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Justification for Moving Decimals in Division
When dividing decimals, the process of 'moving' the decimal point to the right in both the divisor and the dividend in order to make the divisor a whole number is mathematically justified by the Equivalent Fractions Property. Because a division operation can be written as a fraction where the dividend is the numerator and the divisor is the denominator, shifting the decimal points the same number of places is equivalent to multiplying both the numerator and the denominator by the same power of . Multiplying the numerator and denominator by the same nonzero value creates an equivalent fraction, ensuring the value of the quotient remains unchanged.
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
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Dividing $3.99 ÷ 24
A procurement officer is calculating the price per unit for a bulk order of chemicals. The calculation requires dividing the total cost by the total volume, both of which are decimal values. Arrange the steps for dividing decimals in the correct order to ensure an accurate calculation.
A quality control analyst is calculating the density of a material by dividing its mass (12.45 grams) by its volume (2.5 cubic centimeters). To simplify the calculation, the analyst shifts the decimal point in both the mass and the volume one place to the right. Which mathematical property justifies this action?
A financial data analyst is drafting a Standard Operating Procedure (SOP) for auditors to use when manually verifying unit cost calculations. Match each part of the decimal division problem with the specific rule or action required by the standard procedure.
A warehouse manager is calculating the number of units in a shipment by dividing the total weight (84.2 pounds) by the weight of a single unit (0.05 pounds). To make the divisor (0.05) a whole number, the manager moves the decimal point two places to the right. To ensure the quotient remains unchanged, the manager must also move the decimal point in the dividend (84.2) exactly ____ place(s) to the right.
When a financial analyst manually verifies a calculation by dividing one decimal by another, the standard procedure requires placing the decimal point in the quotient directly above its original location in the dividend, before any shifts were made.
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A payroll administrator is processing a series of account corrections and needs to divide a total negative adjustment of -$120.50 (the dividend) by a negative factor of -0.25 (the divisor). According to the standard procedure for dividing decimals, which rule correctly determines the sign of the resulting quotient?
Example of Dividing
Example of Dividing
Example of Dividing
Justification for Moving Decimals in Division
A logistics coordinator is manually calculating shipping rates by dividing a total cost (the dividend) by a weight (the divisor). According to the standard procedure for dividing decimals, what action must be taken if the dividend has fewer decimal places than the number of shifts required to make the divisor a whole number?