What is the value of the expression in standard form?

Question

(4.8 x 10^8) (2.2 x 10^-6) / (1.2 x 10^4)
(2 points)
0.0058
0.00088
0.58
0.088

Answer 1

To evaluate the expression \((4.8 \times 10^8) \times (2.2 \times 10^{-6}) / (1.2 \times 10^4)\), we can follow these steps:

1. Multiply the numbers in the numerator: \[ (4.8 \times 2.2) = 10.56 \]

   Combine the powers of ten: \[ 10^8 \times 10^{-6} = 10^{8 + (-6)} = 10^2 \]

   So the numerator becomes: \[ 10.56 \times 10^2 \]

2. Now we can express the entire numerator: \[ 10.56 \times 10^2 \]

3. Now divide by the denominator: \[ \frac{10.56 \times 10^2}{1.2 \times 10^4} \]

   First we divide \(10.56\) by \(1.2\): \[ \frac{10.56}{1.2} = 8.8 \]

   Now combine the powers of ten: \[ 10^{2 - 4} = 10^{-2} \]

   Therefore, the expression simplifies to: \[ 8.8 \times 10^{-2} \]

4. Convert to standard form: \[ 8.8 \times 10^{-2} = 0.088 \]

Thus, the value of the expression in standard form is: \[ \boxed{0.088} \]