How to do decimal division step by step?
Here's a more visual step-by-step for 4.2 ÷ 0.07:
- Identify the Divisor: 0.07 (This is what we're dividing by).
- Make Divisor Whole: 0.07 needs its decimal moved 2 places to become 7.
- Move Dividend's Decimal: Move the decimal in 4.2 the same 2 places. But 4.2 only has one decimal place, so we add a zero -> 420.
- Rewrite the Problem: New problem: 420 ÷ 7.
- Perform Long Division:
- 7 into 42: 6. (6 x 7 = 42)
- Bring down the 0: 7 into 0: 0.
- So, 420 ÷ 7 = 60.
- Final Answer: 60.
See? Moving the decimal is just a trick to simplify the problem into one we already know how to solve.
Let's break down decimal division with a simple example: 6.45 ÷ 0.5
- Step 1: Make the divisor a whole number. Count how many places you need to move the decimal in the divisor (0.5) to make it a whole number (5). Here, it's 1 place.
- Step 2: Move the dividend's decimal. Move the decimal in the dividend (6.45) the same number of places to the right. So 6.45 becomes 64.5.
- Step 3: Divide as usual. Now your problem is 64.5 ÷ 5. Just do long division. 5 goes into 6 one time, remainder 1. Bring down the 4, making it 14. 5 goes into 14 two times, remainder 4. Bring down the 5, making it 45. 5 goes into 45 nine times exactly.
- Step 4: Place the decimal. Bring the decimal point from the dividend (64.5) straight up into your answer. So, 12.9.
Your final answer is 12.9. The key is to get rid of the decimal in the divisor first!
The best way to think about it is to not be scared of the decimals. A trick my teacher taught me is to think of it as a fraction. So, 6.45 ÷ 0.5 is the same as 6.45 / 0.5. Now, multiply the top and bottom of this fraction by 10 (or 100, etc.) until the bottom is a whole number. (6.45 * 10) / (0.5 * 10) = 64.5 / 5. Now it looks like a normal division problem, right? Just divide 64.5 by 5. You can also check your work by multiplying your answer by the original divisor. 12.9 * 0.5 should equal 6.45, which it does! Practice with a few, and it'll become second nature.