Question 1 Show that the decimals 0.6, 0.1, 0.2, and 0.325 are positive rational numbers. Answer 1 Recall that 0.6 can be read as "six tenths." Once the decimal place is "tenths," you can write it as a fraction with a denominator of 10. 0.6 = 6 10 0.6= 10 6 0.1 is similar, and can be read as "one tenth." The fraction is 0.1 = 1 10 0.1= 10 1 0.2 is also similar, and can be read as "two tenths." The fraction is 0.2 = 2 10 0.2= 10 2 0.325 can be read as "three hundred twenty-five thousandths." Three decimal places is "thousandths," and you can write it as a fraction with a denominator of 1000. 0.325 = 325 1000 0.325= 1000 325 Question 2 The decimals chart in this lesson shows that we line up the decimal points when we add or subtract decimal numbers. Why do we do that? Answer 1 Remember, you can only add numbers together that are in the same place values. Ones are added to ones. Tens are added to tens. Tenths are added to tenths. RESULT: You must line up the decimals because when you add or subtract numbers you must do so according to their place value. Question 3 When multiplying decimals, how do you know where to place the decimal point? Think about this as you do parts (a) through (d) below. a. Write two equations for multiplying 0.3 by 0.16. One equation should express the factors and product using decimals, and one using fractions. b. In part (a), you multiplied tenths by hundredths to get thousandths. Do you always get thousandths if you multiply tenths by hundredths? Why or why not? What do you get if you multiply tenths by tenths? Hundredths by hundredths? Use several examples to justify your answers. c. When a multiplication problem is written using decimals, there is a relationship between the number of decimal places in the parts (or factors) of the problem and the number of decimal places in the answer (or product). d. Describe a shortcut for locating the decimal point in the answer to a problem involving decimal multiplication. Answer 1 a. Equation 1 (decimal form): 0.3 × 0.16 = 0.048 0.3×0.16=0.048 Equation 2 (fraction form): 3 10 × 16 100 = 48 1000 10 3 × 100 16 = 1000 48 b. No, you do not always get thousandths if you multiply tenths by hundredths. The result depends on the total number of decimal places. Tenths × Tenths = Hundredths Tenths × Hundredths = Thousandths Hundredths × Hundredths = Ten-Thousandths c. Multiply as usual, disregarding the decimal points. 3 × 16 = 48 3×16=48 Put the decimal point in the result so that it has the same number of decimal places as the sum of the two original values. In other words, multiply the two values by the number of digits after the decimal point in each; the result should have the same number of digits after the decimal point. 0.3 has 1 decimal place, 0.16 has 2 decimal places, so the answer has 3 decimal places: 0.048 0.048 Question 4 Change the following decimals to fractions. Give each fraction in its simplest form. a) 4.2, b) 0.06, c) 1.85, d) 2.005. Answer 1 a) 4 1 5 4 5 1 b) 3 50 50 3 c) 1 17 20 1 20 17 d) 2 1 200 2 200 1 Question 5 The product of 2 decimals is 20.062. One of the factors has 2 decimals. How many decimals in the other factors? Answer 1 Given two decimals, the product 20.062. One of the factors has 2 decimals. Find the number of decimals in the other factor. The number of decimal places in the product must equal the total number of decimal places in the factors. The decimal number 20.062 has 3 decimal places and one of the factors has 2 decimal places. So the number of decimal places in the other factor = 3 − 2 = 1 =3−2=1.