1. Through dimensional analysis.
Metric Conversions!
Through dimensional analysis.

2. The Metric System Uses SI units (Système International d’Unités)
Universal standard of measurement used in science, and most of the rest of the world
Based on factors of 10

3. ? ENGLISH SYSTEM Ounces, Pounds and Pints 8 ounces make a cup,
2 cups make a pint,
2 pints make a quart,
4 quarts make a gallon.
A pint of water weighs a pound.
An American barrel of dry measure is 105 dry quarts (116 liters), but a liquid barrel is 31.5 gallons (liquid) or 119 liters, unless the barrel contains petroleum, in which case it contains 42 (US) gallons or 159 liters.
The three different ounces:
a fluid ounce is ml
a troy ounce is 31.1 g
an ounce avoirdupois is g
There's also something called "dry measure" with units of pint, quart, peck and bushel for measuring quantities of fruits, grains, and whatnot. 1 pint dry is l, while 1 pint liquid is l. Inches, Rods, Chains and Furlongs
An inch is the outer part of a man's thumb, 25.4 millimeter to be exact.
12 inches to a foot,
2 feet to a cubit or 3 feet to a yard.
A rod/pole is 5.5 yards (16.5 feet): The size of a big stick carried around by builders (hence the name). Four rods make a chain (22 yards) - the distance between two (cricket) wickets. Ten chains make a furlong. A furlong square is ten acres. Eight furlongs make a mile. ?

4. Choose the correct measurement for the job.
Number Economy
Choose the correct measurement for the job.
Instead of saying an object traveled 5,000 meters you can reduce that to 5 kilometers
1 kilometer = 1000 meters

5. Decimal equivalent in SI writing style
SI prefixes
1000n
10n
Prefix
Symbol
Short scale
Long scale
Decimal equivalent in SI writing style
10008
1024
yotta Y
Septillion
Quadrillion
10007
1021
zetta Z
Sextillion
Trilliard (thousand trillion)
10006
1018
exa E
Quintillion
Trillion
10005
1015
peta P
Billiard (thousand billion)
10004
1012
tera T
Billion
10003
109
giga G
Milliard (thousand million)
10002
106
mega M
Million
10001
103
kilo k
Thousand
1 000 -
102
hecto h
Hundred
100
101
deca, deka da
Ten 10
10000
(none)
One 1
10−1
deci d
Tenth
0.1
10−2
centi c
Hundredth
0.01
1000−1
10−3
milli m
Thousandth
0.001
1000−2
10−6
micro
µ (u)
Millionth
1000−3
10−9
nano n
Billionth
Milliardth
1000−4
10−12
pico p
Trillionth
1000−5
10−15
femto f
Quadrillionth
Billiardth
1000−6
10−18
atto a
Quintillionth
1000−7
10−21
zepto z
Sextillionth
Trilliardth
1000−8
10−24
yocto y
Septillionth

6. Measuring Instruments
Time
Temperature
Distance
Mass
Volume
Second (s)
Celcius (oC), Kelvin (K)
Meter (m)
Gram (g)
Liter (L), cm3

7. Write These Down! (Take NOTE of the CASE)
Conversion Factors
Conversion factor
Base units
Prefix
109 (L,m,g,s) = 1 giga (G)
(L,m,g,s) = mega (M)
103 (L,m,g,s) = 1 kilo (k)
102 (L,m,g,s) = 1 hecto (h)
101 (L,m,g,s) = 1 deca (da)
Base units (L, m, g, s)
1 (L,m,g,s) = deci (d)
1 (L,m,g,s) = centi (c)
1 (L,m,g,s) = milli (m)
1 (L,m,g,s) = micro (μ)
1 (L,m,g,s) = nano (n)
1 (L,m,g,s) = pico (p)
Large units
NEED TO MEMORIZE
Base units
Conversion factor
Prefix
Small units
Write These Down! (Take NOTE of the CASE)

