Fractions

Learning Objectives Convert fractions to decimals using division. Convert terminating decimals to fractions in simplest form. Identify and represent repeating decimals. Compare and order numbers presented as both fractions and decimals. Solve real-world problems involving conversions between fractions and decimals. Explain the relationship between fractions and decimals as different representations of the same value. Ever wondered how a recipe calling for 'half a cup' relates to a digital scale showing '0.5 lbs'? 🤔 These are just two ways to express the same amount! In this lesson, you'll discover the close relationship between fractions and decimals, learning how to convert between them and use both forms to solve problems. Understanding this conn...

TermDefinitionExample DecimalA number system that uses place value to represent fractions where the denominator is a power of ten (e.g., tenths, hundredths, thousandths).0.75 represents seventy-five hundredths, or $\frac{75}{100}$. FractionA number that represents a part of a whole, expressed as a ratio of two integers, a numerator over a denominator.$\frac{3}{4}$ represents three out of four equal parts. Terminating DecimalA decimal that has a finite number of digits after the decimal point; it ends.0.5, 0.25, 0.125 are all terminating decimals. Repeating DecimalA decimal that has one or more digits that repeat infinitely after the decimal point. This is often indicated by a bar over the repeating digit(s).0.333... or $0.\overline{3}$ is a repeating decimal, as is $0.1666...$ or $0.1\ove...

Converting a Fraction to a Decimal To convert a fraction to a decimal, divide the numerator by the denominator. This rule applies to all fractions. The result will either be a terminating or a repeating decimal. Use long division if necessary. Converting a Terminating Decimal to a Fraction Write the decimal as a fraction with the digits after the decimal point as the numerator and a power of 10 (10, 100, 1000, etc.) as the denominator, corresponding to the last decimal place. Then simplify the fraction. For example, if the decimal goes to the hundredths place, the denominator is 100. Always simplify the resulting fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor.