 Hello and welcome to the session. In this session, we will learn about conversions of fractions to decimals and decimals to fractions. Now, let us review some of the key facts about fractions and decimals. First is fractions whose denominators are ten, hundred, thousand, etc. are called decimal fractions. The numbers written in decimal form are called decimal numbers. The hardest, the number of digits in the decimal part is the number of decimal places. And when we multiply a number by ten times ten, then the decimal point is shifted to right hand side by as many places as there are number of zeros. An example into ten will be equal to, now you can see there is one zero, so the decimal point will be shifted by one place to the right hand side. And the result will be 35.96. And when we divide a decimal, then the decimal point shifted by as many places as there are numbers. There are number of zeros. Now let us see an example, divided by hundred will be equal to, now in hundred there are two zeros and it will be shifted to left hand side. So the result will be 572. Now let us discuss the conversion to decimal by division method. Now a given fraction a over v can be expressed dividing a by v. Now decimals are of two types, terminating and non-terminating. Now non-terminating decimals are further classified into two forms, one is non-terminating repeating decimals and second is non-terminating non-repeating decimals. First of all let us see what are terminating decimals. Now in the process of converting action into decimal by the division method a zero will mean that after certain number of steps and the division process terminates then the decimal obtain is called the terminating decimal. Now let us see one example. In this we have to convert the fraction that is 7 by 8 into decimals. Now for the solution we will simply divide the numerator by the denominator. Now 7 is not divisible by 8 so we will put 1 0 here and 1 0 here and on subtracting it will give 7. Now we will put 1 decimal here and 1 decimal here in the quotient. So we will put 1 0 on the right of dividend and 1 0 on the right of remainder then and on subtracting it will give 7. Then in the next step we will put 1 0 here on the right of dividend and on the right of remainder then 8 and on subtracting it will give 4. So put 1 0 on the right of dividend and 1 0 on the right of remainder and on subtracting it will give a 0 remainder. So where in the process of converting a fraction into decimal this division process terminates that is we are getting a 0 remainder at a terminating decimal. Therefore 7 by 8 is equal to 0.875 non-terminating decimal, putting a fraction into decimal when the division process of the decimal obtained the non-terminating decimal. If a block of digits repeat now let us see one example we have to convert the fraction 4 by 11. Now in the solution we will simply divide the denominator. Now first one division by 11 so we will put 1 0 here, subtracting it will give then we will put 1 decimal in the dividend and 1 decimal in the quotient then we will put 1 0 in the right of dividend and 1 0 in the right of remainder. Now 11 by 33 is 33 and on subtracting it gives 7. Now again put 1 0 on the right of the dividend and on the right of the remainder. Now 11 into 6 is 66 and on subtracting it gives 4. Now again put 1 0 on the right of dividend and on the right of remainder. Now 11 into 3 is 33 and on subtracting it gives 7. Put 1 0 on the right of dividend and 1 0 on the right of remainder. Division process never ends. 2 is equal to 0.36, 36 and so on. I am repeating the question expressed by putting a bar on the block of digits that repeat. That means it can be written as 0 point the non-terminating repeating decimal. Now next put a repeat and the division process I am repeating for example which is equal to 3.1415 that the division process never ends. It is terminating that in the first step we remove the number in the numerator in the denominator as the number of digits to the decimal point in the given decimal number. Now let us see one example that to convert 0.53 to the solution 0.53 will be equal to and write the resulting number in the numerator which will be 50 field number of digits after the decimal point. So the number of digits after the decimal point are 2 when the decimal is non-terminated BX then in the second step remove the bar without using bars. Then in the next step multiply by 10 if there is 1 digit in the repeated block multiply by 100 if there are up by 1000 if there are 3 digits in the repeated block. Then in the next step we will solve the equations which will be obtained by the step 2 and step 3 and then we will find the value of X. For example in this we have to convert 0 point into fraction start with the solution in the first step 0.205 bar decimal without the bar so it will be 0.1 2 digits in the repeated block so we will multiply on both the sides. So we get 1000 X is equal to and so on and let it be equation number 2 over 999 therefore 0.05 bar is equal to 2 decimal into fractions. In this method the repeated figure is repeated block once and write in the denominator of repeated digits 0.205 bar can be written as the repeated figure which is 2.05 once in the numerator and in the denominator as the number of repeated digits. Now the number of repeated digits are 3 so we will write 23. Now there are 2 digits in the repeated block so the rest will be equal to then 1 2 decimal point. For example 2 1 digits after the decimal point therefore the shortcut method is not applicable so in this fashion we have learnt about 2 decimals and decimals to fractions.