Question

Jim thinks –3/5 is greater than –0.2. You determine that –0.2 is greater than –3/5. Write Jim an explanation that justifies why –0.2 is greater than –3/5. In your explanation, indicate how to use a number line to compare the rational numbers.

Answer 1

First I would introduce the concept of comparing two number using the number line and say: placing two numbers on the number line, the number that is to the right of the other, is the larger number (unless they're equal).

I would then write -0.2 as a fraction: -1/5

Then partition the number line segment between -1 and 0 into fifths and place -1/5 on the first fifth boundary, closes to the 0 point. Then place -3/5 on the boundary of the third fifth (three fifths away from the 0 point into the negative direction). Then ask: which of the two is more to the right on the number line? The answer becomes clear: -1/5 > -3/5 because of the number line comparison concept mentioned at the beginning.

Answer 2

Because 3/5 into a decimal is .60, but since its negative its -0.6 > -0.2