Convert between decimals and fractions or mixed numbers

Learning Objectives Convert any terminating decimal into a simplified fraction or mixed number. Convert any fraction or mixed number into its exact decimal equivalent, identifying it as terminating or repeating. Analyze the prime factors of a fraction's denominator to predict whether its decimal form will terminate or repeat. Convert simple repeating decimals (e.g., 0.555...) into simplified fractions using an algebraic method. Convert complex repeating decimals (e.g., 0.12333...) into simplified fractions using an algebraic method. Apply conversion skills to solve multi-step problems that involve both decimal and fractional representations of numbers. Ever tried to split a $25.50 bill three ways, or measure exactly 5/16 of an inch for a project? 🤔 Understanding how to...

TermDefinitionExample 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 digit 5. Repeating DecimalA decimal number that has a digit or a block of digits that repeats infinitely after the decimal point. The repeating block is called the period.0.454545... is a repeating decimal with a period of '45'. It can be written as 0.\overline{45} using a vinculum. Rational NumberAny number that can be expressed as a quotient or fraction p/q of two integers, where p is the numerator and q is the non-zero denominator.Both 0.75 (which is 3/4) and 0.\overline{3} (which is 1/3) are rational numbers. Mixed NumberA number composed of a whole number and a proper fraction.4 3/8 is a mixed number, r...

Terminating Decimal to Fraction x = \frac{\text{digits after decimal}}{\text{10}^{\text{n}}} To convert a terminating decimal to a fraction, write the digits after the decimal point as the numerator. The denominator is 10 raised to the power of 'n', where 'n' is the number of decimal places. Always simplify the resulting fraction. Fraction to Decimal \frac{a}{b} = a \div b To convert a fraction to a decimal, perform long division of the numerator by the denominator. The result will either terminate or enter a repeating pattern. Algebraic Conversion of Repeating Decimals 1. \text{Let } x = \text{the repeating decimal.} \newline 2. \text{Create two equations by multiplying } x \text{ by powers of 10 to shift the decimal point.} \newline 3. \text{Subtr...