Question

find the value of m. write your answer as a decimal number.
8 m 9
m =

Explanation:

Step1: Determine the interval

The number line spans from 8 to 9. Let's count the number of intervals between 8 and 9. From the diagram, between 8 and 9, there are 10 equal intervals (since from the first mark at 8 to the last at 9, we can see the divisions: let's check the positions. Wait, actually, looking at the marks: from 8 to 9, how many spaces? Let's see, the marks are: 8, then 9 marks later is 9? Wait, no, the number of intervals between 8 and 9: let's count the number of segments. From 8 to the next mark is 1 segment, then to m, then to 9. Wait, actually, from 8 to 9, there are 10 equal parts? Wait, no, let's see: the distance from 8 to 9 is 1 unit. Let's count the number of intervals between 8 and 9. Looking at the number line, from 8 to 9, there are 10 intervals? Wait, no, the marks: 8 is at the first mark, then the next marks, and m is at the 8th mark? Wait, no, let's see: the number of intervals between 8 and 9. Let's count the number of spaces between 8 and 9. From 8 to 9, there are 10 equal intervals? Wait, no, the number of segments: from 8 to the next mark is 1/10 of the interval? Wait, no, let's see: the position of m. Let's count the number of intervals from 8 to m. Wait, 8 is at the first mark, then the next marks: let's see, between 8 and 9, there are 10 intervals (since 8 to 9 is 1, and divided into 10 parts). So each interval is \( \frac{1}{10} = 0.1 \). Now, m is at the 8th interval from 8? Wait, no, let's see: the marks: 8, then 9 marks later is 9. Wait, the number of intervals between 8 and 9: let's count the number of spaces. From 8 to the first mark after 8: 1 space, then to m, then to 9. Wait, actually, looking at the number line, m is at the 8th interval from 8? Wait, no, let's see: the distance from 8 to m: how many intervals? Let's see, from 8 to 9, there are 10 intervals (since 8 + 10*(0.1) = 9). So each interval is 0.1. Now, m is at the 8th interval? Wait, no, let's count the position of m. Let's see, the marks: 8, then the next marks, and m is at the 8th mark? Wait, no, 8 is the first mark, then the second, third, ..., tenth mark is 9. So m is at the 8th mark? Wait, no, 8 is mark 1, then mark 2, ..., mark 9 is m, mark 10 is 9? Wait, no, that can't be. Wait, maybe the number of intervals between 8 and 9 is 10, so each is 0.1. So the position of m: from 8, moving 8 intervals? Wait, no, let's see: 8 + 0.8 = 8.8? Wait, no, wait: 8 to 9 is 1, divided into 10 parts, so each part is 0.1. So the first interval after 8 is 8.1, second 8.2, ..., eighth interval is 8.8? Wait, no, m is at the 8th interval? Wait, no, let's look at the number line: 8, then the next marks, and m is at the 8th mark from 8? Wait, 8 is mark 1, mark 2: 8.1, mark 3: 8.2, ..., mark 9: 8.8, mark 10: 9. Wait, yes! Because 8 + 0.8 = 8.8. So m is at 8.8. Let's verify: from 8 to 9, 10 intervals, each 0.1. So m is at 8 + 0.8 = 8.8.

Step2: Calculate m

Since each interval is 0.1, and m is 8 intervals away from 8 (wait, no, 8 to 9 is 10 intervals, so m is at the 8th interval? Wait, no, 8 is at 0, then each interval is 0.1. So the position of m: 8 + 0.8 = 8.8.

Answer:

8.8