# 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:
1)
Express 534 megameters in meters
2)
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!


kg?
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

PRACTICE PROBLEMS – TRY ON YOUR OWN
3
5.3 10 
6.34 10 
5
0.0000514 =
1,630,000 =
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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