Decimal

What is 6/7 as a decimal?

6/7 as a decimal is 0.857142

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.

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).

Find More Fractions to Decimals

1/1 = 11/8 = 0.1253/4 = 0.757/9 = 0.7
11/16 = 0.68758/9 = 0.87/8 = 0.8754/5 = 0.8
1/2 = 0.51/9 = 0.12/5 = 0.43/10 = 0.3
15/32 = 0.46877/10 = 0.75/9 = 0.54/7 = 0.571
1/3 = 0.31/10 = 0.15/6 = 0.832/11 = 0.18
3/5 = 0.63/11 = 0.279/10 = 0.91/4 = 0.25
1/11 = 0.092/7 = 0.285715/11 = 0.453/7 = 0.428571
6/11 = 0.544/11 = 0.361/5 = 0.21/12 = 0.083
5/7 = 0.714288/11 = 0.726/7 = 0.857147/12 = 0.583
7/16 = 0.43751/6 = 0.161/16 = 0.06253/8 = 0.375
5/12 = 0.4165/8 = 0.6255/16 = 0.312515/16 = 0.9375
1/7 = 0.1428572/3 = 0.62/9 = 0.23/16 = 0.1875
4/9 = 0.413/16 = 0.812519/32 = 0.5937

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

Also, you can read about what is 2/11 as a decimal fraction.

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