To do this problem I could try drawing a picture of 0.08 in a 1←10 machine and attempt to make sense of finding groups of 0.005 in that picture, that is groups of five dots three places to the right of where they should be. Although possible to do, it seems hard to keep straight in my head and it makes my brain hurt!
Here’s a piece of advice from a mathematician: Avoid hard work! Mathematicians will, in fact, work very hard to avoid hard work!
Since converting decimals to fractions makes the multiplication of fractions easier, let’s do the same thing for division.
Here are some examples.
Example: Examine 0.08÷0.005.
A fraction is a number that is an answer to a division problem. And, conversely, we can think of a division problem as a fraction. For example, the quantity 0.08÷0.005 is really this “fraction” 0.0050.08.
(It is okay to have non-whole numbers as numerators and denominators of fractions.)
To make this fraction look friendlier, let’s multiply the top and bottom by factors of ten.
The division problem 580 is much friendlier. It has the answer 16.
(Use a 1←10 machine to compute it if you like!)
Example: Examine 1008.5.
Dividing by 100 is the same as multiplying by 1001. So, 1008.5, for example, can be thought of as
Example: Examine 1.51÷0.07.
If I was asked to compute 1.51÷0.07, I would personally do this problem instead:
I see the answer 2174. If that same person asked me to give the answer as a decimal, then I would have to convert the fraction 74 into a decimal. And that is possible. The next lesson explains how!