How is 0.025 written as a fraction in simplest form? Enter your answer in the box. The dash is above the 25, thanks in advance!
The Correct Answer and Explanation is :
The repeating decimal ( 0.025\overline{25} ) can be written as a fraction. To do this, follow these steps:
Step 1: Let ( x = 0.025\overline{25} )
This means that ( x = 0.025252525… ) where “25” repeats indefinitely.
Step 2: Eliminate the decimal part
To eliminate the repeating part, multiply both sides of the equation by 1000, which shifts the decimal three places to the right:
[ 1000x = 25.252525… ]
Step 3: Subtract the two equations
Now subtract the original equation from this new equation:
[
1000x = 25.252525…
]
[
x = 0.025252525…
]
Subtracting gives:
[
999x = 25.2272725…
]
This eliminates the repeating decimal.
Step 4: Solve for ( x )
Now, divide both sides of the equation by 999 to solve for ( x ):
[
x = \frac{25.2272…}{999}
x = \from equation