Question

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.

Answer 1

To compare the given numbers in scientific notation, we first convert each number.

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 have:

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

Next, we will compare the numbers by examining their scientific notation:

Both \( 31,892 \) and \( 12,786 \) have a power of \( 10^4 \). To compare the coefficients:

- Coefficient for \( 31,892 \): \( 3.1892 \)
- Coefficient for \( 12,786 \): \( 1.2786 \)

Since \( 1.2786 < 3.1892 \), we can conclude that \( 12,786 < 31,892 \).

Next, we compare \( 31,892 \) with \( 123,893 \):

- Since \( 123,893 \) has a power of \( 10^5 \), it is larger than any number with \( 10^4 \).

Thus, the least value among the three numbers is \( 12,786 \).

In scientific notation, \( 12,786 \) is written as:
\[
\boxed{1.2786 \times 10^4}
\]