Select the correct decimal

Learning Objectives Define a rational expression and its decimal forms. Convert a rational number (fraction) into its decimal equivalent using long division. Identify the difference between a terminating and a repeating decimal. Use bar notation correctly to represent repeating decimals. Analyze the prime factors of a denominator to predict whether a rational number's decimal form will terminate or repeat. Evaluate a simple rational expression for a given value and convert the resulting fraction to a decimal. Have you ever noticed that 1/4 of a dollar is $0.25 (it ends), but 1/3 of a dollar is $0.333... (it goes on forever)? 🤔 Let's find out why! This tutorial will teach you how to convert rational expressions, which are essentially fractions with polynomials, in...

TermDefinitionExample Rational ExpressionA fraction in which the numerator and the denominator are polynomials. For our purposes, we will start with the simplest rational expressions: rational numbers.Simple: `3/4`. Algebraic: `(x + 2) / (x - 1)`. Terminating DecimalA decimal number that has a finite number of digits after the decimal point. It ends.`3/8 = 0.375` Repeating DecimalA decimal number that has a digit or a block of digits that repeat infinitely after the decimal point.`2/11 = 0.181818...` Bar Notation (Vinculum)A horizontal line placed over the repeating digit or block of digits in a repeating decimal.`0.181818...` is written as `0.\overline{18}`. Prime FactorizationThe process of breaking down a number into its prime number factors.The prime factorization of 12 is `2 x 2 x 3`...

Fraction to Decimal Conversion To convert a rational number `p/q` to a decimal, perform the division `p ÷ q`. This is the fundamental method for finding the decimal representation of any fraction. The numerator is the dividend and the denominator is the divisor. Terminating Decimal Rule A rational number `p/q`, in its simplest form, will be a terminating decimal if the prime factorization of the denominator `q` consists ONLY of 2s and/or 5s. Formula: `q = 2^a \cdot 5^b` where `a` and `b` are non-negative integers. Use this rule to quickly predict if a decimal will end without doing the full division. First, simplify the fraction, then find the prime factors of the denominator. Repeating Decimal Rule A rational number `p/q`, in its simplest form, will be a repeating dec...