5.126 with a bar over the 126
................................................................._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.
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.
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
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.
_ 5.921
Sorry, but it is not possible to use a notation bar with this browser.
2.16 with a bar on top of the 16
3.58 with the bar only over the 8
In bar notation, it is .42. The bar rests atop the 42.
To convert a fraction to a decimal using bar notation, divide the numerator by the denominator. If the division results in a repeating decimal, you represent the repeating part with a bar over the digits that repeat. For example, the fraction ( \frac{1}{3} ) converts to the decimal 0.333..., which can be expressed as ( 0.\overline{3} ) to indicate that the digit '3' repeats indefinitely.
you just take the first 3 fours and put a line on top of it
A non-example of bar notation is writing a repeating decimal without using a bar, such as 0.3333... or 0.142857142857..., where the repeating part is not clearly indicated. In contrast, using bar notation, these would be represented as (0.\overline{3}) or (0.\overline{142857}), respectively. This lack of clarity in indicating the repeating sequence makes it a non-example of bar notation.
It would be 0.7961 with a bar over the 7961. Using dot notation it would be 0.7961 with a dot over the 7 and another dot over the 1.
.735
Repeating Decimal can be expressed exactly using what
To rewrite the number 2.7666 using bar notation, you identify the repeating part of the decimal. In this case, the digit "6" is the only digit that repeats. Therefore, you can express the number as (2.7\overline{66}), indicating that the "66" repeats indefinitely.