Question

which shows the expression below simplified?
0.00039 + (1.9 × 10⁻⁶)
a. 3.919 × 10⁻⁴
b. 3.919 × 10⁻⁶
c. 1.90039 × 10⁻⁶

Explanation:

Step1: Convert to scientific notation

First, convert \(0.00039\) to scientific notation. \(0.00039 = 3.9\times10^{-4}\), and \(1.9\times10^{-6}=0.0000019\). To add them, we need the same exponent. Convert \(3.9\times10^{-4}\) to \(390\times10^{-6}\) (since \(10^{-4}=100\times10^{-6}\), so \(3.9\times100 = 390\)).

Step2: Add the numbers

Now add \(390\times10^{-6}+1.9\times10^{-6}=(390 + 1.9)\times10^{-6}=391.9\times10^{-6}\). But we can also convert \(0.00039\) to \(3.9\times10^{-4}=390\times10^{-6}\), then add \(1.9\times10^{-6}\): \(390\times10^{-6}+1.9\times10^{-6}=391.9\times10^{-6}\), or another way: convert \(1.9\times10^{-6}\) to \(0.0000019\), and \(0.00039 = 0.0003900\) (adding trailing zeros for alignment). Then \(0.0003900+0.0000019 = 0.0003919\). Now convert \(0.0003919\) to scientific notation: \(3.919\times10^{-4}\) (since moving the decimal 4 places to the right gives 3.919).

Answer:

A. \(3.919\times10^{-4}\)