Convert .121212... into a fully simplified fraction. (1 point)
Let x = 0.121212...
Then, 100x = 12.121212...
Subtracting the two equations, 100x - x = 12.121212... - 0.121212...
Simplifying, 99x = 12
Dividing both sides by 99, x = 12/99
Therefore, the fully simplified fraction is 12/99.
Convert .121212... into a fully simplified fraction. (1 point)
Responses
12/100
12 over 100
3/25
3 over 25
4/33
4 over 33
12/999
Convert 0.5555... to a fraction(1 point)
Responses
55/100
55 over 100
5/10
5 tenths
1/2
1 half
5/9
5 ninths
The correct answer is 5/9.
Evaluate: 8×8−6×2
To evaluate 8 × 8 - 6 × 2, we first perform the multiplications:
8 × 8 = 64
6 × 2 = 12
Next, we subtract the result of the second multiplication from the result of the first multiplication:
64 - 12 = 52
Therefore, the value of the expression is 52.
Evaluate: −4/2^2−(7−4)
To evaluate -4/2^2 - (7 - 4), we begin by working within the parentheses:
7 - 4 = 3
Now, we follow the order of operations and evaluate the exponent:
2^2 = 4
Next, we substitute the results back into the expression:
-4/4 - 3
Finally, we perform the division and subtraction:
-1 - 3 = -4
Therefore, the value of the expression is -4.
To convert the recurring decimal .121212... into a fraction, we can use the concept of geometric series. Let's denote the decimal as x: x = .121212...
To get rid of the repeating part, we multiply both sides of the equation by 100, 1000, or a power of 10 that eliminates all the decimal places after the repeating part. In this case, let's multiply by 100 to eliminate the two decimal places after the repeating "12": 100x = 12.121212...
Next, we subtract the original equation from the equation obtained after multiplying: 100x - x = 12.121212... - .121212...
Simplifying the equation gives us: 99x = 12
Dividing both sides by 99, we have: x = 12/99
Since both 12 and 99 can be divided by 3, we simplify the fraction further: x = 4/33
Therefore, the fully simplified fraction for .121212... is 4/33.