Conversions

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Exponential Notation

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2.54 g O 2 × 1 m o l O 2 32.00 g O 2  inline

2.54 g O 2 × 1 m o l O 2 32.00 g O 2  

 

Pasted into Canvas from screenshot in PowerPoint and then alt text added into Canvas

same as the equation above but the grams of O2 cancel out

Pasted into comstgermain and then image address copied and put into Canvas and then alt text added into Canvas

same as the equation above but the grams of O2 cancel out

 

This is a showing how to solve a problem
Verbal Explanation Equations and Work
the value you want to convert, 2.54 grams of O2 multiplied by 1 mol of O2 divided by 32.00 grams of O2 2.54 g O 2 × 1 m o l O 2 32.00 g O 2
the grams of O2 cancel out on the top and bottom of the equations same as the equation above but the grams of O2 cancel out

 

This is exponential notation where the small number written above and to the right of the base (superscript), indicating how many times the base is multiplied by itself. (example: 23 = 2 x 2 x 2)

this is a image showing exponential notation 

This is a table showing exponential numbers, the operations, and the ordinary number.
Exponential Number What is happening Ordinary Number
1 x 106 10 x 10 x 10 x 10 x 10 x 10 1,000,000
1 x 103 10 x 10 x 10 1,000
1 x 102 10 x 10 100
1 x 101 10 10
1 x 100 100 1
1 x 10-1 LaTeX: \frac{1}{10} 0.1
1 x 10-2 LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} 0.01
1 x 10-3 LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} 0.001
1 x 10-6 LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} x LaTeX: \frac{1}{10} 0.000 001

Scientific Notation

This is standard scientific notation where only significant digits are shown and the decimal is after the first digit. This is followed by a multiplication sign, and then 10, and then the power of 10 in superscript. (example: 3.250 x 103 = 3.250 x 10 x 10 x 10 = 3,250)

This is an image of standard scientific notation

 

Metric Units

This is a table of commonly used metric units.

What you are measuring

Unit (with no prefix)

Symbol

Length

meter

m

Mass

gram

g

Volume

liter

L

Temperature

kelvin

K

Time

seconds

s

Amount of something

(6.022 x 1023 things)

mole

mol

 

Metric Prefixes

Metric prefixes are just words that mean a certain number. These can be used with ANY UNIT.

This is a table of common metric prefixes and their symbols, meaning, and examples.
Prefix Abbreviation Meaning Examples More Examples
tera T 1,000,000,000,000 or 1012 1 Tm = 1012 m
1 Tg = 1012 g
1 TL = 1012 L		 1 TK = 1012 K
1 Ts = 1012 s
1 Tmol = 1012 mol
giga G 1,000,000,000 or 109 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
mega M 1,000,000 or 106 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
kilo k 1,000 or 103 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
hecto h 100 or 102 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
deka da 10 or 101 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
1

1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L

1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
deci d 1/10 or 0.1 or 10-1 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
centi c 1/100 or 0.01 or 10-2 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol
milli m 1/1,000 or 0.001 or 10-3

1 mm = 10-3 m
1 mg = 10-3 g
1 mL = 10-3 L

 

 1 mK = 10-3 K
1 ms = 10-3 s
1 mmol = 10-3 mol
micro LaTeX: \mu 1/1,000,000 or 10-6

1 LaTeX: \mum = 10-6 m
1 LaTeX: \mug = 10-6 g
1 LaTeX: \muL = 10-6 L

 1 LaTeX: \muK = 10-6 K
1 LaTeX: \mus = 10-6 s
1 LaTeX: \mumol = 10-6 mol
nano n 1/1,000,000,000 or 10-9 1 nm = 10-9 m
1 ng = 10-9 g
1 nL = 10-9 L		 1 nK = 10-9 K
1 ns = 10-9 s
1 nmol = 10-9 mol
pico p 1/1,000,000,000,000 or 10-12 1 pm = 10-12 m
1 pg = 10-12 g
1 pL = 10-12 L		 1 pK = 10-12 K
1 ps = 10-12 s
1 pmol = 10-12 mol

 

Common Conversions

This is a table of common conversions.
Conversion Factors / Conversion Rates Description (can convert the reverse as well)
1 milliliter (mL) = 1 centimeter cubed (cm3) or (cm x cm x cm) use to convert a milliliter (mL) volume to a centimeter cubed (cm3) volume  
1 liter (L) = 1000 centimeter cubed (cm3) or (cm x cm x cm) use to convert a liter (L) volume to a centimeter cubed (cm3) volume 
1 inch (in) = 2.54 centimeters (cm) use to convert from inches (standard system) to centimeters (metric system)
1 yard (yd) = 0.9144 meters (m) use to convert from yard (standard system) to meters (metric system)
454 grams (g) = 1 pound (lb)  use to convert grams (metric system) to pounds (standard system)
0.946 liters (L) = 1 quart (qt) use to convert liters (metric system) to quarts (standard system)
1 mole = 6.022 x 1023 things (usually atoms or molecules) can use this to convert in and out of moles (moles to atoms or molecules)

 

How to Convert Anything in World in 3 Steps:

Step 1: Find the conversion rates. 

