 Hello and welcome to this session. In this session we will learn how to write scientific notation of given numbers and to write how many times as much one is then the other. Now we know how to write an expression with positive and negative exponents. For example 1 upon 25 can be written as 1 upon 5 into 5 into 5 which is equal to 1 upon 5 raised to power 3 which is equal to 5 raised to power minus 3 into 2 into 2 which can be written as 2 raised to power 3. So here we have written these expressions in negative and positive exponent form. Now we already know that in 2 raised to power 3 2 is called the base and 3 is called the exponent or power. Now here the numbers are small so we can easily write them in exponent form. But some numbers are very large like 323 are very small like 0.0000056. Now in order to write such numbers which are very large or very small we may use our scientific notations. Now some examples of scientific notations are 4.3 into 10 raised to power 9 then 2 into 10 raised to power 6 and 5.7 into 10 raised to power minus 8. Now in scientific notations we may use our powers of 10 to write numbers. So in scientific notation a number is written as a product of a number which is greater than or equal to 1 but less than 10 and a power of 10 as here you can see this scientific notation is written as a product of a number and a power of 10 where the number 4.3 is greater than 1 but less than 10. Similarly you can observe other scientific notations also. Now let us see in different powers of 10. Now 10 raised to power 5 is equal to 100000 then 10 raised to power 4 is equal to 10000 then 10 raised to power 3 is equal to 1000 10 raised to power 2 is equal to 100 and 10 raised to power 1 is equal to 10. Now 10 raised to power 0 is equal to 1 10 raised to power minus 1 is equal to 1 upon 10 which is equal to 0.1 then 10 raised to power minus 2 is equal to 1 upon 10 raised to power 2 which is equal to 1 upon 100 and this is equal to 0.01 and 10 raised to power minus 3 is equal to 0.001 and then we will have 10 raised to power minus 4, then 10 raised to power minus 5 and so on. Now let us see how to write scientific notation. Now a scientific notation of a number is written as a into 10 raised to power n where a is called the coefficient or factor which is greater than or equal to 1 but less than 10 and n is the exponent or power of 10. Now n can be a negative integer or a positive integer. Now this exponent will be negative when the number to be expressed in scientific notation is between 0 and 1 and the exponent will be positive when this number is greater than 1. Now 0.4 into 10 raised to power 5 is not written in scientific notation because here the factor which is 0.4 is less than 1 and we know that the factor should be greater than or equal to 1 but less than 10. Now let us discuss some examples. Now let us write 783 million in scientific notation. Now here you can see that 783 million is greater than 1 and we know that when the number to be expressed in scientific notation is greater than 1 then power of 10 is positive. Now in the first step we will put a decimal at the end of last 0 in the given number. So here we will put one decimal. Scientific notation in the coefficient a the decimal point is placed after the first digit. We said the decimal should be placed after the first digit. It means here decimal must be after 7 with the decimal point 1, 2, 3, 4 to the left. Now let us place a parent where we have to place a decimal and now count the number of digits between parent and the decimal point. Now here you can see that there are 8 digits between parent and decimal point and the number of digits which is 8 will be the exponent or power of 10 in scientific notation. So in scientific notation we can write the given number as 7.83 into. Now here as the given number is greater than 1 so the power of 10 is a positive integer. Let us discuss another example in which we have to write 0.00456 in scientific notation. Now this number is very small and it is between 0 and 1 and we know that if the number to be expressed in scientific notation is between 0 and 1 then the power of 10 is a negative integer. Now in the first step we will place the first non-zero digit which is 4 and then we will write the remaining digits of the given number which are 5, the number of digits between decimal and parent. Now here we have now the number of digits which is 3 will be the power of 10 in scientific notation but it will be negative because the given number is between 0 and 1. Now in scientific notation we will place the decimal after 4 so it will be 4 into, so here we have moved the decimal 3 places to the right. Now let us see how to change the given scientific rotation in standard form. Now let us discuss it with the help of an example. It is 8 into 10 is to power 5 in standard form. Now we can convert it in standard form by expanding the parts of 10 and multiplying the result with a number which is greater than or equal to 1 but less than 10. Now here the number which is greater than 1 but less than 10 is 7.8 we will expand the powers of 10 then 10 is to power 5 will be equal to 100,000 and we will multiply it with 7.8 and this is equal to 718,000.0. Now here you can see that we have moved the decimal 5 places to the right from its existing position write it as 780,000. Now in the second example we will write 4.56 into 10 is to power minus 3 in standard form. Now this is equal to 4.51 upon 10 raised to power 3 which is 1000 equal to 0.00456. Now here the decimal point moves to the left from its existing position. Now let us see how to find which scientific notation is greater. Now consider these scientific notations. Now suppose we have to arrange these scientific notations from the previous to the least. Now let us group them according to exponents. Now 4.97 into 10 raised to power 7 and 4.89 into 10 raised to power 7 have for comparing these two numbers we will compare the coefficients. Now it is greater than 4. therefore 4.97 into 10 raised to power 7 is greater than 4.89 into 10 raised to power 7. 4.54 into 10 raised to power 9 is greater than 4.26 into 10 raised to power 9. Now 4.89 is greater than so to the least we have into 10 raised to power 9 then 4.26 into 10 raised to power 9 and then 4.97 into 10 raised to power 7 and then the least which is 4.89 into 10 raised to power 7. Now let us learn to write how many times as much one is than the other. Now we know the product quotient rule are used to solve real life problems involving scientific notations like product or division of two scientific notations. Now let us discuss one example. Now in this example it is given that if the population of US is 3.6 into 10 raised to power 8 and the world population is 7.4 into 10 raised to power 9 then show that the world population is 20 times US population. Now let us start with its solution. Now we want to show that world population is 20 times US population that means we have to show that world's population is equal to 20 into the US population that is we have to show that world population upon US population is equal to 20. Now let us find world population upon US population. Now world population is given as 7.4 into 10 raise to power 9. Upon US population is given as 6 into 10 raise to power 8. Now this is equal to 7.4 upon 3 points upon 10 raise to power 8 the whole. Now on calculating this is equal to 2.05 into. Now using the quotient rule this will be 10 raise to power 9 minus h which is equal to 10 raise to power 1. So this is equal to 20.5 that is 20 approximative. So world population upon US population is equal to 20 which means world population is 20 times US population. So in this session we have learnt about scientific mutations and this completes our session. Hope you all have enjoyed the session.