Exercise 22 Page p10

The line over the 21 in the expression 0.21 tells us that the 21 repeats an infinite number of times. 0.21=0.212121... To write the fraction equivalent to this expression, we can use the following equation. x=0.212121... By multiplying both sides of the equation by 100, we create a new equivalent equation. Remember to always follow the Properties of Equality when solving equations.

Now, we can subtract x from both sides to eliminate the repeating decimal. This is possible because we know that x is equal to the decimal part.

Finally, we can divide both sides of the equation by 99 so that the x-variable is isolated. This will leave us with the fraction that is equation to the repeating decimal.