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To find the height of the bottom step, which is given as \(\frac{1}{48}\) of the total height, we can follow these steps:

1. **Identify the total height**: The staircase has a total height of 690 cm.
2. **Determine the fraction**: The bottom step is \(\frac{1}{48}\) of the total height.
3. **Calculate the height of the bottom step**:
   \[
   \text{Height of bottom step} = \frac{1}{48} \times 690
   \]
4. **Perform the multiplication**:
   \[
   \text{Height of bottom step} = \frac{690}{48} = 14.375 \text{ cm}
   \]
5. **Round to one decimal place**:
   \[
   \text{Height of bottom step} \approx 14.4 \text{ cm}
   \]

So, the height of the bottom step is approximately **14.4 cm**.

Would you like further clarification on this solution or have additional questions?

Here are some related questions that might help deepen your understanding:
1. How would you calculate the height if the bottom step was \(\frac{1}{60}\) of the total height?
2. What would the height be if the staircase was 750 cm tall instead of 690 cm?
3. How would you determine the height of a step if it was given as a percentage of the total height?
4. What other real-life problems could be solved using fraction-based calculations like this?
5. How does rounding to different decimal places affect the accuracy of your answer?

**Tip:** When working with fractions, always ensure you multiply by the total to find the part of it represented by the fraction.

A staircase has a total height of 690 cm. The bottom step is 1/48 of the total height. What is the height of the bottom step in centimeters (cm)? Round your answer to 1 decimal place.

Learn how to find the height of the bottom step in a staircase with a total height of 690 cm, where the step is 1/48 of the total height. This problem covers fractions, multiplication, and rounding, ideal for students in Grades 5-7.

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