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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Divide. 24. 12. 1. 36  3 2. 144  6. 3. 68  17 4. 345  115. 3. 4. 5. 1024  64. 16. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Divide. 24 12 1. 36  3 2. 144  6 3. 68  17 4. 345  115 3 4 5. 1024  64 16

  3. California Standards NS1.5 Know that every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions. NS1.3 Convert fractions to decimals and percents and use representations in estimations, computations, and applications.

  4. Vocabulary rational number terminating decimal repeating decimal

  5. A rational numberis any number that can be written as a fraction , where n and d are integers and d  0. n d Any fraction can be written as a decimal by dividing the numerator by the denominator. If the division ends or terminates, because the remainder is zero, then the decimal is a terminating decimal.

  6. If the division leads to a repeating block of one or more digits (where all digits are not zeros) after the decimal point, then the decimal is a repeating decimal. A repeating decimal can be written with a bar over the digits that repeat. So 0.13333… = 0.13.

  7. 9 11 –9 –1 8 11 9 The fraction is equivalent to the decimal 1.2. Additional Example 1A: Writing Fractions as Decimals Write the fraction as a decimal. 11 9 1 .2 .0 The pattern repeats. 0 2 2

  8. 20 7 –0 –6 0 0 –1 0 7 20 The fraction is equivalent to the decimal 0.35. Additional Example 1B: Writing Fractions as Decimals Write the fraction as a decimal. .3 0 5 This is a terminating decimal. 7 20 0 .0 0 7 0 1 0 The remainder is 0. 0

  9. 9 15 –9 0 –5 4 15 9 The fraction is equivalent to the decimal 1.6. Check It Out! Example 1A Write the fraction as a decimal. 15 9 1 .6 .0 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 6 6

  10. 40 9 –0 –8 0 – 8 0 9 40 0 2 0 0 – 2 The fraction is equivalent to the decimal 0.225. Check It Out! Example 1B Write the fraction as a decimal. 9 40 .2 0 2 5 This is a terminating decimal. 0 0 .0 0 9 0 1 0 0 The remainder is 0. 0

  11. 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.

  12. 622 1000 = 311 500 = 37 100 =5 Additional Example 2: Writing Terminating Decimals as Fractions 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.

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

  14. 2625 10,000 = 21 80 = 75 100 =8 3 4 =8 Check It Out! 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.

  15. Additional Example 3: 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 =

  16. Check It Out! Example 3 __ 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.

  17. 5 8 27100 – 2.16 Lesson Quiz Write each decimal as a fraction in simplest form. 1. 0.27 2. –0.625 13 6 3. Write as a decimal. 6. Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.) 0.325

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