To compare the numbers 364,879; 463,000; and 436,765 using scientific notation, we first convert them into scientific notation format.
1. **364,879** can be expressed in scientific notation as:
\[
3.64879 \times 10^5
\]
2. **463,000** can be expressed in scientific notation as:
\[
4.63 \times 10^5
\]
3. **436,765** can be expressed in scientific notation as:
\[
4.36765 \times 10^5
\]
Now, let's compare them based on their coefficients in scientific notation, since they all have the same power of ten (\(10^5\)):
- **3.64879** (from 364,879)
- **4.63** (from 463,000)
- **4.36765** (from 436,765)
Now comparing these coefficients:
- **3.64879** < **4.36765** < **4.63**
Thus, in terms of the original numbers:
- **364,879** is the smallest,
- **436,765** is in the middle,
- **463,000** is the largest.
In conclusion:
- The smallest number is **364,879**.
- The largest number is **463,000**.