1.3 Units and Dimensions

What is the length of an E. coli bacterium (.000005 m) in kilometers?

.000005 m x 1 km/1000 equals 5 x 10^-9 km

What's the length of an E. Coli bacterium in kilometers?

0.000005 m x 1 km/1000 m

A typical E. Coli bacterium is about 0.005 mm in length. Convert this length to meters (m)

0.005 mm x 1 m/1000 mm

Now, what's the volume of the warehouse in cubic meters if its length is 0.012 km and the other dimensions are unchanged?

0.012 km x 1000 m/1 km equals 12 m so, 12 x 10.5 x 4.95= 623.7 m^3

How many milliliters are in 1.2 liters?

1.2 L x 1000 mL/1L equals 1200 mL

How many cm in a millimeter?

1/10

How many m in a cm?

1/100

How many meters in a centimeter?

1/100

How many meters in centimeters?

1/100

How many grams in a milligram?

1/1000

How many km in a m?

1/1000

How many meters in mm?

1/1000

How many liters in a decaliter?

10

A sprinter runs 100 m in 10 seconds, a rough estimate of that speed would be what?

10 m/s

How many centimeters in a meter?

100

How many cm in a meter?

100

How many meters in a hectometer?

100

How many grams in a kilogram?

1000

How many m in km?

1000

How many meters in kilometer?

1000

How many millimeters are in a meter?

1000

How many mm in m?

1000

Kilo Milli Centi

1000 1000 100

Convert 25 mm2/s to km2/day

25mm2 x 1 km/1000000 x 86,400/1 equals 2.16 but then you have to divide by 1,000 twice!

A minivan has a mass of 33,200 g. Give the mass of the minivan in kg and megagrams?

33,200 g x 1kg/1000g = 33.2 kg 33,200 g x 1 mg/10^6g= .0332 mg

Blood in the human aorta can attain a speed of 35.0 cm/s. How fast is this in kilometers per hour?

35.0 cm/1 s x 1 km/100,000 cm ???

The star of Africa, a diamond in the royal scepter of the British crown jewels, has a mass of 530.2 carats, where 1 carat= 0.20 g. Given that 1 kg has a weight of 2.21 lbs, what is the weight of the star of Africa in lbs?

530.2 c x .20 g/1c x 1kg/1000g x 2.21 lbs/1 kg equals 0.2343 lbs

How many seconds in a day?

86,400 seconds 24x60x60

What has nature provided us with?

A fairly accurate timepiece in the revolving earth

Mass

A measure of the amount of matter in an object

Weight

A measure of the gravitational force acting on an object

Another example, (2 x 10^3 ms) x (5 x 10^-2 s) And, these same rules go for dividing sci not w differnt units!

Again, moving from ms to s is going in the positive direction but we need to subtract! So it becomes (2 x 10^0 s) x (5 x 10^-2 s) 10 x 10^-2 Buttt you can't have a 10! so change it to 1.0 x 10^-1 s^2

Why do equations have to be dimensionally consistent?

Answer won't make sense if it's not in the same dimensions

The standard "measuring stick" for s physical quantity is referred to as its ______

Base unit

Physical quantities are measured using ______

Base units

When converting to a larger unit, you

Divide

KHDUDCM

King Henry Died Unexpectedly Drinking Chocolate Milk Kilo x 1000 Hecto x 100 Deca x 10 Base unit x 1 Deci x 1/10 Centi 1/100 Milli 1/1000

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object Weight is a measure of the gravitational force of an object

SI Base Units Name all seven physical quantities and make the units and abbreviations

Mass. Kilogram. kg Length. Meter. m Time. Second. s^a Temp. Kelvin. K Amount of substance. Mole. mol Electric current. Ampere. A Luminous intensity. Candela. cd

Base unit of length

Meter (m)

Based on powers of 10

Metric system

When converting to a smaller unit, you

Multiply

Say you calculated that a runner was moving at 290 m/s. Is that number reasonable to you?

Nope

Base unit of time

Second (s)

For example, (6.5 x 10^-2 m) x (4.0 x 10^3 km) Oh no! The units aren't the same, what do I do?

So, when you're multiplying scientific notation with different units, change them both to the same units! Change then to meters, so on the khdudcm, meters is three units to the right of kilometers, so we add 3 to 3's exponent. Although units get smaller as we go to the right on the khdudcm, we add three (and basically do the opposite) because this is scientific notation, not converting units. So, it becomes (6.5 x 10^-2 m) x (4.0 x 10^6 km) convert to the bigger unit!

SI Unit

Unit of measurement established in 1960

A warehouse is 1980 cm long, 1050 cm wide, and 495 cm high. What is the volume in cubic meters?

V= l x w x h 1980 cm x 1 m/100 cm 19.8 m 1050 cm x 1 m/100cm 10.5 m 495 cm x 1 m/100cm 4.95 m equals 1,029.105 m^3

What are some mathematical equations used in science that you already know?

V=d/t a=v/t F=MA newton's 2nd law

A typical E. Coli bacterium is about 0.005 mm in length. Convert this length to meters.

You see that you are converting to a larger unit so you divide! 0.005 mm x 1 m/1000 equals .000005 m or 5 x 10^-6

Dimensional analysis

a calculation written in terms of dimensions

Prefixes modify the SI base units:

deca. Deci Hecto Centi Kilo. Milli Mega micro Giga Nano Tera. Pico Peta. Femto Exa. Atto Zetta Zepto Yotta Yocto

Any valid equation in physics must be _______

dimensionally consistent

Physical equations are _________

dimensionally consistent

Multiple conversions can be ________

done at once

Nature has provided us with a:

fairly accurate timepiece in the revolving earth

2.8 x 10^-5 / 2.0 x 10^4 g

grams cancel out!

f a physics equation isn't dimensionally consistent, _____ _______ _________

it isn't correct.

Base unit of mass

kilogram (kg)

What dimensional consistency means?

means that each term in physics equation must have the same dimensions. If a physics equation isn't dimensionally consistent it isn't correct.

What can be done at once?

multiple conversions?

Dimensional analysis and unit conversion - The dimension of a physical quantity refers to:

the type of quantity it is, regardless of the units used in the measurement

Why is it important for scientists to use the standard units of measure?

to avoid confusion using standard units of measure allows scientists to compare data and communicate with each other about their results. Using the same measurements makes the process of comparing data and communicating much easier. When using a common measurement system, scientists can make direct comparisons instead of going through the trouble of converting units