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Equivalent Fractions Convert fractions to decimals by using long-division 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational number, locate them approximately on a number line diagram, and estimate the value of expressions. Student know that when a fraction has a denominator that is the product of 2’s and/or 5’s, it has a finite decimal expansion because the fraction can then be written in an equivalent form with a denominator that is a power of 10. WKSP HW Procedure Media Student Outcomes Standard Pre Requisite Fraction Decimal Number Line #25 Spiral #6 Fraction Decimal Number Line Fraction 54 20 7 8 Decimal Equivalent Fraction Long Division Rational Approximation Number Line Fraction Decimal Number Line Fraction Equivalent Fraction Decimal Long Division Rational Approximation 41 6 8 9 When given a fraction, you can look at the denominator to see if it’s decimal form will be finite or infinite. Finite decimal: Infinite decimal: Number Line Fraction Decimal Number Line Name: __________________________________ Pre-Algebra 1. Date: ______ Exit Ticket Convert each rational number into a finite decimal. If the fraction cannot be written as a finite decimal, then state how you know. 1 200 1 = 12 = 1 2. Write the decimal expansion of . 3. Use rational approximation to determine the decimal expansion of 11. 8 35 Fraction Decimal Number Line Name: _______________________________________ Pre-Algebra Date: _____ HW #25 Lesson Summary Fractions with denominators that can be expressed as products of only 2’s and/or 5’s have decimal expansions that are finite. When the denominator of a fraction cannot be expressed as a product of only 2’s and/or 5’s, then the decimal expansion of the number will be infinite. The method of rational approximation can be used to write the decimal expansion of rational numbers. Example: Use rational approximation to find the decimal expansion of 𝑚 1. tenth’s place value 10 < 𝑚< 2. blast everything by ten 50 3. Break-up numerator 11 5 4. How far off are you? 11 = − 5 11 50 11 < 11 4 . 𝑚+1 10 <𝑚+1 4 × 11 10 5 11 = + 6 11 6 110 5. Repeat steps 1-4 replacing tenths with hundredths. 1. Which of the following expressions have a finite decimal? (Circle all that apply) 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 2. Write 3 as a decimal. 250 3. Convert the fraction 3 to a decimal. 8 4. Use rational approximation to determine the decimal expansion of 25. 9 Fraction Decimal Number Line Review: 17 17 3 4. Rodney thinks that √64 is greater than 4 . Sam thinks that 4 is greater. Who is right and why? 3 5. Which number is smaller, √27 or 2.89? Explain. 6. Place the following numbers at their approximate location on the number line: √12, √16, 3 20 6 ̅̅̅, √27 , 3. ̅53 3 4