5.126 with a bar over the 126
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................................................................._0.384333 using the bar notation = 0.3843(the bar should be placed above the repeated decimal. In this case, it should be above the 2nd 3 from the decimal point.
5/20 ~ Your original number 25/100 ~ Decimals are parts of numbers out of the nearest power of ten (100 this time) 0.25 ~ Using decimal notation
The repeating decimal .1111111111 can be represented as the fraction 1/9. This is because the decimal 0.1 can be expressed as 1/10, and when we have a repeating decimal like .1111111111, it is equivalent to 1/10 + 1/100 + 1/1000 + ... which simplifies to 1/9 using the formula for the sum of an infinite geometric series.
You do a long division - using whichever method you have been taught. Don't stop with a remainder but carry on until you see a repeating pattern emerging (after 6 decimal places).
There are three different situations, corresponding to the three types of decimal numbers: terminating, repeating and those which are neither terminating nor repeating. Terminating: If the decimal number has d digits after the decimal point, then rename it as a fraction whose numerator is the decimal number without the decimal point, and the denominator is 10d or 1 followed by d zeros. For example, 34.567 d = 3 so the denominator is 1000. and the fraction is 34567/1000. Repeating: Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, after which you get a repeating pattern of a string of d digits. Then the numerator is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10c*(10d - 1), which is a string of d 9s followed by c 0s. For example 123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3. So the numerator is 12326159 – 12326 = 12313833 and the denominator is 99900 Therefore the fraction is 12313833/99900. Non-terminating and non-repeating: There is no way to get a proper fraction since, by definition, this is an irrational number. The best that you can do is to round it to a suitable number of digits and then treat that answer as a terminating decimal. In all cases, you should check to see if the fraction can be simplified.