Number types
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Number types Number types Presentation Transcript

  • Number Types (and fractions and decimals)
  • The lesson you just studied is fairly comprehensive. Rather than repeat the lesson, the purpose of this presentation is to review major points with the hope of adding clarity in certain areas. Points to review include: • types of numbers. • converting decimals to fractions, and • converting fractions to decimals, You may find that other areas were difficult to grasp. If that is the case, don’t hesitate to talk to Mrs. Kent or to contact me in the evenings.
  • Types of Numbers › Natural Numbers: numbers “naturally” used for counting: 1, 2, 3, . . . › Whole Numbers: the Natural Numbers and zero: 0, 1, 2, 3, . . . › Integers: the Natural Numbers, their opposites, and zero: . . ., -3, -2, -1, 0, 1, 2, 3, . . .
  • Types of Numbers
  • Types of Numbers › Irrational Numbers: any number that isn’t rational. An irrational number can only be approximated as a decimal value because it never repeats and it never terminates (e.g. the square root of a prime number). › Real Numbers: all numbers on the number line.
  • Types of Numbers Natural Numbers (counting numbers) 1, 2, 3, . . . Whole Numbers 0, 1, 2, 3, . . . Integers . . ., -3, -2, -1, 0, 1, 2, 3, . . . Real Numbers
  • A Useful Comparison San Antonio Texas The United States North America Asia The World
  • Types of Numbers Is a person in San Antonio also in Texas? Yes, always. Is a person in Texas also in San Antonio? Maybe, but not necessarily. Is a Natural Number also a Whole Number? Yes, always. Is a Whole Number also a Natural Number? Maybe, but not necessarily.
  • Types of Numbers Is a person in North America also in the USA? Maybe, but not necessarily. If a person in the USA in San Antonio? Yes, always. Is a Rational Number also an Integer? Maybe, but not necessarily. Is an Integer also a Rational Number? Yes, always.
  • Types of Numbers So, as indicated, anyone in one circle is automatically in all those around/above it. If a person is in Texas (but not San Antonio), that person is also in the USA, North America, and, of course, the world. So, as indicated, any number that’s one type is automatically in all those around/above it. If a number is a Whole Number, that number is also an Integer, a Rational Number, and, of course, a Real Number.
  • Determining Which Number Type See if you agree: Natural Number           Whole Number           Integer           Rational Number           Irrational Number           Real Number          
  • Converting Decimals to Fractions
  • Converting Decimals to Fractions
  • Converting Decimals to Fractions › Steps for non-terminating, non-repeating decimals › Determine how many places are sufficient and round › Handle as you would a terminating decimal
  • Converting Fractions to Decimals 0. 7 3 2 8 20 14 60 56 40 35 50 49 10 7 30 28 *Your teacher will tell you how many places “close enough” is. Often it will be just 2 or 3, but sometimes, your teacher will want you to continue to see if there’s a pattern. Do you see the pattern here? .00 428571