Example Question - number representation
Here are examples of questions we've helped users solve.
Base-Nine Number Division
<p>让我们考虑 \(N\) 的最后两位数在九进制表示下是 \(52_{nine}\)。</p> <p>转换为十进制，\(52_{nine} = 5 \times 9 + 2 = 47\)。</p> <p>然后我们除以 \(5\) 来找到余数。</p> <p>\(47 \div 5 = 9\) 余 \(2\)。</p> <p>因此，当 \(N\) 除以 \(5\) 时，余数为 \(2\)。</p>
Finding Base Value for Number Equality
The question asks you to find the value of \( n \) such that the number \( 14 \) in base \( n \) is equal to the number \( 22 \) in base five. To find the value of \( n \), we can convert the given number \( 22 \) in base five to base ten and then equate it to the number \( 14 \) in base \( n \), also represented in base ten. To convert \( (22)_5 \) to base ten, use the following method: - \( (22)_5 = 2 \cdot 5^1 + 2 \cdot 5^0 \) - \( (22)_5 = 2 \cdot 5 + 2 \cdot 1 \) - \( (22)_5 = 10 + 2 \) - \( (22)_5 = 12 \) in base ten. Now that we know \( (22)_5 \) is equal to \( 12 \) in base ten, we can set this equal to \( 14 \) in base \( n \) and also convert that to base ten. The base ten representation of \( 14 \) in base \( n \) is: - \( 1 \cdot n^1 + 4 \cdot n^0 \) - \( n + 4 \) Equating this to the base ten value we found: - \( n + 4 = 12 \) To solve for \( n \), subtract 4 from both sides: - \( n = 12 - 4 \) - \( n = 8 \) Hence, the value of \( n \) is 8.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com