Numbers on a number line

Think of the number line as the address where every number lives. A number line has marks at 1000, 2000, 3000 and so on up to 10,000. Where do 2180 and 2754 go? Both are more than 2000 and less than 3000, so both lie between the 2000 and 3000 marks. 2180 is just a little past 2000, so it sits close to 2000; 2754 is much nearer to 3000.

Sometimes only two marks have numbers, and we must label the rest. First find the step: how much the number goes up from one mark to the next.

On one of the book's lines, 2010 and 2020 are two marks apart, with one mark between them. From 2010 to 2020 is 10, shared equally by 2 steps, so each step is 5. The mark between them is 2015; the mark after 2020 is 2025; the mark before 2010 is 2005.

If two labelled numbers sit on neighbouring marks, the step is just their difference:

• 9996 and 9997 are next to each other, so the step is 1: the next marks are 9998, 9999, 10,000. (There is no whole number between 9996 and 9997, just as nobody stands between you and the brother born right after you.)
• 86,705 and 87,705 are next to each other too, but the step is 1000: the mark before 86,705 is 85,705.