Question

find the value of t. write your answer as a decimal number.
0.9 t 1.0
t = \boxed{}

Explanation:

Step1: Determine the interval length

The distance between 0.9 and 1.0 is $1.0 - 0.9 = 0.1$. From 0.9 to 1.0, there are 10 intervals (count the ticks: from 0.9 to 1.0, how many spaces? Let's see, from 0.9 to 1.0, the number of intervals between them: let's count the ticks. From 0.9 (first tick) to 1.0 (last tick), how many intervals? Wait, looking at the number line: 0.9 is at the first tick, then there are ticks up to 1.0. Let's see, from 0.9 to 1.0, the total length is 0.1, and how many intervals? Let's count the number of spaces between 0.9 and 1.0. From 0.9 to 1.0, there are 10 intervals? Wait, no, let's check the positions. Wait, the tick for 0.9, then how many ticks until 1.0? Let's see, the last tick is 1.0, and t is two ticks before 1.0? Wait, no, let's count the number of intervals between 0.9 and 1.0. The distance from 0.9 to 1.0 is 0.1, and if we divide that into 10 equal parts, each part is $0.1 \div 10 = 0.01$? Wait, no, maybe the number of intervals is 10? Wait, no, looking at the number line: from 0.9 to 1.0, how many ticks? Let's see, 0.9 is the first, then the next ticks: let's count the number of intervals between 0.9 and 1.0. Let's see, 1.0 - 0.9 = 0.1. The number of intervals between 0.9 and 1.0: let's see, from 0.9 to 1.0, there are 10 small intervals? Wait, no, the tick for t is two ticks before 1.0? Wait, no, let's count the positions. Let's list the ticks: 0.9 (tick 1), then tick 2, 3, 4, 5, 6, 7, 8, 9, 10 (which is 1.0). Wait, no, that can't be. Wait, maybe the number of intervals between 0.9 and 1.0 is 10, so each interval is 0.01? Wait, no, 0.1 divided by 10 is 0.01, but then from 0.9 to 1.0, 10 intervals of 0.01 each. But t is at the 8th tick? Wait, no, let's look at the number line again. The tick for 0.9, then t is two ticks before 1.0. Wait, 1.0 is at the last tick, and t is two ticks to the left of 1.0. So how many intervals between t and 1.0? Let's see, from t to 1.0, there are 2 intervals? Wait, no, maybe the total number of intervals from 0.9 to 1.0 is 10, so each interval is 0.01. Wait, 0.9 to 1.0 is 0.1, so 0.1 / 10 = 0.01 per interval. Then, how many intervals from 0.9 to t? Let's see, 0.9 is at tick 1, then each tick is +0.01. Wait, no, maybe the number of intervals between 0.9 and 1.0 is 10, so each step is 0.01. Wait, but 0.9 + 0.01*9 = 0.99, no, 0.9 + 0.01*10 = 1.0. So the ticks are at 0.9, 0.91, 0.92, ..., 1.0. Wait, but in the number line, t is two ticks before 1.0. So 1.0 - 0.01*2 = 0.98? Wait, no, maybe I miscounted. Wait, let's look at the number line: 0.9 is on the left, then t is two ticks before 1.0. Wait, the distance from 0.9 to 1.0 is 0.1, and there are 10 intervals (since from 0.9 to 1.0, how many ticks? Let's count the number of spaces between 0.9 and 1.0. Let's see, the first tick is 0.9, then the next ticks: let's say there are 10 intervals (so 11 ticks) from 0.9 to 1.0. So each interval is 0.1 / 10 = 0.01. Then, t is at the 9th tick? Wait, no, 0.9 is tick 1, tick 2: 0.91, tick 3: 0.92, ..., tick 9: 0.98, tick 10: 0.99, tick 11: 1.0. Wait, but in the number line, t is two ticks before 1.0, so tick 9: 0.98? No, tick 10 is 0.99, tick 11 is 1.0. Wait, maybe the number of intervals between 0.9 and 1.0 is 10, so each interval is 0.01, and t is at the 8th interval from 0.9? Wait, no, let's check the positions again. Wait, the problem is a number line with 0.9 on the left, t somewhere, and 1.0 on the right. Let's count the number of intervals between 0.9 and 1.0. Let's see, from 0.9 to 1.0, there are 10 small segments (intervals), so each segment is 0.1 / 10 = 0.01. Now, how many segments from 0.9 to t? Wait, no, t is two segments before 1.0. So from t to 1.0, there are 2 segments, each 0.01, so t = 1.0 - 2*0.01 = 0.98? Wait, no, maybe the number of intervals is 10, so from 0.9 to 1.0, 10 intervals, so each is 0.01. Then, t is at the 8th interval from 0.9? Wait, 0.9 + 8*0.01 = 0.98? Wait, no, 0.9 + 0.01*8 = 0.98, and then 0.98 + 0.01*2 = 1.0. Yes, that makes sense. So t is 0.98.

Step2: Verify the calculation

The distance between 0.9 and 1.0 is 0.1. The number of intervals between them is 10, so each interval is 0.01. t is 8 intervals away from 0.9 (since 10 - 2 = 8, because it's 2 intervals before 1.0). So 0.9 + 8*0.01 = 0.9 + 0.08 = 0.98. Alternatively, 1.0 - 2*0.01 = 1.0 - 0.02 = 0.98. Both methods give t = 0.98.

Answer:

0.98