Take the 0.37 feet and divide by 0.0833 4.44 inches. Take the decimal fraction of feet and divide by 0.08333 (1/12th) and this will give you inches and decimals of an inch. The bar is positioned above the non-repeating part of the decimal. To convert decimal fractions of an inch to fractions of an inch. For instance, lets say you wanted to convert the following to a fraction: 0.321 0708. Step 1: Separate the non-repeating part of the decimal from the repeating part. on the right side, we are subtracting away the same value. However, if you want to make life a little easier, use our decimal to fraction conversion calculator instead. So when we subtract away x on the left side and subtract away 0.888. This whole number is the numerator of the. Since x is equal to 0.888., this means they are the same value. To get the fractions numerator, multiply the decimal part of the number by the denominator to get a whole number. 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. Step 3 The above generated can’t be simplified further so we consider the above fraction 1/10 as final result. Next, we will multiply both sides of the equation by 10 n, where n is the number of digits in the repeating pattern. Step 2 As there is only 1 number after point so multiply 10 one time to both numerator and denominator. 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: This is due to the divisional limits that the. 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 converting decimals to fractions the result is often rounded to the nearest fraction by the calculator. 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. Up to this point, we have not discussed how to convert a repeating decimal into a fraction. Converting a Repeating Decimal into a Fraction Set the repeating decimal equal to a variable Multiply both sides of the equation by 10n where n is the number. 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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