Use scientific notation to determine which of these numbers has the least value: 123,893, 31,892, or 12,786.

Question

Write your answer in scientific notation, expressed to the exact decimal place. (1 point)

Answer 1

To compare the numbers 123,893, 31,892, and 12,786 using scientific notation, we first convert each number as follows:

1. 123,893 can be written in scientific notation as: \[ 1.23893 \times 10^5 \]

2. 31,892 can be written in scientific notation as: \[ 3.1892 \times 10^4 \]

3. 12,786 can be written in scientific notation as: \[ 1.2786 \times 10^4 \]

Now we can compare the exponents to determine the least value:

• The first number \(1.23893 \times 10^5\) has an exponent of \(5\).
• The second number \(3.1892 \times 10^4\) has an exponent of \(4\).
• The third number \(1.2786 \times 10^4\) also has an exponent of \(4\).

Since \(10^5\) is greater than \(10^4\), both \(31,892\) and \(12,786\) (which have an exponent of \(4\)) are less than \(123,893\).

Next, we compare \(3.1892 \times 10^4\) and \(1.2786 \times 10^4\):

• \(3.1892 < 1.2786\)

Thus, \(1.2786 \times 10^4\) (which corresponds to \(12,786\)) is the smallest.

So, the number with the least value among them is:

\[ \boxed{1.2786 \times 10^4} \]