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A ratio is a comparison of two numbers by division. An integer is a positive or negative whole number. {…, -2, -1, 0, 1, 2, …} Numbers that can be written as a comparison of two integers, expressed as a fraction, are called rational numbers. The root of the word rational number is ratio. Percents Decimals 0.32 = 8/25 19% = 19/100 Fractions and Mixed Numbers RATIONAL NUMBERS: numbers that can be written as a ratio of two integers. Rational Numbers Integers Whole Numbers Natural Numbers Every rational number can be written as a decimal by dividing the numerator (top number) by the denominator (bottom number). The decimals that are formed are either terminating decimals or repeating decimals. Terminating decimals end. For example: 0.35 is a terminating decimal because it stops. Repeating decimals continue on forever with a repeating pattern. Sometimes it is one number that repeats and other times it is multiple numbers that repeat. Either way, we put a bar over the digits that repeat. This is called bar notation. For example: Write each fraction as a decimal. If the fraction is a mixed number, the whole number goes to the left of the decimal point. a. 3 4 b. 2 9 c. 4 13 25 d. 3 1 11 To write a decimal as a fraction, read the place value. That is the denominator of the number. Then you can simplify. For example: 0.45 ends in the hundredths place. To make it a fraction, it would be 45 over 100. Then we can reduce. Writing a repeating decimal as a fraction can be a little tricky. Look at the following example: Write 0.5 as a fraction: Step 1: Assign a variable to the value N = 0.555…. Step 2: Multiply both sides of the equation by 10 10N = 10(0.555…) *Note: We multiply by 10 because one digit repeats. If 2 digits repeat, multiply by 100. If 3 digits repeat, by 1,000…so on and so forth. Step 3: Simplify 10N = 5.555… Step 4: Subtract N to eliminate the repeat 10N = 5.555… -N -N 9N = 5 Step 5: Solve for N N = 5/9 Examples: a. .18 b. 0.14 c. 0.27