# Question #69222

##### 2 Answers

#### Explanation:

Always do your conversions at the smallest measurement to have the best accuracy. Using

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

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

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

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

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