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Procedure for Multiplying a Decimal by a Power of Ten
When multiplying a decimal by a power of ten (, , , etc.), a shortcut avoids the full multiplication algorithm:
- Move the decimal point to the right by the same number of places as there are zeros in the power of . For example, multiplying by (one zero) shifts the decimal point one place right; multiplying by (two zeros) shifts it two places right; multiplying by (three zeros) shifts it three places right.
- Append zeros at the end of the number if there are not enough digits to accommodate the shift.
This shortcut works because each zero in the power of ten corresponds to one factor of , and multiplying by moves every digit one place higher in the place-value system — which is equivalent to shifting the decimal point one position to the right.
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Procedure for Multiplying a Decimal by a Power of Ten
An inventory manager is calculating the total cost of 15.5 units of raw material priced at $4.25 per unit. Arrange the steps of the decimal multiplication procedure in the correct order to find the total cost.
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A payroll clerk is training a new hire on the standard operating procedure for manually calculating employee reimbursements involving decimals. Match each step of the decimal multiplication procedure with the specific rule that must be followed.
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Learn After
A payroll administrator needs to calculate the total budget for 1,000 temporary employees who are each paid a $15.75 daily travel stipend. To use the shortcut for multiplying a decimal by a power of ten, how many places and in which direction should the administrator move the decimal point in the stipend amount?
A warehouse manager is calculating the total weight of 1,000 identical components. To use the shortcut for multiplying a decimal weight by a power of ten, the manager must move the decimal point to the ____.
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A quality control technician is multiplying a precise measurement of 0.4 millimeters by 100 to calculate the total length of a bulk component. According to the shortcut procedure for multiplying a decimal by a power of ten, what is the required step if there are not enough digits to complete the two-place shift to the right?
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During an accounting software orientation, an instructor explains that the system handles multiplication by powers of ten by shifting digits within the place-value system. According to the logic of the decimal shortcut, what is the specific effect on the digits of a number when the decimal point is moved one position to the right?
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