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Aim: How can we express very large and very small numbers easily?

Aim: How can we express very large and very small numbers easily?. Do Now Choose one: Express 534 megameters in meters Describe in full sentences the method for converting between unit prefixes (for example grams to kilograms). Big and small numbers.

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Aim: How can we express very large and very small numbers easily?

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  1. Aim: How can we express very large and very small numbers easily? Do Now Choose one: Express 534 megameters in meters Describe in full sentences the method for converting between unit prefixes (for example grams to kilograms)

  2. Big and small numbers • Do you know this number: 300,000,000 m/sec? • It’s the speed of light! • What about 0.00000000000000000000000000167 kg? • It’s the mass of a single proton.

  3. Scientific Notation • Just like a standard system of units makes measuring easier, using a standard system to express large and small numbers makes doing calculations easier. • We call this system Scientific Notation.

  4. Scientific Notation • Scientific Notation involves using powers of ten to represent the excess zeros. • Move the decimal all the way so it is behind the first significant digit • So the speed of light (300,000,000 m/s) is written as 3.0 x 108 m/s

  5. Scientific Notation Rules • For large numbers, put the decimal after the first digit. That will be your coefficient. • For example 123,000,000,000 • Count how many places you had to move the decimal. That will be your power of 10. • We also call this the order of magnitude. • Write it in Scientific Notation form: 1.23 x 1011

  6. Scientific Notation Rules • For small numbers, put the decimal behind the first non-zero digit in the decimal. • Again, count how many spaces you moved the decimal. That is your negative exponent or order of magnitude. • For example: .00000000139 is 1.39 x 10-9

  7. Practice problems – Try on your own 0.0000514 = 1,630,000 =

  8. Math with Scientific Notation • When multiplying numbers in Scientific Notation: Multiply the coefficients (front numbers), keep the 10 and add the exponents. • 4.0 x 105 * 2.0 x 106 = ??? • When dividing numbers in Scientific Notation: Divide the coefficients (front numbers), keep the 10 and subtract the exponents. • 4.0 x 105/ 2.0 x 106 = ???

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