Question

question
what is the product of 22 and ( 2.1 \times 10^3 ) expressed in scientific notation?
answer attempt 1 out of 2
answer:
(square\times10^{square})
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Explanation:

Step1: Multiply the coefficients

First, multiply 22 and 2.1. So, \(22\times2.1 = 46.2\)

Step2: Multiply the powers of 10

Next, multiply \(10^0\) (since 22 can be written as \(22\times10^0\)) and \(10^3\). Using the rule of exponents \(a^m\times a^n=a^{m + n}\), we get \(10^{0+3}=10^3\)

Step3: Combine the results and adjust to scientific notation

Now, combine the coefficient and the power of 10: \(46.2\times10^3\). But in scientific notation, the coefficient should be between 1 and 10. So, we rewrite 46.2 as \(4.62\times10^1\). Then, multiply by \(10^3\): \(4.62\times10^1\times10^3 = 4.62\times10^{1 + 3}=4.62\times10^4\)

Answer:

\(4.62\times10^{4}\) (So the first box is 4.62 and the second box is 4)