Carry out the following conversions. Report your answers to...

Carry out the following conversions. Report your answers to the correct number of significant figures. (a) $32 \mathrm{~cm}$ to $\mathrm{ft}$ (g) $2.7 \mathrm{lb}$ to $\mathrm{kg}$ (b) $0.579 \mathrm{~kg}$ to $\mathrm{lb}$ (h) $8.320 \mathrm{qt}$ to $\mathrm{mL}$ (c) $22.70 \mu \mathrm{L}$ to $\mathrm{qt}$ (i) $375 \mathrm{~km}$ to $\mathrm{ft}$ (d) $9212 \mathrm{~mm}$ to $\mathrm{km}$ (j) $62 \mathrm{~g}$ to $\mathrm{oz}$ (e) $465 \mathrm{~nm}$ to $\mathrm{mm}$ (k) $752 \mathrm{~mL}$ to gal (f) $4 \mathrm{ft}$ to $\mathrm{cm}$

Carry out the following conversions. Report your answers to the correct number of significant figures.
(a) $32 \mathrm{~cm}$ to $\mathrm{ft}$
(g) $2.7 \mathrm{lb}$ to $\mathrm{kg}$
(b) $0.579 \mathrm{~kg}$ to $\mathrm{lb}$
(h) $8.320 \mathrm{qt}$ to $\mathrm{mL}$
(c) $22.70 \mu \mathrm{L}$ to $\mathrm{qt}$
(i) $375 \mathrm{~km}$ to $\mathrm{ft}$
(d) $9212 \mathrm{~mm}$ to $\mathrm{km}$
(j) $62 \mathrm{~g}$ to $\mathrm{oz}$
(e) $465 \mathrm{~nm}$ to $\mathrm{mm}$
(k) $752 \mathrm{~mL}$ to gal
(f) $4 \mathrm{ft}$ to $\mathrm{cm}$

Key Concepts

Dimensional Analysis

Dimensional analysis is a systematic approach used to convert one set of units to another by using conversion factors. This method involves multiplying the quantity by a series of ratios that cancel out unwanted units and introduce desired ones, ensuring that the overall dimensions remain consistent. It is essential in problems where multiple unit conversions are necessary, as it helps maintain the integrity of the measurement process.

Conversion Factors

Conversion factors are specific numerical relationships between different units that are mathematically equal to one. They allow for the conversion of measurements from one unit system to another without altering the underlying value. This tool is crucial in unit conversion exercises, as it enables the correct introduction and cancellation of units when multiplied by the quantity being converted.

Significant Figures

Significant figures refer to the digits in a number that contribute to its precision, starting from the first nonzero digit. When converting measurements, it is important to round the results to the correct number of significant figures to reflect the precision of the original measurements. Adhering to significant figure rules ensures that the final answers communicate the appropriate level of uncertainty and accuracy inherent in the initial data.

Transcript

00:01 Okay, what we have here is a bunch of conversions.

00:03 So here we go.

00:05 We have letter a, we have 32 centimeters, and we're gonna convert this to feet.

00:13 Well, the conversions i'm using, may you may or may not know, i'm just using a standard table of conversions.

00:19 And with this, i know there are 2 .54 centimeters in one inch, and i know that there are 12 inches in one foot.

00:32 Inches cancel out, centimeters cancel out, leaving me with feet, and i get 1 .05 feet.

00:40 However, this has two significant digits.

00:42 So my answer is going to actually be 1.

00:46 I'm sorry, this is 1 .47.

00:49 So this is gonna be 1 .0 feet.

00:55 All right, letter, well, it's not letter b, it's letter g.

01:00 We have 2 .7 pounds, and we are changing it to kilograms.

01:06 Well, i know that there happens to be 0 .4536 kilograms in one pound.

01:21 My pounds cancel out, notice i have pounds on top and bottom, and that is going to equal 1 .22 kilograms.

01:31 Three significant digits, three significant digits.

01:36 All right, on to letter b.

01:41 In letter b, we have 0 .579 kilograms, and we're changing these to pounds.

01:48 I'm gonna use the same conversion, except this time i'm gonna flip it because kilograms are up here.

01:53 I'm going to put kilograms on the bottom.

01:55 So 0 .4536 kilograms in one pound, and that is going to equal 1 .27 pounds.

02:08 Once again, three significant digits, three significant digits.

02:12 All right, on to letter h.

02:19 Good thing these are in order.

02:22 We have 8 .320 quarts, and i'm changing this to milliliters.

02:29 Well, i know that there are 1 .057 quarts in one liter, and there are 1 ,000 milliliters in one liter, and that is going to equal 7871 milliliters.

02:49 Four significant digits.

02:51 Yes, the zero counts.

02:52 Four significant digits.

02:55 There we go.

02:57 All right, on to letter c.

03:01 We have 22 .70 microliters.

03:08 All right, well, according to my chart, there are 10 to the minus six liters in one microliter, and we have to change this into quarts.

03:23 So i know there are 1 .057 quarts in one liter.

03:29 Once again, notice microliters cancel out, liters cancel out, leaving me with quarts, and that is equal to 2 .399 times 10 to the minus five quarts.

03:46 Once again, four significant digits, four significant digits.

03:55 All right, after letter c, of course, we go to letter i, and letter i, we have 375 kilometers, which we're gonna change to feet.

04:06 I know that there are 1 .609 kilometers in one mile, and i know there are 5 ,280 feet in one mile...

Please give Ace some feedback