What is 5/7 as a decimal?

5/7 as a decimal is 0.7142857142...

Want to practice?

Question 1Convert the fraction

What is 5/7 written as a decimal?

Answer

0.71428571.

Divide 5 by 7.

Question 2Check with multiplication

How can you check the decimal value of 5/7?

Answer

Multiply 0.71428571 by 7; the result is 5.

Multiplication reverses the division used to convert the fraction.

Question 3Convert to a percentage

What percentage is equivalent to 5/7?

Answer

71.4286%.

Multiply the decimal 0.71428571 by 100.

Question 4Place the value on a number line

Between which two consecutive whole numbers does 5/7 lie?

Answer

It lies between 0 and 1.

Its decimal value is 0.71428571.

The decimal form of a fraction is the value of the fraction when the values are divided.

Solution

We perform a long division by dividing 5 by 7.

Here we can see that 7 > 5 and 5 cannot be divided by 7, we start our division by placing a decimal point in the quotient (0.) and adding 0 to make it 50.

As we divide, we get a new remainder in each step, we keep dividing until we get the same remainder again. We can stop dividing when a remainder gets repeated.

Here you can see that the remainder 5 is repeated after 6 steps of division.

What will happen if we continue dividing?

If we continue dividing, we will be getting the same digits in the quotient over and over again. Hence when we do long division, we can always stop dividing once we get any of the remainders we got in the previous steps.

So here our answer to the fraction $$\frac57$$ would be 0.714285714285…….
To indicate that the sequence of digits 714285 is going to be repeated, we use a bar over these numbers and write the answer as $$0.\overline{714285}$$.

The decimal form of the fraction $$\frac57$$ is $$0.\overline{714285}$$.

Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac57$$, the number 5 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

Where can you find out: what is 1/5 as a decimal fraction?