Question

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

Explanation:

Step1: Determine the interval length

The distance between 8 and 9 on the number line is \(9 - 8 = 1\). There are 10 intervals (since from 8 to 9, counting the ticks, there are 10 spaces between 8 and 9? Wait, no, let's count the ticks. From 8 (first tick) to 9 (last tick), how many ticks? Let's see: 8 is the first, then 9 is the 10th? Wait, no, looking at the number line: between 8 and 9, how many segments? Let's count the ticks: 8, then 9 is the 10th tick? Wait, no, the number of intervals between 8 and 9: from 8 to 9, the total length is 1, and the number of intervals (spaces between ticks) from 8 to 9: let's see, the tick for 8, then 9. Let's count the number of intervals between 8 and 9. The first tick is 8, then the next ticks: let's see, from 8 to 9, there are 10 intervals? Wait, no, the distance from 8 to 9 is 1, and if we look at the number of ticks between 8 and 9: let's see, the tick for \(t\) is one before 9. Wait, maybe the number of intervals between 8 and 9 is 10, so each interval is \( \frac{1}{10}=0.1 \). Then, from 8, how many intervals to \(t\)? Let's count: from 8 (first tick) to \(t\): let's see, 8 is the first, then the ticks are: 8, then 8.1, 8.2, ..., 8.9, 9. Wait, \(t\) is the 9th interval? Wait, no, let's see the position of \(t\): \(t\) is one tick before 9. So from 8 to 9, there are 10 intervals (since 8 to 9 is 1, divided into 10 equal parts, each 0.1). So the ticks are 8, 8.1, 8.2, ..., 8.9, 9. So \(t\) is at 8.9? Wait, no, wait: let's count the number of ticks between 8 and 9. Let's see the number line: 8 is the first tick, then 9 is the 10th tick? Wait, no, the number of intervals between 8 and 9: if 8 is the first, and 9 is the 10th, then the number of intervals is 9? No, that's confusing. Wait, maybe a better way: the distance from 8 to 9 is 1, and there are 10 equal segments (since from 8 to 9, the number of spaces between ticks is 10). So each segment is \( \frac{1}{10} = 0.1 \). Then, \(t\) is 9 segments from 8? Wait, no, \(t\) is one segment before 9. So from 8 to 9, there are 10 segments, so each is 0.1. So the tick before 9 is \(9 - 0.1 = 8.9\). So \(t = 8.9\).

Step2: Verify

The number line from 8 to 9 is divided into 10 equal parts, each 0.1. So the ticks are 8, 8.1, 8.2, ..., 8.9, 9. So \(t\) is at 8.9.

Answer:

\( t = 8.9 \)