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MATH 173 DF

MATH 173 DF. Decimals, Significant Digits & Exponents. Announcements. Calter Textbook with WileyPLUS Advanced Standing in Course Quiz – Thursday, Sept 12 th Signed Numbers, Decimals, Significant Digits, Exponents, Radicals, Scientific Notation. Decimals, Sig Digs & Exponents.

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MATH 173 DF

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  1. MATH173 DF Decimals, Significant Digits & Exponents MTH173 - Decimals

  2. Announcements • Calter Textbook with WileyPLUS • Advanced Standing in Course • Quiz – Thursday, Sept 12th • Signed Numbers, Decimals, Significant Digits, Exponents, Radicals, Scientific Notation MTH173 - Decimals

  3. Decimals, Sig Digs & Exponents • Calter & Calter (2008) • Technical Mathematics with Calculus, Canadian Edition • Chapter 1: Numerical Computation • 1-1 The Real Numbers • 1-2 Addition & Subtraction • 1-3 Multiplication • 1-4 Division • 1-5 Powers & Roots • pages 1 - 22 MTH173 - Decimals

  4. Lecture Outline • Decimal System • Significant Digits • Exponents • Radicals MTH173 - Decimals

  5. Decimal System • Base 10 system • 10 units in any place will equal 1 unit in the next higher level • 10 units in the hundreds = 1 unit in the thousands • Positional System • The position of the digit determines its value • Example: 351.2 MTH173 - Decimals

  6. Place Value MTH173 - Decimals

  7. Place Value • Every Canadian uses approximately one tree of a 45 cm diameter and 30.54 m height per year. There are 25.4 trees planted per person in Canada per year. • The 4 has a different meaning (place value) in each number listed MTH173 - Decimals

  8. Place Value • What is the place value of the digit underlined in each number below? MTH173 - Decimals

  9. Convert a Decimal to a Fraction • Write the numbers to the left of the decimal as a whole number • Count the number of digits in the decimal • Divide by 1 followed by the same number of zeroes as there are digits after the decimal 1) 2.345 2) 89.4 3) 674.53 4) 0.087 MTH173 - Decimals

  10. Numbers • Exact Numbers • Have no uncertainty • 24 hours / day, 4 wheels / car, 25.4 mm • Approximate Numbers • Measured quantities, Fractions, Irrational Numbers MTH173 - Decimals

  11. Significant Digits • Working with a calculator, your answer will have multiple numbers after the decimal place. • In Science, you need to know how to present your answer with the correct number of Significant Digits. • What are Significant Digits? Sept 2008 11 MTH173 - Decimals

  12. Significant Digits • Begin counting Significant Digits at the first nonzero digit • Stop counting Significant Digits at the last digit recorded • Exact numbers have an infinite number of Significant Digits Sept 2008 12 MTH173 - Decimals

  13. Significant Digits • Zeros between nonzero digits are counted • Zeros to the right of the decimal are counted • Zeros after a decimal and before a nonzero digit are not counted • Zeros after a number and before a decimal are ambiguous Sept 2008 13 MTH173 - Decimals

  14. Rounding Off • Only once all calculations have been carried out the final answer is to rounded off • If the first digit to be dropped is 0-4 • Leave the preceeding digit unchanged • If the first digit to be dropped is 6-9 • If the first digit to be dropped is a 5 Sept 2008 14 MTH173 - Decimals

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