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Scientific Notation – Justification

- Scientists often work with very large and very small numbers, however these can be cumbersome to work with. To simplify matters we write these numbers using exponents or scientific notation.

Scientific Notation – Broken Down

- The number 123 000 000 000 in scientific notation is written as: ______________________
- Coefficient: this is the first number, 1.23; it must be ____________________________________________
- Base: this is the second number, 10; in scientific notation it must ______________________________
- Exponent: this is the third number, 11; this must always be an _________________
- It can be positive when expressing a ___________________
- i.e.: 123 000 000 000 = 1.23 x 1011

- It can be negative when expressing a ___________________
- i.e.: 0.0000603 = 6.03 x 10-5

- It can be positive when expressing a ___________________

Scientific Notation – Large & Small

- 1. Large numbers - 36000 written in scientific notation is 3.6 x 104. Count the number of decimal places you move to the _______and this becomes the exponent.
- 2. Small numbers - 0.00015 written in scientific notation is 1.5 x 10-4 . Notice that a negative exponent is used when moving the decimal to the ________
- Rule of ThumbWhen you make the number smaller, make the exponent ___________and when you make the number larger, make the exponent ____________

Adding & Subtracting with Scientific Notation

- Scenario 1: Like Exponents
- Add or subtract the numerical coefficient and keep the exponent the same. If the numerical coefficient becomes higher than 10 or lower than 1, adjust the exponent.
- Example:
- ____________________________________________________

- Scenario 2: Unlike Exponents
- Change one of the exponents (usually make the smaller one larger) so both exponents are the same, then add or subtract the numerical values.
- Example:
- ________________________________________
- ________________________________________
- ________________________________________

Multiplying & Dividing with Scientific Notation

- Quantities do not need the exponents to be the same when multiplying or dividing.
- Multiplying: Multiply the numerical coefficients and add the exponents. Don't forget to multiply the units.
- Example:
- _________________________________________________

- Example:
- Dividing: Divide the numerical coefficients and subtract the exponents. Remember to divide the units.
- Example:
- _________________________________________________

- Example:

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