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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

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
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.
scientific notation
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.
scientific notation1
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
scientific notation rules
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
scientific notation rules1
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
math with scientific notation
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 = ???