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Problem 1143

# Find $$0.2525$$ as a quotient of integers.

Expert verified
The decimal $$0.2525$$ can be expressed as the quotient of integers $$\frac{25}{99}$$.
See the step by step solution

## Step 1: Identify the repeating block

Let's work with the decimal number $$0.2525$$. We can see that the repeating block is "25", so our number can be represented as $$0.\overline{25}$$.

## Step 2: Convert the repeating decimal to a fraction

Let's represent the repeating decimal as $$x$$. So our goal is to find a fraction equivalent to the repeating decimal: $x=0.\overline{25}$ To convert this repeating decimal to a fraction, we'll first multiply it by 100 (because there are 2 decimal places in the repeating block, we need two zeroes): $100x = 25.\overline{25}$ Now, subtract the original equation from the new equation: $100x - x = 25.\overline{25} - 0.\overline{25}$ $99x = 25$

## Step 3: Simplify the fraction

To find the fraction, we now just need to solve for $$x$$: $x = \frac{25}{99}$ So, we can express the decimal $$0.2525$$ as the quotient of integers $$\frac{25}{99}$$.

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