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

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?

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 easily?

- 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 easily?

- 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 easily?

- 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 easily?

- 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 easily?

- 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 easily?

- 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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