Question

c. compute the decimal equivalent for \\(\frac{2}{90}\\). choose the correct answer below.\
a. \\(0.00\overline{2}\\)\
\\(\boldsymbol{\odot}\\) c. \\(0.000\overline{2}\\)\
b. \\(0.0\overline{2}\\)\
d. \\(0.0000\overline{2}\\)\
e. \\(0.00\overline{2}\\)

Explanation:

Step1: Simplify the fraction

Simplify \(\frac{2}{90}\) by dividing numerator and denominator by 2: \(\frac{2\div2}{90\div2}=\frac{1}{45}\).

Step2: Perform the division

Divide 1 by 45: \(1\div45 = 0.0222\cdots\), which is \(0.02\overline{2}\) (the bar is over the 2, indicating it repeats). Wait, let's check the options again. Wait, maybe I made a mistake. Wait, \(\frac{2}{90}=\frac{1}{45}\approx0.0222\cdots\), which is \(0.02\overline{2}\), but looking at the options, option B is \(0.02\overline{2}\)? Wait, no, the options: A. \(0.00\overline{2}\), B. \(0.02\overline{2}\), C. \(0.000\overline{2}\), D. \(0.0000\overline{2}\), E. \(0.00\overline{2}\)? Wait, maybe the original fraction is \(\frac{2}{900}\)? No, the problem says \(\frac{2}{90}\). Wait, let's recalculate: \(2\div90 = 0.0222\cdots\), so the repeating decimal is \(0.02\overline{2}\), which is option B? Wait, but the selected option in the image is C, but that must be a mistake. Wait, no, maybe I misread the fraction. Wait, if it's \(\frac{2}{900}\), then \(2\div900 = 0.00222\cdots=0.00\overline{2}\), which is option A. Wait, the problem says \(\frac{2}{90}\) or \(\frac{2}{900}\)? The image shows "2/90", but maybe it's a typo. Wait, let's check the options again. Option B is \(0.02\overline{2}\) (repeating 2 after 0.02), option A is \(0.00\overline{2}\) (repeating 2 after 0.00), option B is \(0.02\overline{2}\). So correct calculation: \(2\div90 = 0.0222\cdots = 0.02\overline{2}\), so the correct option is B. But the image has C selected, which is wrong. So the correct answer should be B.

Step3: Identify the correct option

From the calculation, \(2\div90 = 0.0222\cdots\), which is \(0.02\overline{2}\), corresponding to option B.

Answer:

B. \(0.02\overline{2}\)