The square root of 25 is rational because 25 is a perfect square.
0.666... is rational because it can be expressed as a fraction (2/3).
The square root of 11 is irrational because 11 is not a perfect square.
4/7 is rational because it can be expressed as a fraction.
Determine each equation is it rational or irrational
The square root of 25
0.666...
Square root of 11
4/7
9 answers
What is 121212... as a fully simplified fraction
To determine the fraction form of the repeating decimal 0.121212..., we will let x be equal to the decimal. Hence, we can express it as:
x = 0.121212...
Multiplying both sides by 100 to “shift” the decimal point:
100x = 12.121212...
Subtracting the original equation from this new one:
100x - x = 12.121212... - 0.121212...
Simplifying:
99x = 12
Dividing by 99 on both sides to solve for x:
x = 12/99
This fraction can be further simplified by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3:
x = (12/3)/(99/3)
x = 4/33
Therefore, the fully simplified fraction form of 0.121212... is 4/33.
x = 0.121212...
Multiplying both sides by 100 to “shift” the decimal point:
100x = 12.121212...
Subtracting the original equation from this new one:
100x - x = 12.121212... - 0.121212...
Simplifying:
99x = 12
Dividing by 99 on both sides to solve for x:
x = 12/99
This fraction can be further simplified by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3:
x = (12/3)/(99/3)
x = 4/33
Therefore, the fully simplified fraction form of 0.121212... is 4/33.
What is 0.5555... as a fraction
Let x be equal to the decimal 0.5555...
We can convert this repeating decimal to a fraction by multiplying it by a power of 10 to eliminate the repeating part.
10x = 5.5555...
Now, to get rid of the repeating part, we'll subtract the original equation from this new one:
10x - x = 5.5555... - 0.5555...
Simplifying:
9x = 5
Dividing both sides by 9 to solve for x:
x = 5/9
Therefore, the fraction form of 0.5555... is 5/9.
We can convert this repeating decimal to a fraction by multiplying it by a power of 10 to eliminate the repeating part.
10x = 5.5555...
Now, to get rid of the repeating part, we'll subtract the original equation from this new one:
10x - x = 5.5555... - 0.5555...
Simplifying:
9x = 5
Dividing both sides by 9 to solve for x:
x = 5/9
Therefore, the fraction form of 0.5555... is 5/9.
Evaluate 8×8-6×2
To evaluate the expression 8×8-6×2, we can use the order of operations.
First, we need to perform the multiplications:
8 × 8 = 64
6 × 2 = 12
Then, we subtract the result of the second multiplication from the first multiplication:
64 - 12 = 52
Therefore, 8×8-6×2 equals 52.
First, we need to perform the multiplications:
8 × 8 = 64
6 × 2 = 12
Then, we subtract the result of the second multiplication from the first multiplication:
64 - 12 = 52
Therefore, 8×8-6×2 equals 52.
Evaluate -4/2^2-(7-4)
To evaluate the expression -4/2^2-(7-4), we follow the order of operations (PEMDAS/BODMAS).
First, we simplify the exponent:
2^2 = 2 × 2 = 4.
Next, we simplify the inner parentheses:
7 - 4 = 3.
Now, we substitute the simplified values back into the expression:
-4/4 - 3.
Finally, we perform the division and subtraction:
-1 - 3 = -4.
Therefore, -4/2^2 - (7-4) equals -4.
First, we simplify the exponent:
2^2 = 2 × 2 = 4.
Next, we simplify the inner parentheses:
7 - 4 = 3.
Now, we substitute the simplified values back into the expression:
-4/4 - 3.
Finally, we perform the division and subtraction:
-1 - 3 = -4.
Therefore, -4/2^2 - (7-4) equals -4.
1 answer