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

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# Aim: How can we express very large and very small numbers easily? - PowerPoint PPT Presentation

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?

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
• Do you know this number: 300,000,000 m/sec?
• It’s the speed of light!
• It’s the mass of a single proton.
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 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
• 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 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
• 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 = ???