1. scientific notation
A value written as the product of two numbers: a coefficient and 10 raised to a power.
Ex: 602,000,000,000,000,000,000,000
is 6.02 × 1023
The coefficient in this number is 6.02.
(It is always a number equal to or greater than 1, and less than 10.)
The power of 10, or exponent, is 23.

2. Entering scientific notation correctly in a calculator is important.
Here is the procedure for our classroom calculators:
6.02 × is entered as EE 23
Some calculators may require you to press “2nd EE”, or EXP instead of EE

3. Calculations with Scientific Notation:
Adding: convert all numbers to the same power of 10, then add coefficients.
6.02 X x 1024 =
0.602 x x = 3.61 x 10 24
Subtracting: convert all numbers to the same power of 10, then subtract coefficients.
6.02 X x 1023 =
6.02 x x = 5.72 x 10 24

4. Calculations with Scientific Notation:
Multiplying: multiply coefficients and add exponents.
6.02 X x x = x 10 47
Dividing: divide coefficients and subtract exponents.
6.02 X ÷ x 1023 = x 101

5. SIGNIFICANT FIGURES What are they good for?
They tell us how precise a measurement is. The more significant figures, the more precise the measurement.
How do you know how many you have?
All known digits that you can read from the ruler, graduated cylinder, etc, plus one estimated digit.

6. When is a digit significant? (red ones ARE)
1. Every nonzero digit is significant m, m, and 714 m
2. Zeros between nonzero digits are significant m, m
3. Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders meter
4. Zeros at the end and to the right of a decimal point are significant m, m , m
5. Zeros at the rightmost end, left of an understood decimal point are not significant if they serve as placeholders m, 7000 m, and 27,210 m
(If they ARE known measured values, however, then they would be significant. Writing the value 300m in scientific notation as 3.00 x 102 m makes it clear that these zeros are significant.)
6. Counting values & exactly defined quantities have an unlimited number of significant figures;. 23 students, 60 min = 1 hr

7. When calculating with measurements, how do you know the correct number of significant figures for your answer?
An answer cannot be more precise than the least precise measurement from which it was calculated.
The answer must be rounded to make it consistent with the measurements from which it was calculated.
Density = mass/volume g / 2.1 ml = g/ml
= 5.3 g/ml

8. How do you round the answers?
Once you know the number of significant figures your answer should have, round to that many digits, counting from the left.
* If the digit immediately to the right of the last significant digit is less than 5, drop it and the last significant digit stays the same.
* If the digit in question is 5 or greater, the last significant digit is increased by 1.

9. Adding / Subtracting measurements:
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
12.52 meters
meters
meters
369.8 meters
meters

10. Multiplication and Division
Round the answer to the same number of significant figures as the measurement with the least number of significant figures.
7.55 m x m = m2
= m2
(0.34 meter has the least number of significant figures: two.)

11. Factor Factor prefix symbol value expanded value English name yotta Y
Table 5.  SI prefixes
Table 5.  SI prefixes
Factor
Factor
prefix
symbol
value
expanded value
English name
yotta Y
1024
U.S. septillion; U.K. quadrillion
zetta Z
1021
U.S. sextillion
exa E
1018
U.S. quintillion; U.K. trillion
peta P
1015
U.S. quadrillion
tera T
1012
U.S. trillion; U.K. billion
giga G
109
U.S. billion
mega M
106
million
kilo k
103
1 000
thousand
hecto h
102
100
hundred
deca da
101 10
ten 1
one

12. deci d
10-1
0.1
tenth
centi c
10-2
0.01
hundredth
milli m
10-3
0.001
thousandth
micro u
10-6
millionth
nano n
10-9
U.S. billionth
pico p
10-12
U.S. trillionth; U.K. billionth
femto f
10-15
U.S. quadrillionth
atto a
10-18
U.S. quintillionth; U.K. trillionth
zepto z
10-21
U.S. sextillionth
yocto y
10-24
U.S. septillionth; U.K. quadrillionth