To express the given numbers in scientific notation, we follow the format \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
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For 123,893: \[ 123,893 = 1.23893 \times 10^5 \]
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For 31,892: \[ 31,892 = 3.1892 \times 10^4 \]
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For 12,786: \[ 12,786 = 1.2786 \times 10^4 \]
Now we will compare all three values:
- \( 1.23893 \times 10^5 \) corresponds to 123,893.
- \( 3.1892 \times 10^4 \) corresponds to 31,892.
- \( 1.2786 \times 10^4 \) corresponds to 12,786.
Next, we compare the significant figures (the decimal parts) of the numbers in terms of magnitude:
- The first number \( 1.23893 \times 10^5 \) is in the range of \( 100,000 \) which is the highest value.
- The next two numbers are in the \( 10,000s \):
- \( 3.1892 \times 10^4 \) (approximately \( 31,892 \))
- \( 1.2786 \times 10^4 \) (approximately \( 12,786 \))
Since both of the last two numbers are multiplied by \( 10^4 \), we directly compare their coefficients:
- \( 3.1892 \) (for 31,892) is greater than \( 1.2786 \) (for 12,786).
Thus, the smallest number is \( 12,786 \).
Finally, expressing the least value in scientific notation:
\[ \boxed{1.2786 \times 10^4} \]