Question

Question #69222

Answer 1

`(6830 " yen")/("kg")`

Explanation:

Always do your conversions at the smallest measurement to have the best accuracy. Using `1 "oz" = 28.3495 g`

`(cancel($)2.50)/cancel("oz") xx (77.4 "yen")/(cancel($)1) xx (1 cancel("oz"))/(28.3495 cancel(g)) xx (1000 cancel(g))/(1 kg) ~~(6825.5 "yen")/("kg")`

If you take into account significant figures (smallest number = 3) the answer would be:

`(6830 " yen")/("kg")`

Answer 2

Here's what I got.

Explanation:

For starters, it's completely up to you which conversion factors you want to use to go from ounces to kilograms.

Tyler decided to go from ounces to pounds first, then from pounds to kilograms because he felt like these two conversion factors are easier to memorize.

• `"ounces to pounds"`

`"something in oz" xx "1 lb"/"16 oz" = "something in lb"`

• `"pounds to kilograms"`

`"something in lb" xx "1 kg"/"2.20 lb" = "something in kg"`

So he set up the calculation like this

`(2.50 color(red)(cancel(color(black)("USD"))))/(1color(red)(cancel(color(black)("oz")))) * "77.4 JPY"/(1color(red)(cancel(color(black)("USD")))) * (16 color(red)(cancel(color(black)("oz"))))/(1color(red)(cancel(color(black)("lb")))) * (2.20color(red)(cancel(color(black)("lb"))))/"1 kg" = "6,810 JPY/kg"`

Keep in mind that the answer is rounded to three sig figs, the number of sig figs you have for `"2.50 USD"`.

Now, you can also set up the calculation by using these two conversion factors

• `"ounces to grams"`

`"something in oz" xx "28.35 g"/"1 oz" = "something in g"`

• `"grams to kilograms"`

`"something in g" xx "1 kg"/(10^3color(white)(.)"g") = "something in kg"`

In this case, you will have

`(2.50 color(red)(cancel(color(black)("USD"))))/(1color(red)(cancel(color(black)("oz")))) * "77.4 JPY"/(1color(red)(cancel(color(black)("USD")))) * (1 color(red)(cancel(color(black)("oz"))))/(28.35color(red)(cancel(color(black)("g")))) * (10^3color(red)(cancel(color(black)("g"))))/"1 kg" = "6,830 JPY/kg"`

Once again, the answer must be rounded to three significant figures.

The difference between the two values lies in the conversion factor used to go from pounds to kilograms. Notice that if you take

`"1 kg = 2.20462262 lb"`

you get

`(2.50 color(red)(cancel(color(black)("USD"))))/(1color(red)(cancel(color(black)("oz")))) * "77.4 JPY"/(1color(red)(cancel(color(black)("USD")))) * (16 color(red)(cancel(color(black)("oz"))))/(1color(red)(cancel(color(black)("lb")))) * (2.20462262color(red)(cancel(color(black)("lb"))))/"1 kg" = "6,830 JPY/kg"`

So yes, you can say that Tyler oversimplified the conversions a bit by using

`"1 kg = 2.20 lb"`

but he most likely did so because of the fact that he had three significant figures for `"2.50 USD"` and because that conversion factor is easier to memorize than the full version.

It's always a good idea to use conversion factors rounded to at least one more significant figure than the number of significant figures present in your data.

In this case, something like

`"1 kg = 2.205 lb"`

would have been a better choice because you have three sig figs for `"2.50 USD"`, so a conversion factor that retains four sig figs would have worked better.

Question reference--the `6:11` minute mark