Question

6.8 times 10^2 times by 1.3 times 10^-3? Please how would I do this does anyone know?

Answer 1

`\textsf{Scientific notation}: \quad 8.84 * 10^(-1)`

`\textsf{Numerical value}: \quad 0.884`

Explanation:

Given expression:

`6.8 * 10^2 * 1.3 * 10^(-3)`

Apply the Commutative Property of Multiplication that states that changing the order or position of the numbers does not change the end result.

`\implies 6.8 * 1.3 * 10^2 * 10^(-3)`

Multiply the numbers 6.8 and 1.3:

`\implies 8.84 * 10^2 * 10^(-3)`

`\textsf{Apply the exponent rule} \quad a^b * a^c=a^(b+c):`

`\implies 8.84 * 10^((2+(-3)))`

`\implies 8.84 * 10^((2-3))`

`\implies 8.84 * 10^(-1)`

`\textsf{Scientific notation is written in the form of $a * 10^n$, where $ 1 \leq a < 10$}\\\textsf{and $n$ is any positive or negative whole number}.`

Therefore, the solution is in scientific notation.

When multiplying a number by 10ⁿ (where n is positive), move the decimal place to the right "n" number of times.

When multiplying a number by 10⁻ⁿ (where n is negative), move the decimal place to the left "n" number of times.

Therefore:

`\implies 8.84 * 10^(-1)=0.884`