Question

use dimensional analysis. Will a stand that can hold up to 40 pounds support a 22‐kilogram television? Complete the explanation. Use 2.2 lb = 1 kg.

Answer 1

In dimensional analysis, you set up unit conversion factors that are fractions equal to 1.
Then you multiply the given quantity by the conversion factor fraction that will eliminate the units you don't want and will leave the units you want.

Answer 2

Here is an example.

Question: Convert 10 cm to in. Use 1 in. = 2.54 cm

Solution:
We first need to come up with the conversion fractions.

1 in. = 2.54 cm (Eq. 1)

Divide both sides by 1 in. to get:

\(\dfrac{1~in.}{1~in.} = \dfrac{2.54~cm}{1~in.} \)

The left fractiopn equals 1, so you know that the conversion fraction \(\dfrac{2.54~cm}{in.} \) equals 1.

Now take Eq. 1 again, and divide both sides by 2.54 cm:

\(\dfrac{1~in.}{2.54~cm} = \dfrac{2.54~cm}{2.54~cm} \)

Once again, the fractions above equal 1, so the conversion fractions for inches to cm or cm to inches are:

\(\dfrac{2.54~cm}{in.} = \dfrac{in.}{2.54~cm} \)

Now that we went through all of this, you don't need to do all this work again even with other unit conversions.
Any time you are given an equivalency of units, just write a fraction of one side over the other one.

Now we can actually do the conversion:

\(10~cm \times \dfrac{in.}{2.54~cm} \)

Notice that since we are converting from cm to in., we need the conversion fraction with cm in the denominator so that cm will cancel out. Then we are left with in. which is what we want.

\(10~cm \times \dfrac{in.}{2.54~cm} = 3.94 in.\)

Answer 3

Follow the above example, and then apply the same idea to your problem.