Simplify (3.9 × 10−2)(5.13 × 10−10). Write the final answer in scientific notation.
a) 20.007 × 10−12
b) 2.0007 × 10−11
c) 20.007 × 1020
d) 2.0007 × 1020
To simplify the expression, we multiply the coefficients and add the exponents of the powers of 10.
(3.9 × 10^(-2))(5.13 × 10^(-10)) = (3.9)(5.13) × 10^((-2)+(-10)) = 20.007 × 10^(-12)
The final answer in scientific notation is therefore 20.007 × 10^(-12), which is equivalent to (a) 20.007 × 10^(-12).
To simplify the expression (3.9 × 10^-2)(5.13 × 10^-10), we can multiply the coefficients (3.9 and 5.13) and add the exponents (10^-2 and 10^-10).
Multiplying the coefficients: 3.9 × 5.13 = 20.007
Adding the exponents: 10^-2 + 10^-10 = 10^-12
Therefore, the simplified expression is 20.007 × 10^-12, which is option a) 20.007 × 10^-12.
To simplify the given expression (3.9 × 10^-2)(5.13 × 10^-10), we can use the rules of multiplication with numbers in scientific notation.
Step 1:
Multiply the coefficients (numbers in front of the powers of 10).
3.9 * 5.13 = 20.007
Step 2:
Add the exponents of the powers of 10.
10^-2 * 10^-10 = 10^(-2 - 10) = 10^-12
Step 3:
Write the final answer in scientific notation using the multiplied coefficient from step 1 and the combined exponent from step 2.
The final answer is 20.007 × 10^-12.
Therefore, the correct option is:
a) 20.007 × 10^-12