Fractions and decimals signify the same thing that is the numbers those are not the whole number. For converting fraction to decimal, numerator is divided by denominator. Some of the decimal fractions stop after few decimal places such as 1/2, 1/4, 1/8. These decimals are called as terminating decimals. On the contrary, other fractions become endlessly repeating cycle for same digit such as 1/3, 1/6, 1/7. These decimals are called as repeating or recessing decimal fractions. These recurring fractions can be segregated into 2 types –

1. Some of the decimal factors are just the collection of the digits that repeat right from the beginning such as 0.3 where 3 is repeating forever and 1/7 that is 142857 repeated endlessly. These are called as purely repeating decimal fractions.
2. On the other side, others starts with the fixed set of the digits before they settle down too eventually to endless repetition of same digits like 1/6 = 0.166666 that starts as 0.1 and then cycles 6 for indefinite times. These are called as mixed recurring decimal fractions

Different methods are there those can be used for converting 3/8 into decimal. These are –

Method 1 – it is sort of the cheating way and the answer is 0.375. The computation can be explained as follows –

12→0.5

Halve that and you have

14=0.25

Halve that and you have

18=0.125

But we have 3 of them so this becomes

3×18→31×18=3×11×8=38

Implying that for 38 we have

3×0.125=0.375

It is however good idea to put ‘0’ to the left of decimal point assuming it is 0.

Method 2 – it represents the relationship among decimal and fraction and can be explained as follows –

3/8→3÷8

Step 1

3 < 8 but 3 is the same as 30/10

Note that

3×8=24 and 30−24 = 6 so we now have

(30 ÷8)/10 =3/10+ remainder 6/10

Step 2

Now it is required to split the remainder of 6/10 into eights.

It can be written as 6/10 as 60/100 giving:

3/10 + (60÷8)/100

Note that 7×8=56 and 60−56 = 4 and hence now:

3/10 + (60÷8)/100=3/10+7/100+ remainder of 4/100

Step 3

Now it is required to split the remainder of 4/100 into eights.

It can be written as 4/100 as 40/1000 giving:

3/10+7/100 + (40÷8)/1000

Note that 5×8=40, hence we have                      

3/10+7/100+5/1000

Writing this in decimal form gives: 0.375

Method 3 – it can be explained as follows –

Write as

8∣3.0000

It is irrelevant whether there are too many 0’s as long as enough 0’s are there. Left over if any can be ignored

3 is less than 8 so write the decimal point giving:

8.∣3.0000
     0

Step 2

8<30, hence 30/8 = 3 + remainder of 6

8.∣3.0⁶ 000
     0.  3

Step 3

8 < 60 so 60÷8=7+ remainder 4

8.∣3.0⁶ 0⁴ 00
     0.  3  7

Step 4

8 < 40 so we calculate 40÷8=5

8.∣3.0⁶ 0⁴ 0 0
     0.  3  7  5

As no remainder is there, the sum is finished. Last ‘0’ is redundant so it can be ignored.