# Uses of negative numbers

When numbers are used as scalars, they are used to measure something. Perhaps height, weight or length. Used this way, numbers can be compared. That is, we can say that one number is greater than or less than another.

Often, the measurement is made from an agreed fixed point. Then, measurements made one way from that point are positive, and the other way they are negative. (Usually, physical measurements made upwards and to the right are positive, but there is no rule about that).

## A building elevator

The building shown above has an elevator you can drag up and down. The height of the elevator floor is shown, and is the height above ground level. When it is above ground it is a positive height. Drag the elevator down into the basement. It is now below ground and the height becomes negative.

What has happened here is that we agreed that heights would be measured from ground level. This is the zero height. We further agreed that heights going upward would be positive, and down would be negative. Note: We could have agreed instead that heights would be measured from the basement floor. Then, all heights would have been positive. Both are OK, as long as we know.

## Things to try

• Move the elevator all the way to the bottom, note the height.
• Move it all the way to the top.
• Calculate how far the elevator has moved.