S k i l l
FRACTIONS INTO DECIMALSLesson 23 Section 2 In the previous section, we saw the most frequent |
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"Let the 4 fall into the house" 11 does not go into 4. Write 0 in the quotient, place a decimal point, and add a 0 onto the dividend. (Lesson 11) "11 goes into 40 three (3) times (33) with 7 left over. "11 goes into 70 six (6) times (66) with 4 left over." Since we are dividing 11 into 40 again, we see that this division will never be exact. We will have 36 repeated as a pattern:
exactly as a decimal. However we can approximate it to as many decimal places as we please according to the indicated pattern; and the more
to use that number as a decimal, we must approximate it. Let us approximate it to three decimal places (Lesson 10):
Answer. According to the previous problem,
*
for example, which is .25, is complete.
Fractions, then, when expressed as decimals, will be either complete or incomplete. Which fractions will have complete decimals? Only those in which the factors of the denominator are made up of 2's or 5's. They are fractions with these denominators: 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, and so on. Example 3.
9 goes into 1 zero (0). 9 goes into 10 one (1) time with 1 left over. Again, 9 goes into 10 one (1) time with 1 left over. And so on. This division will never be exact -- we will keep getting 1's in the quotient.
Answer. Divide 73 by 96. Press
Displayed is
Therefore, to three decimal places,
Example 5. In a class of 52 students, 29 were women. a) What fraction were women?
b) Use a calculator to express that fraction as a decimal. Answer. Press
See
This is approximately .558. c) What percent were women? Answer. To change a number to a percent, multiply it by 100. .558 = 55.8% In summary, look at what we have done:
"Out of," with a calculator, always signifies division. Division of a smaller number by a larger. We will return to this in Lesson 30. Please "turn" the page and do some Problems. or Continue on to the next Lesson. Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2007 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |