 Hello and welcome to the session. In this session, we will discuss a question which says that write each number in scientific notation. First part is 684000 and second part is 0.007. Hence evaluate 684000 the whole into 1.4 into 10 raise to power minus 2 the whole this whole upon 0.007. Now before starting the solution of this question, we should know some results. And that is scientific notation of a number is written as a into 10 raise to power n where a is called coefficient of factor which is greater than or equal to 1 but less than 10 and n is the negative or positive exponent or power of 10. If the number to be expressed in scientific notation is greater than 1 then the exponent or power of 10 is a positive integer and if the number is between 0 and 1 then this power is a negative integer. Now these results will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. First of all let us express this number in scientific notation. Now here in the first part we have to express 684000 in scientific notation. Now here you can see that this number is greater than 1 and we know that if the number to be expressed in scientific notation is greater than 1 then the power or exponent of 10 is a positive integer. Now in the step 1 we will put a decimal at the end of last digit. It will be 684000 and we will put a decimal here. Now in coefficient a the decimal point is placed after the first digit as the coefficient of factor is greater than equal to 1 but less than 10. Now as we said the decimal should be placed after first digit which means here decimal must be after the first digit which is 6. Now in the next step count the number of digits between new decimal place and this decimal point. Now here you can see that there are 5 digits between them. Now these number of digits will be the power of 10 in scientific notation. So here exponent of 10 in scientific notation will be 5. Also here the coefficient a will be 6.84. In scientific notation we can write the given number as 6.84 into 10 raised to power 5. Now let us start with the second part. Now in the second part we have to write 0.007 in scientific notation. Now here you can see that this number is very small and it is between 0 and 1 and we know that if number is between 0 and 1 then exponent of 10 in scientific notation is a negative integer. Now here in the step 1 we will place the carrot after the first non-zero digit. Now here 7 is first non-zero digit so we have 0.007 and after this first non-zero digit we will place a carrot. