Answer :
We are given the following natural numbers:
[tex]$$
\begin{aligned}
\text{Option (a): } & 215\,837\,895, \\
\text{Option (b): } & 208\,999\,879, \\
\text{Option (c): } & 215\,937\,786, \\
\text{Option (d): } & 215\,935\,987.
\end{aligned}
$$[/tex]
Let’s determine the largest number step-by-step:
1. Compare the Hundred-Millions Place:
- Option (a): The first three digits are [tex]$215$[/tex].
- Option (b): The first three digits are [tex]$208$[/tex].
- Option (c): The first three digits are [tex]$215$[/tex].
- Option (d): The first three digits are [tex]$215$[/tex].
Clearly, option (b) is smaller because [tex]$208 < 215$[/tex]. So we only need to compare options (a), (c), and (d).
2. Compare the Remaining Digits:
Since options (a), (c), and (d) all begin with [tex]$215$[/tex], we compare the next group of digits (i.e. the digits that follow):
- Option (a) has the next part [tex]$837\,895$[/tex].
- Option (c) has the next part [tex]$937\,786$[/tex].
- Option (d) has the next part [tex]$935\,987$[/tex].
Here, we can see that:
[tex]$$
937\,786 > 935\,987 \quad \text{and} \quad 937\,786 > 837\,895.
$$[/tex]
3. Conclusion:
Hence, the largest number among the given options is:
[tex]$$
215\,937\,786.
$$[/tex]
Thus, the final answer is option (c).
[tex]$$
\begin{aligned}
\text{Option (a): } & 215\,837\,895, \\
\text{Option (b): } & 208\,999\,879, \\
\text{Option (c): } & 215\,937\,786, \\
\text{Option (d): } & 215\,935\,987.
\end{aligned}
$$[/tex]
Let’s determine the largest number step-by-step:
1. Compare the Hundred-Millions Place:
- Option (a): The first three digits are [tex]$215$[/tex].
- Option (b): The first three digits are [tex]$208$[/tex].
- Option (c): The first three digits are [tex]$215$[/tex].
- Option (d): The first three digits are [tex]$215$[/tex].
Clearly, option (b) is smaller because [tex]$208 < 215$[/tex]. So we only need to compare options (a), (c), and (d).
2. Compare the Remaining Digits:
Since options (a), (c), and (d) all begin with [tex]$215$[/tex], we compare the next group of digits (i.e. the digits that follow):
- Option (a) has the next part [tex]$837\,895$[/tex].
- Option (c) has the next part [tex]$937\,786$[/tex].
- Option (d) has the next part [tex]$935\,987$[/tex].
Here, we can see that:
[tex]$$
937\,786 > 935\,987 \quad \text{and} \quad 937\,786 > 837\,895.
$$[/tex]
3. Conclusion:
Hence, the largest number among the given options is:
[tex]$$
215\,937\,786.
$$[/tex]
Thus, the final answer is option (c).
