Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Multiply and write your answer in scientific notation.

[tex]\[ 6 \left(5 \times 10^{-3}\right) \][/tex]

[tex]\[ \boxed{\quad} \][/tex]

Sagot :

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]