Dividing by decimals can seem tricky at first, but with a few steps, it becomes straightforward. Here's a step-by-step guide:

Step 1: Understand the Problem

Let's say you want to divide 8.4 by 0.2.

Step 2: Eliminate the Decimal in the Divisor

The divisor is the number you're dividing by (in this case, 0.2). To make division easier, we can eliminate the decimal by multiplying both the divisor and the dividend (the number being divided) by 10, 100, or another power of 10.

For 0.2, multiplying by 10 moves the decimal one place to the right: $0.2 \times 10 = 2$

Do the same for the dividend: $8.4 \times 10 = 84$

So, the new division problem is: $84 \div 2$

Step 3: Perform the Division

Now, simply divide the two whole numbers: $84 \div 2 = 42$

So, $8.4 \div 0.2 = 42$.

Step 4: Check Your Work (Optional)

You can check your result by multiplying the quotient by the divisor to see if you get back to the original dividend: $42 \times 0.2 = 8.4$ This confirms that your division was correct!

Another Example

Let's divide 4.56 by 0.12.

1. Multiply both by 100 (since 0.12 has two decimal places): $4.56 \times 100 = 456,\quad 0.12 \times 100 = 12$

2. Divide the whole numbers: $456 \div 12 = 38$

So, $4.56 \div 0.12 = 38$.

Would you like more details or have any questions? Here are some related questions:

1. How do you multiply decimals?
2. How can you divide decimals mentally?
3. What happens when both numbers have decimals in division?
4. How do you handle more complex decimal division?
5. What are some common mistakes in dividing by decimals?

Tip: Always move the decimal points the same number of places in both the divisor and dividend to simplify the division process.