Multiplication with Decimals

Definition

Multiplication with decimals is the process of multiplying two numbers that contain decimal places. It involves applying the standard multiplication algorithm while taking into account the placement of the decimal points in the factors to determine the correct decimal placement in the product.

5 Must Know Facts For Your Next Test

1. The number of decimal places in the product of a multiplication with decimals is equal to the sum of the decimal places in the factors.
2. When multiplying a whole number and a decimal, the decimal places in the product are the same as the decimal places in the decimal factor.
3. Multiplying a decimal by a power of 10 (e.g., 10, 100, 1000) can be done by shifting the decimal point of the decimal factor to the right by the same number of places as the power of 10.
4. Rounding the product of a multiplication with decimals may be necessary to express the result in a more practical or meaningful way.
5. Estimation can be used to check the reasonableness of the result when multiplying with decimals.

Review Questions

• Explain the relationship between the number of decimal places in the factors and the number of decimal places in the product when multiplying with decimals.
  • When multiplying two decimal numbers, the number of decimal places in the product is equal to the sum of the decimal places in the factors. For example, if you multiply 2.3 by 4.5, the product will have 2 + 1 = 3 decimal places, resulting in a final answer of 10.35. This is because the decimal places in the factors (2.3 has 1 decimal place, and 4.5 has 1 decimal place) add up to the 3 decimal places in the product.
• Describe the process of multiplying a whole number and a decimal, and how the decimal places are determined in the product.
  • When multiplying a whole number and a decimal, the decimal places in the product are the same as the decimal places in the decimal factor. For instance, if you multiply 7 by 3.2, the product will have the same number of decimal places as the decimal factor, which is 3.2 (2 decimal places). The final answer would be 22.4. This is because the whole number does not contribute any decimal places to the product, and the decimal places are solely determined by the decimal factor.
• Explain how to use rounding and estimation to check the reasonableness of the result when multiplying with decimals.
  • Rounding and estimation can be used to check the reasonableness of the result when multiplying with decimals. Rounding the factors to the nearest whole number or a specified number of decimal places can provide a quick estimate of the product, which can then be compared to the actual result. For example, if you multiply 4.67 by 2.89, you can round the factors to 5 and 3, respectively, and estimate the product to be around 15. This can help you determine if the final answer of 13.5163 is reasonable. Additionally, you can use estimation techniques, such as rounding the factors to the nearest power of 10, to quickly assess the order of magnitude of the product and ensure it aligns with your expectations.

Related terms

Decimal Point: The decimal point is the symbol (.) that separates the whole number part from the fractional part of a decimal number.

Place Value: Place value refers to the value of a digit based on its position in a number, with each place representing a power of 10.

Rounding: Rounding is the process of approximating a number to a specified degree of accuracy, often to a certain number of decimal places or significant figures.