Multiplying and Dividing with Decimals

Understanding the Concept of Multiplication and Division with Decimals

Multiplication and division with decimals follow the same fundamental principles as their whole number counterparts.
When multiplying decimals, it is often easier to ignore the decimals at first, multiply as if they were whole numbers, then reinsert the decimal.
With division, it is sometimes necessary to shift the decimal place of the divisor and dividend in order to make the divisor a whole number.

Without Adjusting the Decimals: Multiply the numbers as if they were whole numbers and then place the decimal point into the product. The location of the decimal is determined by the combined number of digits after the decimal in the original numbers.
- For example, if you are multiplying 4.5 by 0.2:
  - Do the multiplication ignoring the decimals first. So, 45 * 2 = 90.
  - Count the digits after the decimal in the original problem. 4.5 has 1 and 0.2 has 1.
  - After adding these up, you get 2. Thus, there should be 2 digits after the decimal in the answer. Answer = 0.90.

By Adjusting the Decimals: If the divisor (the number you’re dividing by) is a decimal, shift the decimal place to the right until it becomes a whole number; do the same with the dividend (the number you’re dividing).
- For example, if you’re dividing 1.60 by 0.4:
  - First, shift the decimal of both numbers two places to the right making them 160 and 4.
  - Then, perform the division: 160 ÷ 4 = 40.

When working with decimals, always double check to ensure you’ve placed the decimal point in the correct spot.
Constant revision and practice will help with mastering multiplication and division of decimal numbers.
Getting comfortable with these techniques will make working with scientific notation, percentages, and more advanced algebra problems easier.