8. CONVERSION STEPS STEP 1: Draw your table
Problem: convert 2.43 meters (m) into millimeters (mm)
STEP 1: Draw your table
STEP 2: Put given number and unit over 1
2.43 m
NO NAKED NUMBERS!!! EVERY NUMBER NEEDS A UNIT!!! NO UNIT = WRONG ANSWER!!! 1

9. THIS IS THE MOST IMPORTANT AND MISSED STEP
STEP 3: Put given unit downstairs to cancel
2.43 m m 1 m
STEP 4: Put the unit you are looking for on top
2.43 m mm 1 m
STEP 5: Put a 1 in front of larger unit: consult your chart!
THIS IS THE MOST IMPORTANT AND MISSED STEP
2.43 m mm 1 1 m

10. 2.43 E3 mm STEP 8: Reduce and double check your unit
STEP 6: LOOK UP THE PREFIX FOR CONVERSION FACTOR
103
2.43 m mm
milli = 1000 or 103 1 1 m
STEP 7: MULTIPLY ACROSS, NOT CROSS MULTIPLY
103
2.43 m mm
2.43 E3 mm = 1 1 1 m
STEP 8: Reduce and double check your unit
2.43 E3
2.43 E3 mm = 1

11. Step 3 Step 4 Step 2 Step 1 Step 5 Step 6 Step 7 Step 8 5.61 E-1 kL
Problem: Convert 561 liters (L) into kiloliters (kL)
561 L 1 kL
561 kL
5.61 E-1 kL
kilo = 1000 or 103 = 1
103 L
103
Step 3
Step 4
Step 2
Step 1
Step 5
Step 6
Step 7
Step 8

12. Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8 4.39 E13 ns 1
Problem: Convert 4.39 E4 seconds (s) into nanoseconds (ns)
4.39 E4 s
109 ns
4.39 E13 ns
4.39 E13 ns
nano = 109 = 1 1 s 1
Step 3
Step 2
Step 4
Step 1
Step 5
Step 6
Step 7
Step 8

13. Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8 9.36 E-2 Mg
Problem: Convert grams (g) into Megagrams (Mg) g 1 Mg Mg
9.36 E-2 Mg
Mega = 106 = 1
106 g
106
Step 3
Step 2
Step 4
Step 1
Step 5
Step 6
Step 7
Step 8

14. PRACTICE
3.45 Ms to s
1000 m to hm
356 L to pL
1.54 x 107 g to Gg

15. 2 Stage Problems You have to convert to the base unit first
How do you know?
Problem has 2 prefixes and no base unit alone
Example: km to cm, Mg to mg, mL to GL
(L, m, g, s)
Convert to m first
Convert to g first
Convert to L first

16. 2.55 km to cm 2.55 km 103 m 102 cm = 1 1 km 1 m 2.55 x 103 x 102 cm =

17. 1.63 E3 cg to Mg 1.63E3 cg 1 g 1 Mg = 1 102 cg 106 g 1.63E3 Mg =
1.63 x 10-5 Mg
1 x 102 x 106

18. PRACTICE
3.45 Ms to ms
1000 nm to hm
356 mL to pL
1.54 x 107 cg to Gg

19. Answers: 1-5 table conversion
6.91m
100 cm
6.91 E2cm 1 1m
9.10 E12m
1 Gm
9.10 E3 Gm
109 m 1
E6mm
1 m
1.89 E3 m
103 mm 1

20. 231 cm
1 m
2.31 m
102 cm 1
94 km
103 m
9.40 E4 m
1 km 1

21. A C E 1m
100cm 1m
103mm
1km
103m G I K
1Gm
109m
109nm 1m
1Mm
106m

22. F D B
103m
1km
103 mm 1m
100cm 1m L J H
106m
1Mm 1m
109nm
109m
1Gm

23. Meter Stick 10 10 10 1 meter 1 decimeter 1 centimeter 1 1 1 1 1 1 1 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter 1
millimeter
1 centimeter

24. Fractions : Ratios
Q: How do you convert a number into a fraction?
Ex: 2.57
A: Put the number over 1! 1