Converting Decimals to Fractions Flashcards

A decimal that has a finite number of digits after the decimal point, e.g., 0.25.

A decimal in which one or more digits repeat infinitely, e.g., 0.333... or 0.142857142857...

Write the decimal as a fraction with the appropriate power of 10 as the denominator, then simplify.

0.25 = 25/100. Simplify to 1/4.

Let x equal the recurring decimal, e.g., x = 0.333...

Multiply x by a power of 10 to shift the repeating part, e.g., 10x = 3.333...

Subtract the original equation from the new equation to eliminate the repeating part, e.g., 10x - x = 3.333... - 0.333...

Solve for x, e.g., 9x = 3, so x = 3/9, which simplifies to 1/3.

Let x = 0.666..., then 10x = 6.666.... Subtract: 10x - x = 6.666... - 0.666..., so 9x = 6. Solve: x = 6/9 = 2/3.

Always simplify fractions to their lowest terms by dividing the numerator and denominator by their HCF.