![]() ![]() on the right side, we are subtracting away the same value. So when we subtract away x on the left side and subtract away 0.888. Since x is equal to 0.888., this means they are the same value. Now we will subtract the original equation away from the new equation:īefore we go any further, think about why this is legal? We know the addition property of equality allows us to add or subtract the same value to or from both sides of the equation. We will multiply both sides of our equation by 10: This means n is 1 and 10 to the power of 1 is just 10. In our case, we have one digit 8, that repeats forever. Non-terminating decimals are the one that does not have an end term. It is a decimal, which has a finite number of digits (or terms). Next, we will multiply both sides of the equation by 10 n, where n is the number of digits in the repeating pattern. Terminating and Non-Terminating Decimals A terminating decimal is a decimal, that has an end digit. It is normally easier to think about this problem using the ellipsis format. Let's begin by setting our repeating decimal equal to a variable like x: To convert a repeating decimal to a fraction, we rely on our knowledge of the addition property of equality, along with the multiplication property of equality. When we use the ellipsis, we must ensure that the digit that repeats or pattern of repeating digits is crystal clear. We may also see an ellipsis used instead of an overbar: 9138 » The pattern "9138" repeats forever Let's take a look at a few examples.Ģ.5 32 » The pattern "32" repeats foreverĠ. We generally place a bar over the digit or pattern of digits that repeat. ![]() A repeating decimal is a decimal number that repeats the same ending digit or pattern of ending digits forever. 2.1 Converting a terminating decimal to a fraction 2.2 Converting a. ![]() Up to this point, we have not discussed how to convert a repeating decimal into a fraction. In our pre-algebra course, we learned how to convert from a decimal to a fraction and from a fraction to a decimal. ![]()
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