Question

Use the number line to answer the question.

A number line is shown with end points marked at the 2 and 2 tenths and 2 and 3 tenths. There are 9 tick marks between the two end points. Point H is on the third mark after 2 and 2 tenths.

(1 point)
What is the decimal value of point H? Enter the answer in the box.

Answer 1

To find the decimal value of point H, we first need to determine the increments between the tick marks on the number line.

1. The endpoints are marked at 2.2 (which is 2 and 2 tenths) and 2.3 (which is 2 and 3 tenths).
2. The distance between the two endpoints is 2.3 - 2.2 = 0.1.
3. There are 9 tick marks between the two endpoints, so we need to divide the total distance (0.1) by the number of intervals (10) between those marks (since there are 9 intervals created by 10 tick marks).

The size of each interval is:
\[
\frac{0.1}{10} = 0.01
\]

Now, we locate point H:
- Point H is on the third mark after 2.2.
- Starting from 2.2 (2 and 2 tenths), we add the interval size for each mark:

1. First mark after 2.2:
\[
2.2 + 0.01 = 2.21
\]

2. Second mark after 2.2:
\[
2.21 + 0.01 = 2.22
\]

3. Third mark after 2.2:
\[
2.22 + 0.01 = 2.23
\]

Thus, the decimal value of point H is:
\[
\boxed{2.23}
\]