Convert the following quantities into SI units with the...

Convert the following quantities into SI units with the correct number of significant figures: $$ \begin{array}{llll}{\text { (a) } 5.4 \mathrm{in.}} & {\text { (b) } 66.31 \mathrm{lb}} & {\text { (c) } 0.5521 \mathrm{gal}}\end{array} $$ $$ \text{(d)}65 \mathrm{mi} / \mathrm{h} \quad \text { (e) } 978.3 \mathrm{yd}^{3} \quad \text { (f) } 2.380 \mathrm{mi}^{2} $$

Convert the following quantities into SI units with the correct number of significant figures:
$$
\begin{array}{llll}{\text { (a) } 5.4 \mathrm{in.}} & {\text { (b) } 66.31 \mathrm{lb}} & {\text { (c) } 0.5521 \mathrm{gal}}\end{array}
$$
$$
\text{(d)}65 \mathrm{mi} / \mathrm{h} \quad \text { (e) } 978.3 \mathrm{yd}^{3} \quad \text { (f) } 2.380 \mathrm{mi}^{2}
$$

Key Concepts

Significant Figures

Significant figures reflect the precision of a measurement, indicating which digits in a number are known reliably. In conversions, it is important to maintain the correct number of significant figures to ensure that the precision of the original measurement is preserved. This involves rounding the final SI unit results according to the rules of significant figures.

Dimensional Analysis

Dimensional analysis is a method used to ensure that the conversion of units is performed correctly by treating conversion factors as fractions and ensuring that the units are consistently canceled. This technique verifies that the resulting expression has the correct dimensions corresponding to the desired SI unit.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equivalent to another unit. They are used in unit conversions to multiply the original measurement, allowing non-SI units to be systematically translated into SI units. They are essential in bridging the gap between different measurement systems.

Unit Conversion

Unit conversion is the process of changing a quantity expressed in one set of units to an equivalent value in another set of units. In this context, it involves converting quantities from the imperial system (or customary units) to the International System of Units (SI). Correct conversion requires multiplying by conversion factors that relate the original units to the SI units.

SI Units

SI Units, or the International System of Units, are a standardized set of measurement units used worldwide. This system is designed to provide a clear and consistent method for quantitative measurements. In the problem, various non-SI units such as inches, pounds, gallons, miles per hour, cubic yards, and square miles are converted to their corresponding SI units like meters, kilograms, liters, meters per second, cubic meters, and square meters.

Transcript

00:01 We need to convert six different non -si measurements into proper si measurements.

00:07 We're going to start with the first one, which is 5 .4 inches.

00:13 Now probably the most logical comparison to the inch would be the centimeter.

00:18 But the main unit in metrics for conversion would probably be the meter.

00:26 So we're going to work towards that.

00:29 And the conversion is that for every one inch, so that my units here are lined up and will thus cancel.

00:36 There are 0 .254 meters because 1 inch is equal to 2 .54 centimeters and we can convert it back to meters this way.

00:51 These inches will cancel and will be left just with meters which is what we want and that works out to be 0 .13716 meters however, we only have two significant figures given to us, so we have to simplify that down to two significant figures, which will be 0 .14 meters.

01:12 Next up, we are given 66 .31 pounds, which, in imperial, is not metric, a unit of weight.

01:29 But the most common metric unit is the newton for weight, but it's not really used in these cases.

01:38 So we're going to work with the kilogram, since it's most equatable to the pound.

01:44 And for every pound, there are 0 .453 .592 kilograms.

01:55 Once that is punched into a calculator, you'll get it as being 30 .0753 .7.

02:01 7, 68552 kilograms, but we only have four significant figures.

02:07 So we're going to simplify that down by rounding to 30 .08 kilograms.

02:16 Next up, we'll look at part c, which is 0 .552 gallons, a volume measurement in the imperial system.

02:29 We're going to stick with our theme of going with whatever would probably be most common, and in this case it would be cubic meters.

02:36 For every gallon there's 0 .0037 -84541 cubic meters.

02:45 So my gallons will cancel and i'll just be left with what i've requested.

02:50 In this case it's 0 .002089925 cubic meters...

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