1150 day 10

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1150 day 10

  1. 1. RepeatingDecimalsandIrrationalNumbers
  2. 2. Repeating Decimals•Can be represented as a fraction•The denominator of the simplified form of thefraction has prime factors other than 2 or 5Writing repeating decimals 0.3 = 0.3333… 3.465 = 3.4656565…
  3. 3. Write 5 as a decimal 22 0. 2272722 5 0 44 0.227 60 44 160 154 60 44 160
  4. 4. Order from smallest to largest: 3.6, 3.6, 3.76, 3.631 3.6 = 3.60000…3 3.6 = 3.66666…4 3.76 = 3.76666…2 3.63 = 3.63636… 3.6, 3.63, 3.6, 3.76
  5. 5. Write 0.12 as a fraction in simplest form100x = 12.121212… x = 0.121212… 99x = 12 99 99 x = 12 99 = 4 33
  6. 6. Write 3.6 as a fraction in simplest form 10x = 36.66666… x = 3.66666… 9x = 33 9 9 x = 11 3
  7. 7. Real NumbersCounting Numbers: 1, 2, 3, 4, …Whole Numbers: 0, 1, 2, 3, …Integers: …, -3, -2, -1, 0, 1, 2, 3, …Rational Numbers: can be written as fractionsIrrational Numbers: non- repeating, non- terminating decimals Some irrational Numbers: π 2 3 10 7.272272227...
  8. 8. What are the square roots of 36? 6 because 62 = 36 -6 because (-6)2 = 36Every positive number has two square roots.The principal square root of a number is itspositive square root.
  9. 9. Find:a) The square roots of 25 5 and -5b) The principal square root of 25 5c) 25 = 5d) 25 = -5
  10. 10. How long is 2? Square’s Length of area side 1 1 2 2 4 2 2 9 3 2 is between 1 and 2
  11. 11. Simplifying roots 1 1 4 2 9 3 18 2 33 3 2 75 35 5 5 3 3 3 8 2 2 2 23 3 3 24 2 2 2 3 2 3
  12. 12. Order from smallest to largest: 31 8.9, 65%, 65 , 4 4 8.9 = 8.9 1 65% = 0.65 3 65 = A little larger than 8 2 31 = 7 3 4 4 31 65%, , 65 , 8.9 4
  13. 13. MAP 8th-gradereleased item, 2006
  14. 14. Pythagorean Theorem•Relates the sides of a right triangle b c a2 + b2 = c2 a x2 + 42 = 62 x 6 x2 + 16 = 36 -16 -16 4 x2 = 20 x = 20 or 2 5
  15. 15. DESE Sample MAP item, grade 8
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