Question

a student answered the answer to a multiplication problem as 2.8 e -4. which expression is equivalent to 2.8 e -4?
\bigcirc\\ 2.8^{-4}
\bigcirc\\ 2.8 \times 10^{-4}
\bigcirc\\ 2.8 \times 10^{4}
\bigcirc\\ 2.8 \times (-4)

Explanation:

Step1: Recall scientific notation

Scientific notation uses \( a\times10^{n} \) where \( 1\leq|a|\lt10 \) and \( n \) is an integer. The notation "E - 4" (or "e - 4") is a shorthand for \( \times10^{-4} \).

Step2: Analyze the given number

The number is given as \( 2.8\text{ E}-4 \). Using the scientific notation shorthand, this translates to \( 2.8\times10^{-4} \). Let's check the options:

• Option 1: \( 2.8^{-4} \) is \( \frac{1}{2.8^{4}} \), not equivalent.
• Option 2: \( 2.8\times10^{-4} \) matches the translation of \( 2.8\text{ E}-4 \).
• Option 3: \( 2.8\times10^{4} \) is \( 2.8\times10000 = 28000 \), while \( 2.8\text{ E}-4 \) is a small number, so not equivalent.
• Option 4: \( 2.8\times(-4)= - 11.2 \), not equivalent.

Answer:

B. \( 2.8 \times 10^{-4} \) (assuming the second option is labeled B, adjust label as per actual option numbering; if options are unlabeled, describe the correct one as the second option in the list)