Conversion of units

Metric conversion

• Unlike English units like the pound, ounce, foot, yard… metric units are related by multiples of 10

• There are 10 mm in every cm• There are 100 cm (10*10) in every m• There are 1000 m (10*10*10) in every km

Metric Symbols

• Used as prefixes before units

• Ex: • Km = kilometer• Cg = centigram• Ghz = Gigahertz• Pm = picometer

How to convert using the chart

Convert on scale

Giga 100, 10, Mega 100, 10, Kilo Hecto Deka Base deci centi milli 1/ 1/ micro 1/ 1/ Nano 000, 000, 000 000 meter 1000 10, 10, 100, 000 000 gram 000 000, 000, second 000 000

1. Determine direction: Put your finger on original prefix. Does your finger move left or right to reach the final prefix?

2. The direction your finger travels is the direction the decimal moves.3. Move the decimal once for each step moved 4. If you run out of numbers, fill in with zeros.

Conversion to smaller units

• If you are converting to a smaller unit (going down the steps) , multiply the unit by the number of 10’s equal to # of steps.

• This is same as moving the decimal to the RIGHT as the number of steps

Example

• 16.0 m = _____ mm

• You walk down 3 stairs from meters level to millimeters level

• Walking down means you multiply 16.0 by 3 10’s OR move the decimal place to the right 3 spaces

• Either way the correct answer is 16,000 mm

In comp book

• Practice questions:

• How many cm equal 15.7 km?

• How many ms (milliseconds) equal 45.3 Ds (Dekaseconds)?

Answers• 1,570,000 cm

• 453,000 ms

• Notice that converting to smaller units result in larger values

• It takes more of the tinier unit to equal a single big unit (ex. 100 cm needed to = 1 m)

Other examples

Convert to larger units

• If you are converting to a larger unit, divide the unit by the number of 10’s equal to number of steps

• This is the same as moving to the LEFT the number of spaces equal to the number of steps

Example

• Determine the number of km that equal 1340 m

• You move up 3 steps from meter level to kilometer level

• This requires you to divide 3 10’s in the value or move the decimal 3 spaces to the left

• Either way the correct answer is 1.34 km

Try these in your comp book

3. Convert 298,000 mm to an equal number of Hm (hectometers).

4. Convert 456 g (grams) to and equal number of kg (kilograms)

Answers

3. Answer = 2.98 hm4. Answer is 0.456 kg

5. Notice that the final numbers are smaller than the originals.

6. Notice also that the units (grams, seconds, meters) were all dealt with the same way

Conversion Factors we use most often :

• 1 meter = 100 centimeters• 1 meter = 1000 millimeters• 1 kilometer = 1000 meters

• Could interchange seconds, grams, Newtons, Joules for meter

Shortcut Conversion for velocity

• Divide your velocity in (km/hr) by 3.6 to get the velocity in (m/s)

OR• To convert from m/s to km/h multiply by 3.6

• To convert from km/h to m/s divide by 3.6

Time conversions

• 1 minute = 60 seconds• 1 hour = 60 minutes• 1 day = 24 hours• 1 year = 365 days (approximation)

Dimensional analysis

• A method to convert time or any other complex value with many units

• All that is done is multiply value by 1 or more forms that have the value of one.

Forms of one

• Math wise: 1 = 2/2 =5/5 = 13/13 = 8.2 /8.2

• If 1 minute = 60 seconds • then 1 min/60 s = 1 = 60 s / 1 min

• Any fraction where the value of the top = the value of the bottom has an overall value of 1

Multiplying value by 1

• Any value multiplied by 1 has the original value

• But there is a way to change the units

An Example:

• Convert 645 seconds into the equivalent number of minutes

• To do so…• Take 645 s and multiply by [ 1 min / 60 s]

• 645 s * 1 min /60 s– Second units cancel out, leaving minutes– (645*1)/60 = 10.75 min

Try these in your comp book

• 47.5 minutes = _____ hr

• 8 days = ______ min

Answers

• About 0.79 hr

• 11,520 min

SCIENTIFIC NOTATION

Scientific Notation

• A way to write very large or very small• Used to determine precision of value

A number between 1-10 x 10 to an exponentPositive exponents for large #Negative exponents for small #

To convertSmall # to Sci Notation

• To convert a small number to scientific notation, multiply the number by 10 as many times as is needed to get a digit value greater than 1 and less than 10. Multiply this digit value by an exponential term where the exponent is the negative number of times you have multiplied by 10.

Large # to Sci Notation• To convert a large number to

scientific notation, divide the number by 10 as many times as is needed to get a digit value less than 10 and greater than 1. Multiply this digit value by an exponential term where the exponent is the number of times that you have divided by 10.

0.0000000123 = 1.23x10-8 1230000000 = 1.23x109

Engineering button

Try

• 6,907,800,000

• Answer

• 6.9078 x109

Try

• 0.000 000 080 07

• Answer:

• 8.007 x 10-8