Convert between decimals and fractions or mixed numbers

Learning Objectives Convert any terminating decimal into a simplified fraction or mixed number. Convert any repeating decimal into a simplified fraction. Convert any fraction or mixed number into its decimal equivalent. Identify the correct power of 10 to use for place value when converting decimals to fractions. Apply the algebraic method to convert complex repeating decimals into fractions. Simplify all resulting fractions to their lowest terms. Distinguish between fractions that produce terminating decimals and those that produce repeating decimals. Ever seen a batting average of .275 and wondered what that looks like as a fraction? 🤔 This skill is your key to understanding the numbers that describe our world! This tutorial will teach you how to fluently convert numbe...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. All terminating and repeating decimals are rational numbers.0.5 is rational because it can be written as 1/2. 7 is rational because it can be written as 7/1. Terminating DecimalA decimal number that has a finite number of digits after the decimal point.0.625 is a terminating decimal because it ends after the '5'. Repeating DecimalA decimal number that has a digit or a block of digits that repeat infinitely. The repeating part is often indicated with a bar over the digits (vinculum).0.333... or 0.\overline{3} is a repeating decimal. 2.142857142857... or 2.\overline{142857} is another example. Mixed NumberA number composed of a whole number and a p...

Terminating Decimal to Fraction Conversion Decimal = \frac{\text{Digits after decimal point}}{10^n} Use this for decimals that end. 'n' is the number of digits after the decimal point. Write the digits that come after the decimal point in the numerator and a power of 10 (10, 100, 1000, etc.) in the denominator. Always simplify the resulting fraction. Fraction to Decimal Conversion \frac{a}{b} = a \div b To convert any fraction to a decimal, simply divide the numerator (a) by the denominator (b). The result will be either a terminating or a repeating decimal. Repeating Decimal to Fraction (Algebraic Method) 1. x = \text{repeating decimal} \newline 2. 10^k x = \text{decimal shifted} \newline 3. (10^k - 1)x = \text{integer} \newline 4. x = \frac{\text{integer}}{...