Simplify the expression and write your answer in Scientific Notation.
(5.8 x 10^−9
) / (2.3 x 10^4
)
A. 2.5 x 10^−5
B. 13.3 x 10^−5
C. 2.5 x 10^−13
D. 13.3 x 10^−13
To simplify the given expression and write in scientific notation, we can follow these steps:
Step 1: Divide the coefficient 5.8 by 2.3, which gives 2.52.
Step 2: Divide the powers of 10 by subtracting the exponent in the denominator from the exponent in the numerator, which gives 10^(-9 - 4) = 10^-13.
Step 3: Write the answer as the product of the coefficient and the power of 10 in scientific notation, i.e., 2.52 x 10^-13.
Therefore, the answer is option C: 2.5 x 10^-13.
To simplify the given expression and write the answer in scientific notation, we need to divide the two numbers and then adjust the decimal and exponent to express the result in proper scientific notation.
First, divide the two numbers:
(5.8 x 10^−9) / (2.3 x 10^4) = (5.8 / 2.3) x (10^−9 / 10^4)
Simplifying the division of the coefficients, we have:
= 2.5217391304347826 x 10^(−9−4)
= 2.5217391304347826 x 10^−13
Now, we need to express the coefficient in scientific notation. Starting from the left, count the number of decimal places until you reach the first non-zero digit. In this case, the coefficient is 2.5217391304347826, so there are no non-zero digits before the decimal point. Thus, we move the decimal point one place to the right to get a coefficient between 1 and 10.
After moving the decimal point, we have:
= 2.5217391304347826 x 10^−12
So, the final answer is 2.5 x 10^−12, which is approximately equal to 2.5217391304347826 x 10^−12.
Therefore, the correct choice is C. 2.5 x 10^−13.
To simplify the expression (5.8 x 10^−9) / (2.3 x 10^4), you can divide the numbers and subtract the exponents:
(5.8 / 2.3) x 10^(-9 - 4)
Simplifying the numerator, 5.8 divided by 2.3 equals 2.5:
2.5 x 10^(-9 - 4)
Combining the exponents, -9 - 4 equals -13:
2.5 x 10^(-13)
Therefore, the answer is C. 2.5 x 10^−13.