Solve Decimal Division: 0.412 ÷ 0.01 Step-by-Step

Q: Why do we multiply both numbers by 100?

We need to eliminate both decimal places from the divisor 0.01. Since 0.01 has 2 decimal places, we multiply both numbers by $ 10^2 = 100 $ to make fair, equivalent fractions.

Q: What if the divisor has more decimal places than the dividend?

Always use the number with more decimal places to determine your multiplier. If dividing 0.5 ÷ 0.001, multiply both by 1000 since 0.001 has 3 decimal places.

Q: Can I just move the decimal points instead of multiplying?

Yes, but be careful! Moving decimal points is the same as multiplying by powers of 10. Just make sure you move the same number of places in both numbers.

Q: Why does dividing by 0.01 make the answer bigger?

Dividing by a number smaller than 1 always gives a larger result! Think of it as asking "How many 0.01s fit into 0.412?" - lots of tiny pieces fit into a bigger piece.

Q: How do I know I moved enough decimal places?

Keep moving until the divisor becomes a whole number. For 0.01, you need 2 places to get 1. For 0.003, you'd need 3 places to get 3.

Decimal Division with Place Value Conversion

$0.412:0.01=$

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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 100 to make division easier

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

00:34 Any number divided by 1 is always equal to itself

00:37 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

$0.412:0.01=$

Step-by-step solution

To solve the problem of dividing the decimal numbers $0.412$ by $0.01$ , we'll simplify the division by eliminating the decimal points:

Step 1: Recognize that dividing by a decimal can be simplified by converting both the dividend and the divisor to whole numbers.
Step 2: Multiply both $0.412$ and $0.01$ by $100$ to make both numbers integers:

$0.412 \times 100 = 41.2$
$0.01 \times 100 = 1$

Step 3: The division $0.412 \div 0.01$ simplifies to $41.2 \div 1$ .
Step 4: Dividing $41.2$ by $1$ gives a result of $41.2$ .

Therefore, the solution to the problem is $41.2$ .

Final Answer

$41.2$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numbers by same power of 10 to eliminate decimals
Technique: Multiply 0.412 and 0.01 by 100 to get 41.2 ÷ 1
Check: Verify that 41.2 × 0.01 = 0.412 using multiplication ✓

Common Mistakes

Avoid these frequent errors

Moving decimal points different amounts in dividend and divisor
Don't move the decimal point 2 places in 0.412 but only 1 place in 0.01 = unequal scaling! This changes the problem's value completely. Always multiply both numbers by the exact 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 do we multiply both numbers by 100?

We need to eliminate both decimal places from the divisor 0.01. Since 0.01 has 2 decimal places, we multiply both numbers by $10^2 = 100$ to make fair, equivalent fractions.

What if the divisor has more decimal places than the dividend?

Always use the number with more decimal places to determine your multiplier. If dividing 0.5 ÷ 0.001, multiply both by 1000 since 0.001 has 3 decimal places.

Can I just move the decimal points instead of multiplying?

Yes, but be careful! Moving decimal points is the same as multiplying by powers of 10. Just make sure you move the same number of places in both numbers.

Why does dividing by 0.01 make the answer bigger?

Dividing by a number smaller than 1 always gives a larger result! Think of it as asking "How many 0.01s fit into 0.412?" - lots of tiny pieces fit into a bigger piece.

How do I know I moved enough decimal places?

Keep moving until the divisor becomes a whole number. For 0.01, you need 2 places to get 1. For 0.003, you'd need 3 places to get 3.

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