Conversion

Metric Conversions Conversion using meter as the base (will be the same with gram or liter as the base)

megameter (Mm) 1,000,000 meters = 1 Mm kilometer (km) 1,000 meters = 1km hectometer (hm) 100 meters = 1hm decameter (dam) 10 meters = 1 dam meter 1m = 1m decimeter (dm) 1m = 10 dm centimeter (cm) 1 m = 100 cm millimeter (mm) 1m = 1,000 mm micrometer (μm) 1m = 1,000,000 μm nanometer (nm) 1m = 1,000,000,000nm

Conversions as Fractions 1. Saying 1 m =100 cm is the same as

saying 1 m per 100 cm or

2. 1 km = 1,000 m or 1000 m = 1km

3. As a fraction:

cm 100

m 1

km 1

1000m

1000m

1kmor

Example 1 To convert one unit to another simply

write the unit you want to change and multiply it by the conversion factor written with the units you want on the top.

Convert 13mm to meters

Notice that the units you started with cancel with the units in the denominator of the conversion factor.

m 013.01000mm

m 1 mm 13

Example 2

Convert 2.5 kg to centigrams. Convert to grams first.

Then convert to centigrams:

g 2,5001kg

g 1000 Kg 2.5

cg 250,000 1g

cg 100 g 2,500

Example 2 Continued

This may be done by combining steps. Combine steps and perform the calculation at the end. Multiply all the numbers in the numerator and divide if the number is in the denominator.

cg 250,000g 1

100cg

1Kg

g 1000 Kg 2.5

Conversions within theEnglish Systems

Example 1: If you live 13.5 miles from the high school, how many inches away from the high school do you live?

We do not have a conversion factor to go from miles to inches so we need to solve the problem in more than one step

yd 23,760 mi 1

yd 1,760mi 5.13

ft 280,71yd 1

ft 3

1

yd 760,23

in 855,360ft 1

in 12

1

ft 280,71

You must show units!!!! Align the conversions so that all the units cancel out except the desired ones. Stay organized and show all your work!!!!

855,000in855,360in ft 1

in 12

yd 1

ft 3

mi 1

yd1760

1

mi 5.13

Conversions between metric and English units:

Example 1: How many pounds does 3.44 kilograms weigh on Earth? This is a one step problem to convert kilograms to pounds.

lbsKg

lbsKg58.7

1

204623.2

1

44.3

Example 2: How many ounces does 590 grams weigh?

Convert grams to kilograms, kilograms to pounds, and finally pounds to ounces.

ozlb

oz

Kg

lbs

g

Kgg21

1

16

1

204623.2

000,1

1

1

590

Fraction Conversions

You can convert units in both the numerator and denominator

Example: Convert 25.8 mi/hr to m/s

s

m

s

m

s

hr

km

m

mi

km

hr

mi 5.11533632.11

60

min1

min60

1

1

1000

1

609344.18.25

Power Conversions

3333

3 000,560,1849.207,562,154.2

1

1

1006.25 inin

cm

in

m

cmm

You must be using the same type of units. (volume, area)

Example: Convert 25.6m2 to in2

Scientific Notation

A condensed method for writing very large or very small number.

Does not change the value or the accuracy of a number.

Significant figures in the number must be reported in scientific notation.

All non-significant zeros can and must be dropped.

When a number is written in proper scientific notation, all the digits are significant figures.

How do we write numbers in proper scientific notation?

602,200,000,000,000,000,000,000 = (6.022)(100,000,000,000,000,000,000,000)

Recognize that multiples of ten can be rewritten as powers of ten.

1 = 100 10 = 101

100 = 102

1,000 = 103

10,000= 104

100,000,000,000,000,000,000,000 = 1023

Notice that the number of zeros on the left side of the equation is equal to the power on the right side of the equation.

602,200,000,000,000,000,000,000 atoms can be written as

6.022 x 1023 atoms

Notice that the initial measurement contained 4 significant figures, as does the measurement in scientific

notation.

A negative power means to take the reciprocal of the number.

1313

10

110

000,000,000,000,100

350.400043500000000000.0

mm

1414

10350.410

350.4 xm

Steps to convert number into scientific notation

Identify all the significant figures in the measurement.

13,280,000,000 m has 4 significant figures which must be retained

In proper scientific notation, the decimal place should be immediately to the right of the first non-zero number.

1.328 x 10,000,000,000 m = 1.328 x 1010 m

Remember these two rules:

If you move the decimal place to the left, you add one to the power.

If you move the decimal place to the right, you subtract one from the power.

Check to make sure your answer has the same number of significant

figures.