What is the value of the expression simplified in Standard Notation: (3.2×10^−2))(4.2×10^(6)) over (5.2×10^(5))

Question

(1 point)
Responses

0.26
0.26

0.0026
0.0026

0.00026
0.00026

2.6

Answer 1

To simplify the given expression \((3.2 × 10^{-2}) (4.2 × 10^{6}) / (5.2 × 10^{5})\), we can break it down step-by-step.

1. Multiply the numerators:
   \((3.2 × 10^{-2}) (4.2 × 10^{6}) = 3.2 × 4.2 × 10^{-2} × 10^{6} = 13.44 × 10^{4}\) (because \(-2 + 6 = 4\))

2. Now divide by the denominator:
   To divide by \(5.2 × 10^{5}\), we write it in the expression:
   \(\frac{13.44 × 10^{4}}{5.2 × 10^{5}}\)

   Dividing the coefficients:
   \(\frac{13.44}{5.2} = 2.58\) (approximately)

   Now for the powers of ten:
   \(\frac{10^{4}}{10^{5}} = 10^{4 - 5} = 10^{-1}\)

   Combining these gives:
   \(2.58 × 10^{-1}\)

3. Convert to standard notation:
   \(2.58 × 10^{-1} = 0.258\)

Looking at the provided responses, none of them quite match \(0.258\). However, the closest could be interpreted with rounding or estimation could lead to \(0.26\).

Thus, the simplified result from the options available is:

0.26.