1 - Weebly
All real numbers can be grouped into either of the following two categories:
Rational Numbers - Any number that can be expressed as a fraction; Irrational Numbers - Any other number.
All integers (positive and negative whole numbers), terminating decimals (0.36, 0.125, ...) and recurring or repeating decimals (0.3333333333, 0.121212121212, ...) are rational.
All non-terminating decimals such as or [pic], are irrational.
1. [pic]is a recurring decimal. Without using a calculator, write [pic] in decimal form. What will [pic]be in decimal form? What will [pic] be? (Check each prediction with a calculation.)
2. Are all fractions with a denominator of 9 recurring decimals? Investigate.
3. Which other values for the denominator produce recurring decimals? Using a calculator, the decimal value displayed for the fraction [pic] is 0.2857 142. Could this be a recurring decimal? Without using a calculator, write [pic] as a decimal (produce at least 12 values after the decimal point).
4. Investigate the recurring decimals for [pic]. Investigate the recurring decimals for [pic]
5. Investigate fractions with a denominator of 13. Investigate fractions with a denominator of 17.
6. Investigate to find which denominators give recurring decimals and which give terminating decimals. Can all fractions be written as either a repeating or a terminating decimal? What factors must the denominator have if the fraction is a recurring decimal? What if the recurring decimal has some non recurring digits at the beginning?
What is the fraction for 0. 1212121212 Let x=0.12121212121212 (1)
Therefore l00x= 12.121212121212 (2) (2)-(1) 99x=12
Therefore [pic]or 4/33.
7. Investigate the fractions for other recurring decimals. Be sure to include decimals such as 0.6666666666..., 0.1666666666..., 0.27272727..., 0.214214214 , 0.3214214214...
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