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➕pre-algebra review

Division Involving Decimals

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Division involving decimals refers to the process of dividing a number that contains a decimal point by another number that also contains a decimal point. This operation is used to find the quotient, or the result of the division, when both the dividend and divisor have decimal places.

5 Must Know Facts For Your Next Test

  1. To divide a decimal by a decimal, you can first convert both numbers to whole numbers by moving the decimal point the same number of places to the right in both the dividend and divisor.
  2. The number of decimal places in the quotient will be equal to the number of decimal places in the dividend minus the number of decimal places in the divisor.
  3. If the divisor is a whole number, you can divide the dividend by the divisor and then place the decimal point in the quotient the same number of places to the right as there are in the dividend.
  4. Dividing a decimal by a decimal can be used to solve problems involving rates, ratios, and unit conversions.
  5. Proper placement of the decimal point in the quotient is crucial when dividing decimals to ensure the final answer is accurate.

Review Questions

  • Explain the process of dividing a decimal by a decimal, including how to determine the placement of the decimal point in the quotient.
    • To divide a decimal by a decimal, first convert both the dividend and divisor to whole numbers by moving the decimal point the same number of places to the right in both numbers. For example, to divide 12.45 by 3.7, you would move the decimal point two places to the right in both numbers, making the dividend 1245 and the divisor 370. Then, divide 1245 by 370 to get the quotient of 3.36. The number of decimal places in the quotient will be equal to the number of decimal places in the dividend minus the number of decimal places in the divisor, which in this case is two.
  • Describe how dividing a decimal by a decimal can be used to solve problems involving rates, ratios, and unit conversions.
    • Dividing a decimal by a decimal is often used in problems involving rates, ratios, and unit conversions. For example, if you need to convert miles per hour to feet per second, you would divide the rate in miles per hour by the conversion factor of 1.467 (the number of feet in a mile divided by the number of seconds in an hour). This division of a decimal by a decimal allows you to convert the rate from one unit of measurement to another. Similarly, dividing a decimal quantity by a decimal divisor can be used to calculate ratios or rates, such as the number of calories per gram of a food item or the miles per gallon of a vehicle.
  • Analyze the importance of properly placing the decimal point in the quotient when dividing decimals, and explain the potential consequences of incorrect placement.
    • Proper placement of the decimal point in the quotient is crucial when dividing decimals to ensure the final answer is accurate. If the decimal point is placed incorrectly, the quotient will be off by a power of ten, leading to a significant error in the final result. For example, if you were to divide 12.45 by 3.7 and incorrectly place the decimal point, resulting in a quotient of 33.6 instead of the correct 3.36, the error would be magnified in any subsequent calculations or applications of that result. Accurate decimal point placement is essential for maintaining the integrity of the division process and producing reliable solutions, especially in fields like finance, engineering, and scientific research where precise calculations are paramount.