Using your knowledge of metric units, English units, and the information on the back inside cove

Using your knowledge of metric units, English units, and the...

Key Concepts

Metric Units

Metric units are part of the International System of Units (SI) and are based on decimals, making calculations and conversions simpler. They include units such as meters, liters, and kilograms, and rely on standard prefixes to indicate multiples or fractions of the base units.

English Units

English units, often referred to as Imperial units in some countries, are used predominantly in the United States and include measurements like gallons, feet, and pounds. Converting between English units and metric units requires specific conversion factors that bridge the two systems.

SI Prefixes

SI prefixes are used in the metric system to denote powers of ten, such as kilo (10^3), milli (10^-3), and micro (10^-6). They allow for easier interpretation and conversion of large or small values by standardizing scaling factors across measurements.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. They are used by multiplying by the proper ratio to convert a measurement from one unit to another, ensuring that the dimensions cancel out appropriately during the process.

Dimensional Analysis

Dimensional analysis is a systematic method to check and guide conversions between different units. By treating units as algebraic quantities, it helps in setting up conversion equations that ensure the final result is expressed in the desired units.

Transcript

00:01 Very much going to be practicing dimensional analysis in order for us to go ahead and to carry out these conversions.

00:08 So we have a conversion from using kilometers per hour to meters per second, milliliters to microliters to micoleters, picoseconds to seconds and cubic meters to a gallon.

00:20 So we can start with our first one here.

00:22 We're going to use the marker.

00:25 So we're going to convert kilometers per hour to meters per second.

00:29 So we can start with just writing out a km and then we can put over our hour.

00:37 And with dimensional analysis, the most important things that we have to cross units out to make sure that we end up with the right ones at the very end.

00:44 So what we can do is start converting our kilometers into our meters.

00:49 And we know that for every kilometer, there are 1 ,000 meters present.

00:54 Right, kilo, it means 1 ,000.

00:56 So we can put 1km here is equal to 1 ,000 meters.

01:11 And then now that we've converted it to meters, we can go ahead and convert our hours to seconds.

01:20 Now we have an hour over here, and so we know that for every one hour, there are 3 ,600 seconds present.

01:35 You can also do this a longer way in which we can put 1 hour, there are 60 minutes, and then for every 60 minutes or for every minute is 60 seconds.

01:45 And you can do that a little bit longer way if you're more comfortable.

01:48 All i did was just simply go ahead and essentially just multiply that already and i already just did the seconds here like that.

02:01 And so now we know that our kilometers cancel out.

02:05 So we left with meters.

02:06 Our hours cancel out.

02:07 So we're left essentially with meters over seconds.

02:11 And so all we have to do is essentially just divide our 1 ,000 by our 3 ,600 seconds.

02:19 And that would get you the conversion factor to get from meters to seconds.

02:24 And then the next one, we have our middle liters to micrometers...