Carry out the following conversions. a. 5.52 ×10^4 mL to L b. 0.207 g to mg c. 186 km to m d.

Carry out the following conversions. a. 5.52 ×10^4 mL to L...

Carry out the following conversions.
a. $5.52 \times 10^{4} \mathrm{~mL}$ to $\mathrm{L}$
b. $0.207 \mathrm{~g}$ to $\mathrm{mg}$
c. $186 \mathrm{~km}$ to $\mathrm{m}$
d. $1.66 \mathrm{~m}^{2}$ to $\mathrm{cm}^{2}$
e. $78 \mu$ s to $\mathrm{ms}$

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Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used in science to convert between units by ensuring that the dimensions on both sides of an equation match. It involves the systematic use of conversion factors to cancel out unwanted units until the desired units are obtained, ensuring consistency and accuracy in calculations.

Metric Prefixes

Metric prefixes are standardized prefixes used to indicate multiples or submultiples of units in the metric system. They facilitate the expression of very large or very small numbers by assigning powers of ten to specific prefixes, such as kilo, milli, micro, etc., making it easier to work with a wide range of measurements.

Unit Conversion

Unit conversion is the process of converting a measure of physical quantity from one unit to another. This requires understanding the relationship between the units involved and applying a conversion factor to accurately translate the quantity without changing its value.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equivalent to another unit. They are used in calculations to multiply by a quantity in order to cancel out the original unit and introduce the desired unit, ensuring that the final result is expressed in the correct measurement system.

Transcript

00:04 Whenever we want to do conversions, the first thing is that you should be proficient in a process called dimensional analysis.

00:14 And in dimensional analysis, we are going to take a value and we are going to multiply it by a fraction where the numerator and the denominator are equal to each other, but in different units.

00:33 If, for example, you have meters and you want to go to kilometers, you would need to use the fact that there are 1 ,000 meters in one kilometer.

00:48 And by multiplying by a fraction where those equal pieces on top of each other, we're really multiplying by a fraction that is equal to the number one.

00:57 Meters cancel and then you do your regular division and multiplication.

01:02 So each of those fractions that we multiply by, we call a conversion factor.

01:08 And so if we want 5 .52 times 10 to the fourth milliliters and we want to get it to liters, we have to multiply by the conversion factor of one liter for a thousand milliliters.

01:23 And when we do this answer, what it comes out to, right, milliliters cancel.

01:28 This becomes 10 to the 1 and it becomes 55 .2 liters.

01:39 186 kilometers.

01:43 It is 1 ,000 meters for every 1 kilometer.

01:49 So we wind up with 186 ,000 meters.

01:57 Grams to milligrams, there are 1 ,000 millimeters.

02:05 In one gram...