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Converting Decimals to Fractions in Simplest Form

Learn how to convert decimals to fractions in simplest form. Practice exercises and examples provided.

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Converting Decimals to Fractions in Simplest Form

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  1. Week 6, Day One HW # 21- HOLT p. 68 # 19-52 even Warm up Write each decimal as a fraction in simplest form. A. 8.75 • B. 0.2625 • 0.27 • –0.625 • Write 13/6 as a decimal.

  2. 2625 10,000 = 27100 5 / 8 21 80 = 75 100 =8 2.16 3 4 =8 A. 8.75 Warm Up Response 8.75 5 is in the hundredths place, so write hundredths as the denominator. Simplify by dividing by the greatest common divisor. B. 0.2625 5 is in the ten-thousandths place. 0.2625 Simplify by dividing by the greatest common divisor. C.0.27 D.–0.625 E.Write as a decimal. 13/ 6 0.325

  3. Homework Check Guided Practice # 1,11,17 • 0.625 11) ¾ 17) 3 21/100

  4. Goals for Today • Writing Repeating Decimals as Fractions • Chapter 1 quiz – pass back (≤20 pts see me at PT) • Factor Trees II worksheet- compare with your neighbor • DO class work: p. 68 # 1-18 AND 27, 37, 45 • Clean out your binder and put your MMC project in your spiral (if you have not done this already).

  5. To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

  6. 622 1000 = 311 500 = 37 100 =5 For Example Write each decimal as a fraction in simplest form. A. 5.37 7 is in the hundredths place, so write hundredths as the denominator. 5.37 B. 0.622 2 is in the thousandths place, so write thousandths as the denominator. 0.622 Simplify by dividing by the greatest common divisor.

  7. Remember! A fraction is in reduced, or simplest, form when the numerator and the denominator have no common divisor other than 1.

  8. 2625 10,000 = 21 80 = 75 100 =8 3 4 =8 Example 2 Write each decimal as a fraction in simplest form. A. 8.75 5 is in the hundredths place, so write hundredths as the denominator. 8.75 Simplify by dividing by the greatest common divisor. B. 0.2625 5 is in the ten-thousandths place. 0.2625 Simplify by dividing by the greatest common divisor.

  9. Example: Writing Repeating Decimals as Fractions _ Write 0.4 as a fraction in simplest form. x = 0.44444… Let x represent the number. Multiply both sides by 10 because 1 digit repeats. 10x = 10(0.44444…) 10x = 4.444444… Subtract x from both sides to eliminate the repeating part. Since x = 0.44444…, use 0.44444… for x on the right side of the equation. -x = -0.44444… 9x = 4 9x = 4 9 9 Since x is multiplied by 9, divide both sides by 9. 4 9 x =

  10. Example 2 __ Write 0.36 as a fraction in simplest form. x = 0.363636… Let x represent the number. Multiply both sides by 100 because 2 digits repeat. 100x = 100(0.363636…) 100x = 36.363636… Subtract x from both sides to eliminate the repeating part. Since x = 0.363636…, use 0.363636… for x on the right side of the equation. -x = -0.363636… 99x = 36 99x = 36 99 99 Since x is multiplied by 99, divide both sides by 99. 36 99 4 11 x = = Write in simplest form.

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