Question

Simplify (2.6 x 10-6) + (3.2 x 10-2) (1.94 x 10-4) write answer in scientific notation

Answer 1

`8.808 * 10^(-6)`

Explanation:

Given expression:

`(2.6 * 10^(-6))+(3.2 * 10^(-2))(1.94 * 10^(-4))`

The grouping of numbers by parentheses in a different way does not affect their product. Also, changing the order or position of the product of two numbers does not change the end result.

`\implies (2.6 * 10^(-6))+(3.2 * 1.94 * 10^(-2) * 10^(-4))`

Multiply the numbers 3.2 and 1.94:

`\implies (2.6 * 10^(-6))+(6.208* 10^(-2) * 10^(-4))`

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

`\implies (2.6 * 10^(-6))+(6.208* 10^(-2-4))`

`\implies (2.6 * 10^(-6))+(6.208* 10^(-6))`

Factor out the common term 10⁻⁶:

`\implies 10^(-6)(2.6+6.208)`

Add the numbers 2.6 and 6.208:

`\implies 10^(-6)(8.808)`

`\implies 8.808 * 10^(-6)`

Scientific notation is written in the form a × 10ⁿ , where 1 ≤ a < 10 and n is any positive or negative whole number. Therefore, the final answer is in scientific notation.