To solve \( 5000 \div 2.5 \), 15 times in succession, we'll go step by step and include the results at each stage.

### Step-by-Step Process:

1. **First division:**
   \[
   5000 \div 2.5 = \frac{5000}{2.5} = 2000
   \]
2. **Second division:**
   \[
   2000 \div 2.5 = \frac{2000}{2.5} = 800
   \]
3. **Third division:**
   \[
   800 \div 2.5 = \frac{800}{2.5} = 320
   \]
4. **Fourth division:**
   \[
   320 \div 2.5 = \frac{320}{2.5} = 128
   \]
5. **Fifth division:**
   \[
   128 \div 2.5 = \frac{128}{2.5} = 51.2
   \]
6. **Sixth division:**
   \[
   51.2 \div 2.5 = \frac{51.2}{2.5} = 20.48
   \]
7. **Seventh division:**
   \[
   20.48 \div 2.5 = \frac{20.48}{2.5} = 8.192
   \]
8. **Eighth division:**
   \[
   8.192 \div 2.5 = \frac{8.192}{2.5} = 3.2768
   \]
9. **Ninth division:**
   \[
   3.2768 \div 2.5 = \frac{3.2768}{2.5} = 1.31072
   \]
10. **Tenth division:**
    \[
    1.31072 \div 2.5 = \frac{1.31072}{2.5} = 0.524288
    \]
11. **Eleventh division:**
    \[
    0.524288 \div 2.5 = \frac{0.524288}{2.5} = 0.2097152
    \]
12. **Twelfth division:**
    \[
    0.2097152 \div 2.5 = \frac{0.2097152}{2.5} = 0.08388608
    \]
13. **Thirteenth division:**
    \[
    0.08388608 \div 2.5 = \frac{0.08388608}{2.5} = 0.033554432
    \]
14. **Fourteenth division:**
    \[
    0.033554432 \div 2.5 = \frac{0.033554432}{2.5} = 0.0134217728
    \]
15. **Fifteenth division:**
    \[
    0.0134217728 \div 2.5 = \frac{0.0134217728}{2.5} = 0.00536870912
    \]

### Final Result:
After dividing 5000 by 2.5 fifteen times, the final result is approximately:
\[
0.00536870912
\]

Would you like further clarification on any step?

---

**Related Questions:**
1. What happens if you divide by numbers other than 2.5?
2. How would multiplying by 2.5 fifteen times affect the outcome?
3. What is the effect of dividing by smaller fractions?
4. Can you generalize this process for other numbers?
5. How does repeated division compare to repeated subtraction?

**Tip:** Each time you divide by a number greater than 1, the result becomes smaller at an exponential rate.

Explore a detailed, step-by-step process of dividing 5000 by 2.5 fifteen times in succession. Learn how repeated division results in exponential decay, with clear explanations for students in Grades 6-8.

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