Question

Perform the operations and answer in scientific and standard notation: (4 × 10^5) / (8 × 10^–3)

a) 5 × 10^7; 500,000.
b) 5 × 10^3; 50,000.
c) 5 × 10^10; 5,000,000.
d) 5 × 10^4; 500,000.

Answer 1

(4 × 10^5) / (8 × 10^–3)

To simplify this expression, we can divide the numbers in front and subtract the exponents of 10:

4 ÷ 8 = 0.5
10^5 ÷ 10^–3 = 10^(5-(-3)) = 10^8

So, the answer in scientific notation is 5 × 10^7, and in standard notation, it is 50,000.

Answer 2

Option (a), The operation (4 × 10^5) / (8 × 10^-3) results in 5 × 10^7 in scientific notation, and 50,000,000 in standard notation.

Step-by-step explanation:

To find the result of the operation (4 × 10^5) / (8 × 10^-3), you first divide the numerical coefficients and then subtract the exponents of the powers of ten according to the laws of exponents. Performing the division of coefficients gives 4 / 8 = 0.5.

For the exponents, you subtract the exponents from the denominator from those in the numerator: 5 - (-3) = 5 + 3 = 8. Thus, the expression simplifies to 0.5 × 10^8, which can be written in proper scientific notation as 5 × 10^7.

Next, to convert scientific notation to standard notation, you move the decimal point to the right the number of times equal to the exponent when the exponent is positive. So, 5 × 10^7 becomes 50,000,000.

Therefore, the answer to the operation in scientific notation is 5 × 10^7, and in standard notation, the answer is 50,000,000.