Compare Very Large and Very Small Numbers Practice

Question

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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)
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Answer 1

To compare the numbers 123,893, 31,892, and 12,786 using scientific notation, we first convert each number to its scientific notation form.

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

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

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

Now we can compare the numbers:

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

Next, we notice that:

• \( 10^5 \) is larger than \( 10^4 \), so \( 1.23893 \times 10^5 \) is the largest of these numbers.
• Between \( 3.1892 \times 10^4 \) and \( 1.2786 \times 10^4 \), we can see that \( 1.2786 \) is less than \( 3.1892 \).

Therefore, the smallest number among the three is:

\[ 1.2786 \times 10^4 \]

Thus, the answer in scientific notation, indicating the least value, is:

\[ 1.2786 \times 10^4 \]