What is 8/11 as a decimal?

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What is 8/11 as a decimal?

8/11 as a decimal is 0.727272…

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Long Devision Method

The long division method is used to find the decimal form of a fraction.
In this method, the numerator is the dividend and the denominator is the divisor.

The long division method includes dividing by placing the decimal point in the answer. The division is done either till we get a remainder of 0 or till the remainder gets repeated.

Let us try the long division method for a fraction $$\frac8{11}$$.

8 over 11 as a decimal

Steps of division

  • Find the number of times 11 can divide 8. Since 11 > 5, add 0 to the right of 5 after placing a decimal point in the quotient.
  • 80 is divisible by 11 seven times giving 77.
  • Subtract 77 from 80 to get a remainder of 3.
  • As the decimal is already marked, 0 can be added to the right of 3 to make it 30.
  • 11 divides 30 two times giving 22.
  • Subtract 22 from 30 to get a remainder of 8.

Repetition of remainder

  • From this point, it can be seen that the remainder 8 is repeated from step 1.
  • If the division is continued, the values 7 and 2 will be repeated infinitely.
  • Hence the division can be stopped with the answer 0.7272….

The decimal numbers that have repeating digits in a sequence are called repeating decimals.

what_is_8_11_as_a_decimal_6

This is denoted as $$0.\overline{72}$$.

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Hence the decimal form of the fraction is $$0.\overline{72}$$

Remember

Here are some common terms you should be familiar with.

  • In the fraction $$\frac8{11}$$, the number 8 is the dividend (our numerator)
  • The number 11 is our divisor (our denominator)

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