To solve the multiplication problem [tex]\(6 \cdot \left(5 \times 10^{-3}\right)\)[/tex], let's go through the steps in detail:
1. Identify the components: We have the number [tex]\( 6 \)[/tex] and the scientific notation [tex]\( 5 \times 10^{-3} \)[/tex].
2. Multiply the coefficient by the number:
[tex]\[
6 \cdot 5 = 30
\][/tex]
3. Account for the exponent:
When multiplying by a term in scientific notation like [tex]\( 10^{-3} \)[/tex], we need to multiply the result [tex]\( 30 \)[/tex] by [tex]\( 10^{-3} \)[/tex]:
[tex]\[
30 \times 10^{-3}
\][/tex]
4. Adjust the notation to proper scientific form:
To write [tex]\( 30 \times 10^{-3} \)[/tex] in proper scientific notation, we need to express 30 as [tex]\( 3.0 \times 10^1 \)[/tex]:
[tex]\[
3.0 \times 10^1
\][/tex]
Now, combine this with the exponent [tex]\( 10^{-3} \)[/tex]:
[tex]\[
(3.0 \times 10^1) \times 10^{-3}
\][/tex]
5. Simplify the exponents:
When multiplying exponents with the same base, we add the exponents:
[tex]\[
10^1 \times 10^{-3} = 10^{1 + (-3)} = 10^{-2}
\][/tex]
6. Final expression:
The result is:
[tex]\[
3.0 \times 10^{-2}
\][/tex]
Thus, the product [tex]\( 6 \cdot \left(5 \times 10^{-3}\right) \)[/tex] written in scientific notation is:
[tex]\[
\boxed{3.0 \times 10^{-2}}
\][/tex]
