Dividing with decimal numbers involves a few key steps to ensure accurate results. The core idea is to transform the divisor (the number you're dividing by) into a whole number.
Here's a breakdown of the process:
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Set up the division problem: Write the problem as you normally would for long division, with the dividend (the number being divided) inside the division symbol and the divisor outside.
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Move the decimal point in the divisor: Count how many places you need to move the decimal point in the divisor to the right to make it a whole number.
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Move the decimal point in the dividend: Move the decimal point in the dividend the same number of places to the right as you did in the divisor. You might need to add zeros to the end of the dividend if you run out of digits. This does not change the value of the dividend.
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Perform the division: Divide as you would with whole numbers. Place the decimal point in the quotient (the answer) directly above the decimal point in the new dividend.
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Check your answer: You can check your answer by multiplying the quotient by the original divisor. This should equal the original dividend.
Example:
Let's say you want to divide 3.15 by 0.9.
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Write the problem: 0.9 | 3.15
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Move the decimal in the divisor (0.9) one place to the right to make it 9.
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Move the decimal in the dividend (3.15) one place to the right to make it 31.5.
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Now the problem is: 9 | 31.5
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Divide:
- 9 goes into 31 three times (3 x 9 = 27). Write 3 above the 1 in 31.
- Subtract 27 from 31, which leaves 4.
- Bring down the 5. You now have 45.
- 9 goes into 45 five times (5 x 9 = 45). Write 5 above the 5 in 31.5
- Subtract 45 from 45 which leaves 0.
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The answer is 3.5
Another Example
Let's say you want to divide 3150 by 0.9:
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Write the problem: 0.9 | 3150
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Move the decimal in the divisor (0.9) one place to the right to make it 9.
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Move the decimal in the dividend (3150) one place to the right. Since 3150 is a whole number, the decimal is understood to be at the end. So, 3150 becomes 31500.
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Now the problem is: 9 | 31500
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Divide: 31500/9 = 3500
