What is the decimal equivalent of 20/9
The Correct Answer and Explanation is:
The correct answer is A. 2.2̅.
To determine the decimal equivalent of the fraction 20/9, you need to perform the division of the numerator (20) by the denominator (9). This process reveals the decimal value.
We can solve this using long division:
- Start by dividing 20 by 9. The number 9 goes into 20 two times (2 × 9 = 18). This gives us the whole number part of the answer, which is 2.
- Subtract 18 from 20, which leaves a remainder of 2 (20 – 18 = 2).
- Since we have a remainder, we add a decimal point to our answer and bring down a zero next to the remainder, making it 20.
- Now, we divide this new number, 20, by 9. Again, 9 goes into 20 two times (2 × 9 = 18). We write a 2 after the decimal point in our answer.
- Subtracting 18 from 20 again gives us a remainder of 2.
At this point, we can see a pattern emerging. Each time we bring down a zero, we will be dividing 20 by 9, which will always result in the digit 2 and a remainder of 2. This means the digit 2 will repeat infinitely after the decimal point. The resulting decimal is 2.222…
This is known as a repeating decimal. The standard mathematical notation for a repeating decimal is to place a horizontal bar (called a vinculum) over the repeating digit or sequence of digits. Therefore, 2.222… is correctly written as 2.2̅.
Let’s examine the other options. Option B, 2.2, is an approximation but not the exact value. Option C, 20.9, is an incorrect calculation. Option D, 0.45, is the decimal equivalent of the inverted fraction, 9/20. Thus, option A is the only choice that accurately represents the decimal equivalent of 20/9.
