Use scientific notation to determine which of these numbers has the least value:

Question

123,893, 31,892, or 12,786. Write your answer in scientific notation, expressed to the exact decimal place. (1 point)

Answer 1

To determine which of the given numbers has the least value, we can convert each of them into scientific notation.

1. 123,893 \[ 123,893 = 1.23893 \times 10^5 \]

2. 31,892 \[ 31,892 = 3.1892 \times 10^4 \]

3. 12,786 \[ 12,786 = 1.2786 \times 10^4 \]

Now, we compare these expressions:

• \(1.23893 \times 10^5\) for 123,893
• \(3.1892 \times 10^4\) for 31,892
• \(1.2786 \times 10^4\) for 12,786

Since \(10^5\) (which equals 100,000) is greater than both \(10^4\) (which equals 10,000), we will convert the first number's exponent to match the others for easier comparison:

• \(1.23893 \times 10^5 = 12.3893 \times 10^4\)

Now we can compare all three numbers:

• \(12.3893 \times 10^4\) for 123,893
• \(3.1892 \times 10^4\) for 31,892
• \(1.2786 \times 10^4\) for 12,786

It's evident that \(1.2786 < 3.1892 < 12.3893\).

Therefore, the number with the least value is:

\[ \boxed{1.2786 \times 10^4} \] (for 12,786).