To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?
To convert a repeating decimal to a rational number, you can set it equal to x and multiply both sides of the equation by the appropriate power of 10. In this case, the repeating decimal is 0.264¯¯¯¯¯¯¯¯, so you would multiply both sides of the equation by 1000 (since there are three repeating digits) to eliminate the repeating part.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000.
Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?
To determine which of the given numbers is irrational between 5 and 7, we need to evaluate each expression.
1. 6–√: This is an irrational number since the square root of a non-perfect square is irrational. However, when we compute it, 6–√ = 6-2.449 = 3.551, which is not between 5 and 7.
2. 12−−√: This is also an irrational number since the square root of a non-perfect square is irrational. When we compute it, 12−−√ ≈ 3.464, which is not between 5 and 7.
3. 27−−√: This is an irrational number since the square root of a non-perfect square is irrational. When we compute it, 27−−√ ≈ 5.196, which is between 5 and 7.
4. 36−−√: This is a rational number since the square root of a perfect square is rational. When we compute it, 36−−√ = 6, which is not between 5 and 7.
Therefore, the only irrational number between 5 and 7 among the given options is √27.
What is the largest integer whose square root is an irrational number between 3 and 4?
To find the largest integer whose square root is an irrational number between 3 and 4, we need to evaluate the square roots of integers greater than 3 and less than or equal to 4 until we find the largest one that gives an irrational value.
When we evaluate the square root of 16, we get √16 = 4, which is not an irrational number.
However, when we evaluate the square root of 15, we get √15 ≈ 3.873, which is an irrational number between 3 and 4.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 15.