1. Handling Very Big and Very Small Numbers
Scientific Notation
Handling Very Big and Very Small Numbers

2. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

3. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
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4. Scientific Notation: n is an integer
A method of representing very large or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is an integer

5. . 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

6. 2.5 x 109
The exponent is the number of places we moved the decimal.

7. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

8. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

9. Change to standard form.
1.87 x 10–5 =
3.7 x 108 = 370,000,000
7.88 x 101 = 78.8
2.164 x 10–2 =

10. Change to scientific notation. 12,340 = 1.234 x 104
To manipulate these numbers on a
calculator, one needs to use the
EE or EXP keys.

11. EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023:
How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2
Don’t do it like this…
WRONG! 6
y x . 3 2
WRONG!
…or like this… x 1 6 . 2 EE 3
…or like this:
TOO MUCH WORK.
y x 3 2 x 1 6 .

12. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
–09
Calculator gives…
E–09
or…
This is NOT written…
4.3–9
4.3 x 10–9
4.3 E –9 or
But instead is written…