Question

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