Decimal Notation - XYZ Custom Plus

228Chapter 4 Decimal Notation2. Change each decimal to a fractionand multiply. Write youranswer as a decimal.a. 0.5 3 0.007b. 0.05 3 0.07Example 2Change each decimal to a fraction and multiply: 0.05 3 0.003Solution 0.05 3 0.003 555 3} 3 } Change to fractions100 1,00015}} 100,000Multiply numerators andmultiply denominators5 0.00015 Write the answer in decimal formThe result is 0.00015, which has a total of five digits to the right of the decimalpoint.Looking over these first two examples, we can see that the digits in the resultare just what we would get if we simply forgot about the decimal points andmultiplied; that is, 3 3 5 5 15. The decimal point in the result is placed so that thetotal number of digits to its right is the same as the total number of digits to theright of both decimal points in the original two numbers. The reason this is truebecomes clear when we look at the denominators after we have changed fromdecimals to fractions.3. Change to fractions and multiply:a. 3.5 3 0.04b. 0.35 3 0.4Example 3Multiply: 2.1 3 0.07Solution 2.1 3 0.07 5 2 1 } 1035 } 21 73 } 10 1007} 100Change to fractions5 147 } 1,000Multiply numerators andmultiply denominators5 0.147 Write the answer as a decimalAgain, the digits in the answer come from multiplying 21 3 7 5 147. The decimalpoint is placed so that there are three digits to its right, because that is the totalnumber of digits to the right of the decimal points in 2.1 and 0.07.We summarize this discussion with a rule.RuleTo multiply two decimal numbers:1. Multiply as you would if the decimal points were not there.2. Place the decimal point in the answer so that the number of digits to itsright is equal to the total number of digits to the right of the decimal pointsin the original two numbers in the problem.4. How many digits will be to theright of the decimal point in thefollowing products?a. 3.706 3 55.88b. 37.06 3 0.5588Answers2. Both are 0.00353. Both are 0.14 4. a. 5 b. 6Example 4How many digits will be to the right of the decimal point inthe following product?2.987 3 24.82Solution There are three digits to the right of the decimal point in 2.987 andtwo digits to the right in 24.82. Therefore, there will be 3 1 2 5 5 digits to the rightof the decimal point in their product.