To determine the total vertical height of the stairway, we need to follow these steps:
1. Convert the height of each stair from a mixed number to a decimal: The height of each stair is given as [tex]\(8 \frac{3}{8}\)[/tex] inches.
2. Convert the mixed number to an improper fraction:
- The whole number part is 8.
- The fractional part is [tex]\(\frac{3}{8}\)[/tex].
- To combine these, we convert the whole number to a fraction with the same denominator: [tex]\(8 = \frac{8 \cdot 8}{8} = \frac{64}{8}\)[/tex].
- Now, add the fractional part: [tex]\(\frac{64}{8} + \frac{3}{8} = \frac{64 + 3}{8} = \frac{67}{8}\)[/tex].
3. Convert the improper fraction to a decimal:
[tex]\(\frac{67}{8} = 8.375\)[/tex] inches.
4. Calculate the total height of the stairway:
- There are 10 stairs, each [tex]\(8.375\)[/tex] inches high.
- Multiply the height of one stair by the number of stairs: [tex]\(8.375 \times 10 = 83.75\)[/tex] inches.
Therefore, the vertical height of the stairway is [tex]\(83.75\)[/tex] inches.
So, filling in the blank, we get:
The height of the stairway is [tex]\(83.75\)[/tex] inches.
