Which decimal is equivalent to 2/9?
A. 2.2
B. 2.9
C. 22222
D. 0.2
The Correct Answer and Explanation is :
The decimal equivalent of ( \frac{2}{9} ) is ( 0.2222\ldots ), which is a repeating decimal represented as ( 0.\overline{2} ). However, in the options provided, it looks like the only option that closely matches this is C. 22222, though it isn’t in decimal form. The more accurate representation should be clarified, but let’s break down how to arrive at the decimal form.
To convert the fraction ( \frac{2}{9} ) to a decimal, you can perform long division. Divide 2 by 9:
- 9 goes into 2 zero times, so we put 0 as the integer part and add a decimal point.
- Now consider 20 (adding a zero after the decimal). 9 goes into 20 two times (since ( 9 \times 2 = 18 )).
- Subtract 18 from 20, which gives you 2. Bring down another 0 to make it 20 again.
- Repeat this process: 9 goes into 20 two times, yielding another 18, and the remainder is again 2.
This process shows that the remainder repeats, resulting in the decimal ( 0.2222\ldots ) (or ( 0.\overline{2} )).
To summarize, the fraction ( \frac{2}{9} ) converts to a repeating decimal. The correct and simplified answer for the decimal form is ( 0.2222\ldots ), indicating that the digit ‘2’ repeats indefinitely. While option C may seem close, it’s important to note that it’s not presented in decimal form. This example illustrates the concept of repeating decimals and highlights the division method for converting fractions to decimals.