\frac{6}{2} = \frac{60}{20} = 3$ - the ratio stays the same.

What if the decimals have different decimal places?

Multiply by the highest power of 10 needed! For $0.75 \div 0.5$ , multiply both by 100 to get $75 \div 50$ .

Can I just count decimal places instead?

Counting works but understanding the multiplication method helps you see why it works. Both methods give the same answer!

How do I check my decimal division answer?

Multiply your answer by the original divisor. If you get the original dividend back, you're correct! $7 \times 0.1 = 0.7$ ✓

What if I get a decimal answer instead of a whole number?

That's completely normal! Not all decimal divisions result in whole numbers. Just make sure your decimal answer makes sense when you check it.

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