Number: Recurring Decimals Definition and Simple Conversion to Fraction Form. By I Porter

Definition: Recurring Decimal A Recurring Decimal is a rational number that can not be written with a power of 10 as its denominator, in which a set of digits to the right of the decimal point cycle (repeat) endlessly. Examples a) b) c) d) Single digit repeating.Six digits repeating. Two digits repeating.

Converting Recurring Decimals to Fractions 1) Prove that, as a fraction is. Examples Solution: Let If 1 digit repeats, multiply by 10 = 10 1 Subtract the two equations. The repeating decimal digit should be eliminated. Make x the subject by dividing by the multiplier in fraction form p / q. Simplify the fraction ( use your calculators fraction key is the easiest method). Therefore, as required. Always check your answer with your calculator!

Converting Recurring Decimals to Fractions 2) Prove that, as a fraction is. Examples Solution: Let If 2 digits repeat, multiply by 100 = 10 2, keep the decimal part the same length. Subtract the two equations. The repeating decimal digits should be eliminated. Make x the subject by dividing by the multiplier in fraction form p / q. Simplify the fraction ( use your calculators fraction key is the easiest method). Therefore, as required. Always check your answer with your calculator!

Converting Recurring Decimals to Fractions 3) Express, in the form p / q, where p and q have no common factors. Examples Solution: Let If 1 digit repeat, multiply by 10 = 10, keep the decimal part the same length. Subtract the two equations. The repeating decimal digit should be eliminated. Make x the subject by dividing by the multiplier in fraction form p / q. Simplify the fraction ( use your calculators fraction key is the easiest method) Or multiply by 10 / 10, to change to a correct fraction. Therefore, as required. Always check your answer with your calculator!

Converting Recurring Decimals to Fractions 4) Express, in the form a b / c, where b and c have no common factors. Examples Solution: Let If 3 digits repeat, multiply by 1000 = 10 3, keep the decimal part the same length. Subtract the two equations. The repeating decimal digit should be eliminated. Make x the subject by dividing by the multiplier in fraction form p / q. Simplify the fraction ( use your calculators fraction key is the easiest method) Or multiply by 10 / 10, to change to a correct fraction. Most calculator will have trouble with this fraction. Therefore, as required. Always check your answer with your calculator!

Exercise: Convert each of the following to a fraction in simplest form. 1)2) 3)4) 5)6)