Exercicios Sobre Fração Geratriz May 2026

(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.

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. exercicios sobre fração geratriz

1. What is a Geratrix Fraction? A geratrix fraction (Portuguese: fração geratriz ) is the common fraction that generates a repeating decimal (also called a recurring decimal). In other words, it is the fraction in lowest terms that, when divided, produces a given decimal expansion that eventually repeats. Both terminating and repeating decimals have a geratrix

(0.\overlineabc\ldots = \frac\textrepeating block10^n - 1) where (n) = number of digits in the block. In other words

(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)

(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.