To divide a smaller decimal by a larger whole number, follow these steps:
Steps for Dividing a Decimal by a Whole Number
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Set up the division problem: Write the problem as a long division problem, placing the decimal (the dividend) inside the division symbol and the whole number (the divisor) outside.
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Place the decimal point in the quotient: Immediately place the decimal point in the quotient (the answer) directly above the decimal point in the dividend. This maintains the correct place value.
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Divide as with whole numbers: Perform the division just as you would with whole numbers, ignoring the decimal point for now.
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Annex zeros if needed: If the decimal dividend is smaller than the whole number divisor, or if you encounter a remainder, annex zeros to the right of the decimal in the dividend. Annexing zeros does not change the value of the dividend but allows you to continue the division.
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Continue dividing: Keep dividing until you reach a point where:
- There is no remainder (the division terminates).
- The quotient begins to repeat in a pattern. In this case, you can round the quotient to a desired level of precision.
Example
Let's divide 0.75 by 5:
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Set up:
______ 5 | 0.75 -
Place the decimal:
0.____ 5 | 0.75 -
Divide: 5 goes into 0, zero times. 5 goes into 7, one time.
0.1___ 5 | 0.75 -5 --- 2 -
Bring down the 5:
0.1___ 5 | 0.75 -5 --- 25 -
Divide: 5 goes into 25, five times.
0.15 5 | 0.75 -5 --- 25 -25 --- 0
Therefore, 0.75 รท 5 = 0.15
Key Considerations
- Place Value: Remember that the placement of the decimal point is crucial for accuracy.
- Annexing Zeros: Annexing zeros is a common and valid technique to continue the division process, especially when the dividend is smaller than the divisor or a remainder occurs.
- Repeating Decimals: If the division results in a repeating decimal, you may need to round the answer to a specific number of decimal places.
By following these steps carefully, you can successfully divide any smaller decimal by a larger whole number.
