What is 6/7 as a decimal?

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What is 6/7 as a decimal?

6/7 as a decimal is 0.857142

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Nick is working on converting the fraction $$\frac67$$ to a decimal. After getting three digits in the quotient, he is unsure if the answer is finite or a recurring decimal. Can you help him?

Solution

6 over 7 as a decimal

Recurring fractions are fractions that have one or more digits that occur repeatedly in a pattern. The type of decimal that we will arrive at in a long division can be of two types:

  • a) Finite decimal or terminating decimal: The digits in the decimal do not repeat after any number of steps. They do not form a pattern. The division ends with a remainder of 0.
  • b) Infinite decimal or non-terminating decimal: The digits in the decimal repeat after a certain number of steps. Once the decimal value begins to repeat, it can be concluded that the same values are going to follow. The division does not end in remainder 0 and is stopped when the remainder value is repeated.
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Hence to find the correct type of decimal for a fraction, Nick should continue to divide until he gets are repeated digits pattern or 0.

Let us carry out the division as below:

6/7 as a decimal number

It can be observed that the remainder 6 is arrived at after 6 steps of division that is found in the first step. Hence all the digits following are recurring. So the answer to the fraction would be

$$\frac67=0.857142857142…=0.\overline{857142}$$

Remember

Here are some common terms you should be familiar with.

  • In the fraction $$\frac67$$, the number 6 is the dividend (our numerator)
  • The number 7 is our divisor (our denominator)

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We invite you to read other articles on decimal and fraction, on our blog, to find out how converting decimal to fraction.

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