Solve Division Problem: 4.2 ÷ 0.001 Step-by-Step

Q: Why do I multiply both numbers by 1000?

You multiply by 1000 because the divisor 0.001 has 3 decimal places. Multiplying by 1000 moves the decimal point 3 places right, turning 0.001 into 1, which makes division much easier!

Q: What if I forget to multiply both numbers?

You'll get the wrong answer! Division is like a fraction - if you only change the top or bottom, you change the whole value. Always multiply both numbers by the same amount.

Q: Can I solve this problem a different way?

Yes! You can think of it as $ 4.2 ÷ 0.001 = 4.2 × \frac{1}{0.001} = 4.2 × 1000 = 4200 $. Division by a decimal equals multiplication by its reciprocal.

Q: Why is the answer so much bigger than what I started with?

When you divide by a number less than 1, the result is always bigger! Think about it: how many 0.001s fit into 4.2? A lot! That's why you get 4200.

Decimal Division with Small Divisors

$4.2:0.001=$

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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 1000 to make division easier

00:35 Let's divide between the new numbers and calculate the quotient

00:40 Any number divided by 1 is always equal to itself

00:44 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

$4.2:0.001=$

Step-by-step solution

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

Step 1: Adjust the decimal places to simplify the division.
Step 2: Scale the numbers to eliminate the decimal point in the divisor.
Step 3: Perform the division with whole numbers.

Now, let's work through each step:
Step 1: We need to divide $4.2$ by $0.001$ .
Step 2: Multiply both the dividend $4.2$ and the divisor $0.001$ by $1000$ to avoid decimal division. This gives us:

$4.2 \times 1000 = 4200$
$0.001 \times 1000 = 1$

Step 3: Now, divide $4200$ by $1$ :

$4200 \div 1 = 4200$

Therefore, the solution to the problem is $4200$ .

Final Answer

$4200$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numbers by same power of 10 to eliminate decimal divisor
Technique: Multiply by 1000: 4.2 × 1000 = 4200, 0.001 × 1000 = 1
Check: Verify 4200 × 0.001 = 4.2 using multiplication ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point incorrectly
Don't just move the decimal point in the dividend without adjusting the divisor = wrong answer! Moving 4.2 to 42 while keeping 0.001 gives 42,000 instead of 4,200. Always multiply both numbers by the same value to maintain the ratio.

Practice Quiz

Test your knowledge with interactive questions

$$ 2.6:0.1= $$

FAQ

Everything you need to know about this question

Why do I multiply both numbers by 1000?

You multiply by 1000 because the divisor 0.001 has 3 decimal places. Multiplying by 1000 moves the decimal point 3 places right, turning 0.001 into 1, which makes division much easier!

What if I forget to multiply both numbers?

You'll get the wrong answer! Division is like a fraction - if you only change the top or bottom, you change the whole value. Always multiply both numbers by the same amount.

How do I know how many zeros to use when multiplying?

Count the decimal places in the divisor. For 0.001, there are 3 decimal places, so multiply by 1000 (which has 3 zeros). For 0.01, you'd multiply by 100.

Can I solve this problem a different way?

Yes! You can think of it as $4.2 ÷ 0.001 = 4.2 × \frac{1}{0.001} = 4.2 × 1000 = 4200$ . Division by a decimal equals multiplication by its reciprocal.

Why is the answer so much bigger than what I started with?

When you divide by a number less than 1, the result is always bigger! Think about it: how many 0.001s fit into 4.2? A lot! That's why you get 4200.

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