Answer :
To solve the problem of rounding \(\frac{55}{99}\) to the nearest half, let's go through a detailed, step-by-step solution:
1. Compute the Fraction Value:
First, calculate the value of \(\frac{55}{99}\):
[tex]\[ \frac{55}{99} \approx 0.5556 \][/tex]
2. Understanding Rounding to the Nearest Half:
To round this value to the nearest half, we need to consider the nearest numbers that are multiples of \(0.5\). These numbers are \(0\), \(0.5\), \(1\), and \(1.5\).
3. Rounding Process:
- For values between \(0\) and \(0.25\), the nearest half is \(0\).
- For values between \(0.25\) and \(0.75\), the nearest half is \(0.5\).
- For values between \(0.75\) and \(1.25\), the nearest half is \(1\).
- For values between \(1.25\) and \(1.75\), the nearest half is \(1.5\).
Given our value \(0.5556\), it falls within the range \(0.25\) to \(0.75\).
4. Determine the Nearest Half:
Since \(0.5556\) is between \(0.25\) and \(0.75\), the nearest half is \(0.5\).
5. Compare with the Choices:
Let's compare this with the choices provided:
- \(0\) (A)
- \(\frac{1}{2}\) which is \(0.5\) (B)
- \(1\) (C)
- \(1 \frac{1}{2}\) which is \(1.5\) (D)
The value \(0.5\) matches choice \(B\).
6. Final Answer:
Therefore, the value \(\frac{55}{99}\) rounded to the nearest half is:
[tex]\[ \boxed{\frac{1}{2}} \][/tex]
1. Compute the Fraction Value:
First, calculate the value of \(\frac{55}{99}\):
[tex]\[ \frac{55}{99} \approx 0.5556 \][/tex]
2. Understanding Rounding to the Nearest Half:
To round this value to the nearest half, we need to consider the nearest numbers that are multiples of \(0.5\). These numbers are \(0\), \(0.5\), \(1\), and \(1.5\).
3. Rounding Process:
- For values between \(0\) and \(0.25\), the nearest half is \(0\).
- For values between \(0.25\) and \(0.75\), the nearest half is \(0.5\).
- For values between \(0.75\) and \(1.25\), the nearest half is \(1\).
- For values between \(1.25\) and \(1.75\), the nearest half is \(1.5\).
Given our value \(0.5556\), it falls within the range \(0.25\) to \(0.75\).
4. Determine the Nearest Half:
Since \(0.5556\) is between \(0.25\) and \(0.75\), the nearest half is \(0.5\).
5. Compare with the Choices:
Let's compare this with the choices provided:
- \(0\) (A)
- \(\frac{1}{2}\) which is \(0.5\) (B)
- \(1\) (C)
- \(1 \frac{1}{2}\) which is \(1.5\) (D)
The value \(0.5\) matches choice \(B\).
6. Final Answer:
Therefore, the value \(\frac{55}{99}\) rounded to the nearest half is:
[tex]\[ \boxed{\frac{1}{2}} \][/tex]
