Question

Simplify (3.9 × 10^-2)(5.13 × 10^-10) in scientific notation.

Answer 1

The simplified form of the expression (3.9 ×
`10^{-2`)(5.13 ×
`10^{-10`) in scientific notation is 2.0007 ×
`10^{-11`. You multiply the coefficients and add the exponents, adjusting the coefficient to keep it between 1 and 10.

Step-by-step explanation:

To simplify the expression (3.9 ×
`10^{-2`)(5.13 ×
`10^{-10`) in scientific notation, we will follow the rules for multiplying numbers in scientific notation. We first multiply the coefficients (the numbers out front) and then add the exponents.

Step 1: Multiply the coefficients
3.9 × 5.13 = 20.007

Step 2: Add the exponents
-2 + (-10) = -12

Now, we need to adjust our coefficient to be between 1 and 10 to properly express it in scientific notation.

Step 3: Adjust the coefficient
20.007 can be written as 2.0007 ×
`10^1`

Finally, we incorporate the exponent from our previous step.

Final result:
2.0007 ×
`10^1` ×
`10^{-12`= 2.0007 ×
`10^{-11`