Exercicios Sobre Fração Geratriz _best_ Online

Both terminating and repeating decimals have a geratrix fraction. Irrational decimals (e.g., (0.1010010001\ldots)) do not. Case 1: Terminating Decimal Write the decimal as a fraction with a power of 10 in the denominator, then simplify.

(0.3\overline18) (x = 0.3181818\ldots) Multiply by 10: (10x = 3.181818\ldots) (now pure repeating: (3.\overline18)) (1000x = 318.181818\ldots) (since (10x \times 100 = 1000x)) Wait — better method: Let (x = 0.3\overline18) Multiply by 10: (10x = 3.\overline18) (pure repeating) Now (10x = 3 + 0.\overline18) (0.\overline18 = \frac1899 = \frac211) So (10x = 3 + \frac211 = \frac33+211 = \frac3511) Thus (x = \frac35110 = \frac722) exercicios sobre fração geratriz

(0.\overline72) (x = 0.727272\ldots) (100x = 72.727272\ldots) Subtract: (100x - x = 72 \Rightarrow 99x = 72 \Rightarrow x = \frac7299 = \frac811) Case 3: Mixed Repeating Decimal Let (x) be the decimal. Multiply by a power of 10 to move the decimal point to just before the repeating block, and by another power to include the whole repeating part. Subtract. Both terminating and repeating decimals have a geratrix

(0.375 = \frac3751000 = \frac38) Case 2: Pure Repeating Decimal Let (x) be the decimal. Multiply by (10^n) where (n) is the length of the repeating block. Subtract the original equation to eliminate the repeating part. exercicios sobre fração geratriz