MATHMATH173 DF173 DF

Decimals, Significant Digits & Exponents

Sept 2008 MTH173 - Decimals 1

AnnouncementsAnnouncements

Calter Textbook with WileyPLUS

Advanced Standing in Course

Quiz – Thursday, Sept 12th

• Signed Numbers, Decimals, Significant Digits, Exponents, Radicals, Scientific Notation

Sept 2008 MTH173 - Decimals 2

Decimals, Sig Digs & ExponentsDecimals, 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

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Lecture OutlineLecture Outline

Decimal System Significant Digits Exponents Radicals

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Decimal SystemDecimal 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

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Place ValuePlace Value

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Place ValuePlace Value

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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

Place ValuePlace Value

What is the place value of the digit underlined in each number below?

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1) 1 234 g2) 0.003 04 mL3) 3.5234 g4) 1 021 L5) 1.234 km6) 1 234 567.890 m7) 445 000 kg8) 23.000 234 mm9) 3 456 335.00 g10) 5 000 cal

Convert a Decimal to a FractionConvert 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

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NumbersNumbers

Exact Numbers

• Have no uncertainty

• 24 hours / day, 4 wheels / car, 25.4 mm

Approximate Numbers

• Measured quantities, Fractions, Irrational Numbers

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Significant DigitsSignificant 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?

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Significant DigitsSignificant 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

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Significant DigitsSignificant 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

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Rounding OffRounding 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

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