What is the decimal of 1/7

Question

I am lost and don't know the answers im doing decimals and it just keeps going on and on and on but there all diff numbers 

Answer 1

Here are some helpful hints:

simplify the fraction

write the prime factorization of the denominator

if you get all 2's, all 5's, or a combination of 2's and 5's only, you will have a terminating decimal

if there are any other prime numbers in the factorization, other than 2's or 5's, then you will have a repeating decimal

what repeats is called the repetend

the maximum number of digits that can possibly repeat is 1 less than the denominator

this does not mean that you will always get the maximum number of digits in the repetend

Here are some examples:

Terminating decimals

3/4=0.75          4=2*2

3/5=0.6            5=5

7/8=0.875        8=2*2*2

17/25=0.68      25=5*5

39/40=0.975    40=2*2*2*5

37/50=0.74      50=2*5*5

99/125=0.792  125=5*5*5

count the number of 2's and count the number of 5's

whichever is greater, that's how many digits will be in the answer

 

Repeating decimals

2/3=0.666...

5/6=5/(2*3)=0.8333...

4/7=0.571428571428571428... (here you get the maximum number of digits in the repetend)

7/11=0.636363...

5/12=5/(2*2*3)=0.41666... (the 2's caused the 41 to come up before the repetend-this is called the lag)

12/17=0.705882352941176470588235294117647058823529411764... (here you get the maximum number of digits)

13/18=0.7222... (18=2*3*3, 2 causes the lag and 9 causes the repetend)

How to determine the number of digits in the repetend:

Determine the power of 10, minus1, that the denominator divides into evenly (disregard any 2's and 5's)

2/3=0.666.. 3 divides evenly into 10-1=9 and 10=10^1

7/9=0.777... 9 divides evenly into 10-1=9

8/11=0.727272... 11 divides evenly into 100-1=99 and 100=10^2

19/37=0.513513513... 37 divides evenly into 1000-1=999 and 1000=10^3

6/7=0.857142857142857142... 7 divides evenly into 1,000,000-1=999,999 and 1,000,000=10^6

Answer 2

Hi Trevon;

 

This just a division problem

1 ÷ 7 = 0.142857143

 

All we need to know is how many

decimal places to round to.  Does

your problem say where to round to?

 

2 places:  0.14

3 places: 0.143

4 places: 0.1429

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