Question

Which shows the expression below in simplified form?

(6.4 × 10^6) ÷ (8 × 10^2)
A) 80,000
B) 800
C) 8,000
D) 800,000

Answer 1

`\frac{6.4 * {10}^(6) }{8 * {10}^(2) } = .8 * {10}^(4) = 8000`

The correct answer is C.

Answer 2

To simplify the expression (6.4 × 10^6) ÷ (8 × 10^2), divide the coefficients and subtract the exponents separately. The result, 0.8 × 10^4, is equivalent to 8 × 10^3 or 8000 in standard notation. Therefore, the correct answer is C) 8,000.

Step-by-step explanation:

The question asks us to simplify the expression (6.4 × 10^6) ÷ (8 × 10^2) and select the correct simplified form from the given options. To simplify this expression, we can separate it into two parts: dividing the coefficients (6.4 ÷ 8) and subtracting the exponents of 10 (10^6 ÷ 10^2), as per the properties of exponents.

Firstly, dividing the coefficients gives us 0.8. Next, subtracting the exponents results in 10^(6-2) or 10^4. Combining these results, we get 0.8 × 10^4 which is equivalent to 8 × 10^3 since 0.8 is the same as 8 × 0.1 (or 8 × 10^-1). Therefore, the simplified form of the expression is 8 × 10^3.

Finally, when we convert 8 × 10^3 into standard notation, it becomes 8000. Hence, the correct answer is option C) 8,000.