Question

Using words, explain all steps of dimensional analysis when converting 6.7 hectometers to meters. You must explain the set up of the problem and give your final answer.

A minimum of 4 complete sentences are

Answer 1

`\large \boxed{\text{670 m}}`

Step-by-step explanation:

Dimensional analysis uses the fact that any number can be multiplied by one without changing its value.

You want to convert hectometres to metres, so you multiply the hectometres by a conversion factor that equals one.

For example, you know that hecto means "× 10², so

1 hm = 100 m

If we divide each side by 1 hm, we get 1 = 100 m/1 hm.

If we divide each side by 100 m, we get 1 hm/100 m = 1.

So, we can use either (100 m/1 hm) or (1 hm/100 m) as a conversion factor, because each fraction equals one.

We choose the former, because it has the desired units on top.

The calculation becomes

`\text{Distance} = \text{6.7 hm} * \frac{\text{100 m}}{\text{1 hm}} = \textbf{670 m}\\\\\text{6.7 hm} =\, $\large \boxed{\textbf{670 m}}$}`