Question

look at the number line below.
what point is marked on the number line?

Explanation:

Step1: Determine the interval length

Between -2 and -1, and -1 and 0, and 0 and 1, the number of small ticks. From -2 to -1, there are 10 small ticks (since from -2 (marked) to -1 (marked) has 10 intervals? Wait, looking at the number line: from -2 (the first bold tick) to -1 (the next bold tick) is 1 unit, and between them, how many small ticks? Let's see: from -2 to -1, the bold ticks are at -2, then -1, and 0, 1. Between -2 and -1, let's count the small ticks. Wait, the blue dot is after -1. Wait, maybe the interval between each small tick is $\frac{1}{10}$? Wait, no, let's check the distance between -1 and 0. From -1 (bold tick) to 0 (bold tick) is 1 unit, and there are 10 small ticks between them? Wait, no, in the number line, from -1 to 0, the bold tick at 0, and between -1 and 0, how many small ticks? Wait, the blue dot is 1 tick after -1? Wait, no, let's re-examine.

Wait, the number line has bold ticks at -2, -1, 0, 1. Between -2 and -1: let's count the small ticks. From -2 (bold) to -1 (bold), there are 10 small ticks? Wait, no, maybe each small tick is $\frac{1}{10}$? Wait, no, maybe the interval between each small tick is $\frac{1}{10}$? Wait, no, let's see the position of the blue dot. The blue dot is 1 tick to the right of -1? Wait, no, looking at the number line: from -1 (bold tick) to the blue dot, how many small ticks? Wait, the bold tick at -1, then the next small tick is -0.9, then -0.8, etc.? Wait, no, maybe the interval between -2 and -1 is divided into 10 equal parts, so each part is $\frac{1}{10} = 0.1$. Wait, -2 to -1 is 1 unit, divided into 10 small ticks, so each tick is 0.1. So from -2, each small tick is +0.1. Wait, no, from -2, moving right, each small tick is -2 + 0.1, -2 + 0.2, ..., until -1 (which is -2 + 1.0). Then from -1, moving right, each small tick is -1 + 0.1, -1 + 0.2, etc. Wait, the blue dot is 1 tick to the right of -1? Wait, no, in the number line, the blue dot is at -1 + 0.1? Wait, no, maybe the interval between each small tick is $\frac{1}{10}$, so each small tick is 0.1. Wait, but let's check the distance from -1 to the blue dot. The blue dot is 1 small tick to the right of -1? Wait, no, looking at the number line: from -1 (bold tick) to the blue dot, there is 1 small tick? Wait, no, maybe the number of small ticks between -1 and 0 is 10, so each is 0.1. So -1 + 0.1 = -0.9? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, the number line: bold ticks at -2, -1, 0, 1. Between -2 and -1: let's count the small ticks. From -2 to -1, there are 10 small ticks, so each is 0.1. So -2 + 0.1 = -1.9, -2 + 0.2 = -1.8, ..., -2 + 1.0 = -1 (bold tick). Then from -1 (bold tick), moving right, each small tick is -1 + 0.1 = -0.9, -1 + 0.2 = -0.8, etc. Wait, the blue dot is 1 tick to the right of -1, so that would be -1 + 0.1 = -0.9? Wait, no, that seems off. Wait, maybe the interval between -1 and 0 is divided into 10 parts, so each part is 0.1, so the blue dot is at -1 + 0.1 = -0.9? Wait, no, that can't be. Wait, maybe the number line is divided into tenths. Wait, let's see: from -1 to 0, 10 small ticks, so each is 0.1. So the blue dot is 1 tick to the right of -1, so -1 + 0.1 = -0.9? Wait, no, that would be -0.9, but that seems like it's closer to -1. Wait, maybe the interval between -2 and -1 is 10 ticks, so each tick is 0.1, so from -2, each tick is +0.1. So -2, -1.9, -1.8, ..., -1 (after 10 ticks). Then from -1, each tick is -0.9, -0.8, etc. Wait, the blue dot is 1 tick after -1, so -0.9? Wait, no, that doesn't seem right. Wait, maybe the number line is marked with each small tick as 0.1, so the position of the blue dot is -1 + 0.1 = -0.9? Wait, no, maybe I'm miscalculating. Wait, let's look at the number line again. The bold ticks are at -2, -1, 0, 1. Between -2 and -1: 10 small ticks (since from -2 to -1 is 1 unit, 10 ticks, so each is 0.1). So from -2, moving right, each tick is -2 + 0.1k, where k is the number of ticks. So at k=10, we reach -1 (since -2 + 10*0.1 = -2 + 1 = -1). Then from -1, moving right, each tick is -1 + 0.1m, where m is the number of ticks. The blue dot is at m=1, so -1 + 0.1*1 = -0.9? Wait, but that would be -0.9, but maybe the interval is different. Wait, maybe the number of ticks between -1 and 0 is 10, so each is 0.1, so the blue dot is at -0.9? Wait, no, maybe the interval is 0.1, so the blue dot is at -0.9? Wait, but let's check the number line again. The blue dot is 1 tick to the right of -1, so if each tick is 0.1, then it's -1 + 0.1 = -0.9. Wait, but maybe the interval is 0.1, so the answer is -0.9? Wait, no, maybe I made a mistake. Wait, maybe the number line is divided into 10 parts between -1 and 0, so each part is 0.1, so the blue dot is at -1 + 0.1 = -0.9. Wait, but let's confirm. Alternatively, maybe the interval between -2 and -1 is 10 ticks, so each tick is 0.1, so from -2, the ticks are -1.9, -1.8, ..., -1. Then from -1, the ticks are -0.9, -0.8, ..., 0. So the blue dot is at -0.9? Wait, but that seems like -0.9, but maybe the problem is that the interval is 0.1, so the blue dot is at -0.9. Wait, but let's check again. The bold ticks are at -2, -1, 0, 1. Between -1 and 0, there are 10 small ticks, so each is 0.1. So the first tick to the right of -1 is -0.9, then -0.8, etc. So the blue dot is at -0.9? Wait, no, maybe the number of ticks between -1 and 0 is 10, so each is 0.1, so the blue dot is at -1 + 0.1 = -0.9. Wait, but maybe I'm wrong. Wait, another way: the distance from -1 to the blue dot is 1/10 of the distance from -1 to 0? No, the distance from -1 to 0 is 1, so 1/10 is 0.1, so the blue dot is at -1 + 0.1 = -0.9. So the point marked is -0.9, which is $-\frac{9}{10}$ or -0.9. Wait, but let's check the number line again. The blue dot is 1 tick to the right of -1, so if each tick is 0.1, then it's -0.9. So the answer is -0.9, or $-\frac{9}{10}$.

Wait, maybe I made a mistake in the number of ticks. Let's count the small ticks between -1 and 0. From -1 (bold) to 0 (bold), how many small ticks? Let's see the number line: from -1 to 0, the bold tick at 0, and between them, there are 10 small ticks? Wait, no, in the image, from -1 (bold) to 0 (bold), there are 10 small ticks? Wait, the blue dot is 1 tick to the right of -1, so that's -0.9. So the point is -0.9, which is $-\frac{9}{10}$ or -0.9.

Step2: Confirm the position

The number line has bold ticks at -2, -1, 0, 1. Each small tick between two bold ticks (e.g., -1 and 0) represents a value of $\frac{1}{10} = 0.1$. The blue dot is 1 small tick to the right of -1, so its value is $-1 + 0.1 = -0.9$.

Answer:

$-0.9$ (or $-\frac{9}{10}$)