Question

Perform the operations and answer in scientific and standard notation: (4 × 10^3) × (3 × 10^5) / (3 × 10^–2)-

a) 4 × 10^8; 400,000,000.
b) 4 × 10^10; 4,000,000,000.
c) 4 × 10^6; 4,000,000.
d) 4 × 10^5; 400,000.

Answer 1

The expression (4 × 10^3) × (3 × 10^5) / (3 × 10−2) simplifies to 4 × 10^10 in scientific notation, which is 40,000,000,000 in standard notation.

Step-by-step explanation:

The question involves performing operations on numbers expressed in scientific notation and then expressing the result in both scientific and standard notation. To solve the expression (4 × 10^3) × (3 × 10^5) / (3 × 10−2), we can handle the powers of 10 separately from the coefficients.

First, multiply the coefficients: 4 × 3 = 12.
Next, add the exponents when multiplying the powers of 10: 10^3 × 10^5 = 10^(3+5) = 10^8.
Then, when dividing by 3 × 10−2, keep in mind that dividing powers of 10 with the same base results in subtracting the exponents: 10^8 / 10−2 = 10^(8 - (-2)) = 10^(8+2) = 10^10.
And since we need to divide the coefficient by 3 as well, 12 / 3 = 4.

Therefore, the expression evaluates to 4 × 10^10 in scientific notation. In standard notation, this value is 40,000,000,000.

The correct answer is option b): 4 × 10^10; 40,000,000,000