To express the given numbers in scientific notation, we write each number in the form of \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
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For 123,893:
To express this in scientific notation:
\[ 123,893 = 1.23893 \times 10^5 \] -
For 31,892:
To express this in scientific notation:
\[ 31,892 = 3.1892 \times 10^4 \] -
For 12,786:
To express this in scientific notation:
\[ 12,786 = 1.2786 \times 10^4 \]
Now we can compare the numbers:
- \( 1.23893 \times 10^5 \) for 123,893 is equivalent to 123,893.
- \( 3.1892 \times 10^4 \) for 31,892 is equivalent to 31,892.
- \( 1.2786 \times 10^4 \) for 12,786 is equivalent to 12,786.
Now we have the following values for comparison:
- \( 1.23893 \times 10^5 \) (which is 123,893)
- \( 3.1892 \times 10^4 \) (which is 31,892)
- \( 1.2786 \times 10^4 \) (which is 12,786)
To determine the least value, we observe the scientific notation:
- The term \( 3.1892 \times 10^4 \) represents 31,892.
- The term \( 1.2786 \times 10^4 \) represents 12,786.
Since \( 31,892 \) and \( 12,786 \) are both represented by \( 10^4 \), we only need to compare the coefficients \( 3.1892 \) and \( 1.2786 \).
Because \( 1.2786 < 3.1892 \), we conclude that:
The number with the least value is 12,786, and in scientific notation, it is: \[ \boxed{1.2786 \times 10^4} \]
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