What is 6/7 as a decimal?

6/7 as a decimal is 0.857142

Want to practice?

Question 1Convert the fraction

What is 6/7 written as a decimal?

Answer

0.85714286.

Divide 6 by 7.

Question 2Check with multiplication

How can you check the decimal value of 6/7?

Answer

Multiply 0.85714286 by 7; the result is 6.

Multiplication reverses the division used to convert the fraction.

Question 3Convert to a percentage

What percentage is equivalent to 6/7?

Answer

85.7143%.

Multiply the decimal 0.85714286 by 100.

Question 4Place the value on a number line

Between which two consecutive whole numbers does 6/7 lie?

Answer

It lies between 0 and 1.

Its decimal value is 0.85714286.

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

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:

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 = 1	1/8 = 0.125	3/4 = 0.75	7/9 = 0.7	11/16 = 0.6875	8/9 = 0.8	7/8 = 0.875	4/5 = 0.8
1/2 = 0.5	1/9 = 0.1	2/5 = 0.4	3/10 = 0.3	15/32 = 0.4687	7/10 = 0.7	5/9 = 0.5	4/7 = 0.571
1/3 = 0.3	1/10 = 0.1	5/6 = 0.83	2/11 = 0.18	3/5 = 0.6	3/11 = 0.27	9/10 = 0.9
1/4 = 0.25	1/11 = 0.09	2/7 = 0.28571	5/11 = 0.45	3/7 = 0.428571	6/11 = 0.54	4/11 = 0.36
1/5 = 0.2	1/12 = 0.083	5/7 = 0.71428	8/11 = 0.72	6/7 = 0.85714	7/12 = 0.583	7/16 = 0.4375
1/6 = 0.16	1/16 = 0.0625	3/8 = 0.375	5/12 = 0.416	5/8 = 0.625	5/16 = 0.3125	15/16 = 0.9375
1/7 = 0.142857	2/3 = 0.6	2/9 = 0.2	3/16 = 0.1875	4/9 = 0.4	13/16 = 0.8125	19/32 = 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.