Convert between decimals and fractions or mixed numbers

Learning Objectives Convert terminating decimals to fractions in simplest form. Convert fractions to terminating or repeating decimals using division. Convert simple repeating decimals (e.g., 0.333..., 0.1212...) to fractions. Convert mixed numbers to decimals. Convert decimals greater than one to mixed numbers or improper fractions. Identify rational numbers as numbers that can be expressed as a fraction p/q where q ≠ 0. Ever wonder why a recipe calls for '3/4 cup' of flour, but your measuring cup only has decimal markings? Or how your batting average of .333 relates to hitting 1 out of every 3 pitches? ⚾ In this lesson, you'll master the essential skill of converting between decimals, fractions, and mixed numbers. This ability is crucial for understanding...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q$ is not zero. Decimals that terminate or repeat are rational numbers.$\frac{3}{4}$, $0.75$, $-5$, $0.\overline{3}$ Terminating DecimalA decimal that has a finite number of digits after the decimal point; it stops.$0.25$, $1.7$, $-3.125$ Repeating DecimalA decimal that has one or more digits that repeat infinitely after the decimal point. A bar is placed over the repeating digit(s).$0.\overline{3}$ (which is $0.333...$), $0.\overline{12}$ (which is $0.121212...$) FractionA number that represents a part of a whole, expressed as a ratio of two integers, a numerator over a denominator.$\frac{1}{2}$, $\frac{7}{8}$, $\frac{10}{3}$ Mixed NumberA number consistin...

Converting Terminating Decimals to Fractions 1. Write the decimal as a fraction with the decimal number (without the decimal point) as the numerator. 2. For the denominator, use a power of 10 corresponding to the decimal's place value (e.g., tenths, hundredths, thousandths). 3. Simplify the fraction to its lowest terms. This rule is used when a decimal ends. The number of decimal places tells you which power of 10 to use (1 decimal place = 10, 2 decimal places = 100, etc.). Example: $0.75 = \frac{75}{100} = \frac{3}{4}$ Converting Fractions to Decimals Divide the numerator by the denominator. This rule applies to all fractions. The result will either be a terminating decimal or a repeating decimal. Example: $\frac{3}{8} = 3 \div 8 = 0.375$ Example: $\frac{1}{3} = 1 \div...