Convert .45 repeated to a rational simplest form
To convert .45 repeating to a rational simplest form, let's call the repeating decimal x.
Since .45 is equivalent to 45/100, we can write:
x = 45/100 + x/100
Multiplying both sides by 100 to eliminate the decimal:
100x = 45 + x
Subtracting x from both sides:
99x = 45
Dividing both sides by 99:
x = 45/99
Thus, .45 repeating can be written in rational simplest form as 45/99.
To convert .45 repeated (or .454545...) to a rational simplest form, we can follow the steps below:
Step 1: Let x = .454545...
Step 2: Multiply x by 100 to move the decimal two places to the right: 100x = 45.454545...
Step 3: Subtract x from 100x: 100x - x = 45.454545... - .454545...
This simplifies to: 99x = 45
Step 4: Divide both sides of the equation by 99: 99x / 99 = 45 / 99
This simplifies to: x = 45/99
Therefore, the rational simplest form of .45 repeated is 45/99.
To convert the decimal number .45 repeated to a rational simplest form, we can set it up as a fraction.
Let's assume x = .45 repeated.
We can multiply both sides of the equation by 100 to shift the decimal point two places:
100x = 45.45 repeated
To eliminate the repeated decimal, we subtract x from both sides:
100x - x = 45.45 repeated - x
99x = 45
Now, we can divide both sides of the equation by 99:
99x / 99 = 45 / 99
Simplifying the fraction gives:
x = 5 / 11
So, .45 repeated in rational simplest form is 5/11.