Recurring Decimals Flashcards

A decimal number that has a repeating pattern of digits after the decimal point.

A decimal number that has a finite number of digits after the decimal point.

A recurring decimal is written with a dot or a line above the repeating digits (e.g., 0.333... = 0.3̇).

To convert a recurring decimal to a fraction, use algebra to form an equation and solve for the fraction.

For 0.3̇, let x = 0.3̇. Then 10x = 3.3̇. Subtract x from 10x to get 9x = 3, so x = 3/9 = 1/3.

A decimal where only part of the digits after the decimal point repeat (e.g., 0.1666... = 0.16̇).

Split the decimal into a terminating part and a recurring part, then convert each part to fractions and combine.

Multiply the decimal by a power of 10 to align the repeating parts, then subtract to eliminate the recurring part.

Let x = 0.12̇. Then 100x = 12.12̇. Subtract x from 100x to get 99x = 12, so x = 12/99 = 4/33.

Recurring decimals can be identified by a repeating pattern of digits, often shown with a dot or line above the repeating part.