Finally we subtract and divide to find the fraction form of that repeating decimal. Then we multiply by 100 again to move an entire repeat pattern left of the decimal. If we have to convert 0.27565656 into a fraction, we first multiply by 100 to move the decimal point 2 places right past the 27 since those digits don't repeat. Now we subtract the 1st equation from the 2nd Now we multiply by 100 to move the decimal 2 more places, past a complete repeat pattern.
![decimal to fraction converter infinite decimal to fraction converter infinite](https://cdn.extendoffice.com/images/stories/doc-excel/convert-between-fraction-decimal/doc-convert-between-fraction-decimal-4.png)
We start with 10 x instead of x like this: To set it up so the repeating digits start immediately right of the decimal point, Notice that the "2" doesn't repeat - just the 787878. Let's do another example with what I call problem child repeating decimals to see what to do when the repeating pattern doesn't start immediately right of the decimal point.Įxample: Find the fraction equivalent to 0.2787878. In both these examples, the repeating pattern started immediately after the decimal place in the tenths column. On the right side, we get a whole number since the repeating digits (after the decimal point) cancel each other out.įinally, we divided by the coefficient (multiple) of x on the left to get the fraction equivalent to the repeating decimal. This gave us a whole number multiple of x on the left side of the equation. Next, we subtracted the first equation from the 2nd. Then we multiplied by the correct power of 10 to move the decimal point to the right of one complete repeat pattern. We did this because there were 2 repeating digits in the decimal.įirst, we named the repeating decimal x to create an equation. Here, we multiplied by 100 to move the decimal 2 places to the right. We did this because there was only one repeating digit in this decimal.Įxample 2: convert 0.090909. Here, we multiplied by 10 to move the decimal one place to the right. Let's do 2 examples before we discuss the procedure.Įxample 1: convert 0.33333. To convert a repeating decimal to a fraction, we use multiplication, subtraction,and division. Note: The number of zeros in the denominator = the number of decimal places.Ĭonverting Repeating Decimals to Fractions Then, if we can, we reduce the fraction to lowest terms. We just write the decimal's digits in the numerator of a fraction with the appropriate power of ten in the denominator. Infinite decimals cannot be expressed as fractions.Ī finite decimal is easily converted to a fraction. They are exact only to the hundredths place. The actual value of pi to 5 decimal places is 3.14159. These are called irrational numbers because they can't be expressed as a fraction (rational number). The decimal digits never repeat and never end. Infinite or Non-repeating Decimals: are numbers like pi and the square roots of 2 or 3. The repeating decimals above are written this way: We indicate repeating decimals with either a dot or (better) a "bar" over the repeating digits. They represent fractions with denominators that are prime numbers other than 2 or 5.Ġ.3333., 0.11111., and 0.090909. Repeating Decimals: are decimals in which one or more digits keep repeating without end. Like the name says, these decimals end at a specific place value.Ġ.175, 0.00093, 0.5478931 are terminating decimals. Terminating Decimals: have a finite (countable) number of digits. Terminating, repeating and infinite or never ending decimals. Today, what with calculators, we can use our regular decimal system to measure angles but we still use the sexagesimal system to measure time. The number 3.5 was written 3° 30'back then because 30 minutes is one half of a degree, and 9.75 was written 9 ° 45', since 45 minutes is ¾ of 60 = 0.75 of a degree. The table of equivalences is:ġ° (degree) = 60' (minutes), and 1' (minute) = 60" (seconds).Īs always in math, there are symbols ( °, ', and " ) to represent degrees, minutes and seconds. With angles, whole numbers are called degrees not hours.
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On the clock, an hour (whole) is divided into 60 minutes, and each minute is divided into 60 seconds. We still use it today on clocks and to measure angles. In ancient days, mathematicians and scientists used the sexagesimal notation for fractions with 60 as its base. They were developed so we could express parts of a whole (fractions) with the same place value system we use for whole numbers. Their denominators are exclusively powers of 10. Decimals to fractions DECIMALS TO FRACTIONSĭecimals are fractions.