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Understanding Decimals, Significant Digits, and Exponents in MTH173

This course focuses on the fundamentals of decimals, significant digits, and exponents as part of the MTH173 curriculum. Students will learn about the decimal system, place values, the conversion of decimals to fractions, and the importance of significant digits in presenting numerical results. The coursework includes an overview of operations such as addition, subtraction, multiplication, and division, along with how to handle powers, roots, and rounding off. Mastering these topics is essential for success in technical mathematics and calculus.

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Understanding Decimals, Significant Digits, and Exponents in MTH173

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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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