a refresher on scientific notation and commonly used SI prefixes in science

1. Scientific Math
Exponential expressions & prefixes

2. Scientific Notation
 We use it to express large numbers quickly
 Use it to express numbers ≥1 or ≤10
ex: 2578 >>>> 2.57 x 103
DON’T write is as 25.7 x 102
 Generally, you’ll use it to write really big numbers

3. “Fudge the Numbers”
“I forget which way I move the decimal and the
exponent on the 10”
 If a number is written in scientific notation
remember these 2 hints
1. Positive exponents increase (>>>>) the
placement of the decimal point when you
write it out.
1.456 x 108 = 145,600,000.
2. Negative exponents decrease (<<<<) the
placement of the decimal point when you
write it out.
2.543 x 10-5 = 0.00002543

4. “Fudge the Numbers”
“I forget which way I move the decimal and the
exponent on the 10”
 If a number is written out remember these 2 hints
1. If you have big numbers, you want to “hide them”:
$13,000,000,000,000 deficit
$1.3 x 1013
2. If there are really small numbers, you want to
downplay that:
.001304 jobs increase
1.304 x 10-3 the downplay is a negative exp.

5. “Fudge the Numbers
Planet Miles from sun Miles from sun in
(longhand) scientific not.
Mercury 35,000,000
Venus 6.5 x 107
Earth 9.3 x 107

6. RAPID PRACTICE!
beat mr. basso
2.847 X 103
3.982 X 104
5.843 X 105
1.457 X 105
5.47 X 106
9.002 X 107

7. RAPID PRACTICE!
beat mr. basso
2.847 X 10-2
3.982 X 10-4
5.843 X 10-5
1.457 X 10-5
5.47 X 10-6
9.002 X 10-7

8. Prefixes
they’re Mega important
Prefixes are used mainly to express numbers with units
Ex: 10 millimeters = .01 meters
It’s helpful to use the prefixes so we can have a better grasp
on what is being measured
When talking about how fast a motorcycle is travelling, we
don’t want to say it’s speed is 60,000 meters per hour.
Instead we say 60 kilometers per hour, or 60 km/h
The prefix you use should be most appropriate for the
quantity being measured. Don’t measure a snails pace in km/h
.0013 km/h ,
write it as 1.3 meters per hour or 1.3 m/h

9. Table of Prefixes
above base zero (100)
Prefix Multiplied by Symbol Meaning
giga 1,000,000,000 G x billion
mega 1,000,000 M x million
kilo 1,000 k x thousand
hecto 100 h x 100
deca 10 da x 10

10. Table of Prefixes
below base zero (100)
Prefix Multiplied by Symbol Meaning
deci -10 d x .1
centi -100 c x .01
milli -1,000 m x .001
micro -1,000,000 μ x .000001
Nano -1,000,000,000 n x .000000001

11. Practice time
1.21 GigaWatts

12. Practice time
3100 centimeters

13. Practice time
45.089 millimeters

14. Practice time
9.81 kilograms

15. Practice time
200 milliWatts

16. Practice time
2.8 nanometers

17. Practice time
18456 Liters

18. Practice time
.0048 Newtons

19. Practice time
904535 grams

20. Practice time
28 meters

21. Practice time
200000000 tons