Almost any two values with units with an equals sign between them can be a conversion rate or conversion factor (same thing, different name). You can find conversion rates in this tutorial, in your book, on the internet, on food menus, etc. Directly below is a generic version of a conversion rate

LaTeX: value1unit1=value2unit2

Below are some conversion rates. 

Number Conversion Rate Description
1 USD$1.00 = MXN$18.67 This means 1 US dollar is equivalent to 18.67 Mexican pesos. This will allow you to convert from pesos to dollars and dollars to pesos.
2 $0.99 = 2 tacos This means 2 tacos is equivalent to 0.99 of a dollar (99 cents). This will allow you to convert from tacos to dollars and dollars to tacots.
3 1000 g = 1 kg  This means 1000 grams is equal to 1 kilogram. This will allow you to convert from grams to kilograms and kilograms to grams.
4 1 nmol = 10-9 mol This means 1 nanomole is equal to 0.000 000 001 moles. This will allow you to convert from moles to nanomoles and nanomoles to moles.
5 LaTeX: \large\frac{12.01gCarbon}{1molCarbon} This means 12.01 grams of carbon is equal to 1 mole of carbon. This will allow you to convert from grams of carbon to moles of carbon and from moles of carbon to grams of carbon. Conversion rates can be written as a fraction. More information is below.

Step 2: Write the conversion rate as a fractions

Any of the conversion rates above can be written in different forms which include fractions.

Number Form: one equals the other Form: one fraction Form: the other fraction
1 USD$1.00 = MXN$18.67 LaTeX: \large\frac{MXN\$18.67}{USD\$1.00} LaTeX: \large\frac{USD\$1.00}{MXN\$18.67}     
2 $0.99 = 2 tacos LaTeX: \large\frac{\$0.99}{2tacos} LaTeX: \large\frac{2tacos}{\$0.99}
3 1000 gram (g) = 1 kilogram (kg)  LaTeX: \large\frac{1 kg}{1000 g} LaTeX: \large\frac{1000 g}{1 kg}
4 1 nanomole (nmol) = 10-9 mole (mol) LaTeX: \frac{1nmol}{10^{^{-9}}mol} LaTeX: \large\frac{10^{-9}mol}{1nmol}
5 12.01 g C = 1 mol C LaTeX: \large\frac{12.01gC}{1molC} LaTeX: \large\frac{1molC}{12.01gC}

Step 3: Multiply what you are trying to convert by the fraction.

Use the conversion rate above to multiply by the value you are trying to convert. Use the fraction that has the same unit as the original value on the bottom. Cancel out anything that is the same on top of the fraction line and the bottom of the fraction line.

Number  Original Value (what you are trying to convert) Conversion Rate Problem Work (see the units cancelling out) Answer (any units that don’t cancel carry over to the answer)
1 USD$ 5.00 LaTeX: \large\frac{MXN\$18.67}{USD\$1.00} LaTeX: \large USD\$5.00\times\frac{MXN\$18.67}{USD\$1.00} LaTeX: \large 5.00\times\frac{MXN\$18.67}{1.00} MXN$ 93.35
2 4 tacos LaTeX: \large\frac{\$0.99}{2tacos} LaTeX: \large 4 tacos\times\frac{\$0.99}{2tacos} LaTeX: \large 4 \times\frac{\$0.99}{2} $1.98
3 327 grams LaTeX: \large\frac{1 kg}{1000 g} LaTeX: \large 327 g\times\frac{1 kg}{1000 g} LaTeX: \large 327\times\frac{1 kg}{1000} 0.327 kg
4 4.1 x 10-6 nmol LaTeX: \large\frac{10^{-9}mol}{1nmol} LaTeX: \large 4.1\times10^{-6}nmol \times\frac{10^{-9}mol}{1nmol} LaTeX: \large 4.1\times10^{-6}\times\frac{10^{-9}mol}{1} 4.1 x 10-15 mol
5 47.3 g C LaTeX: \large\frac{1molC}{12.01gC} LaTeX: \large 47.3gC\times\frac{1molC}{12.01gC} LaTeX: \large 47.3\times\frac{1molC}{12.01} 3.94 mol C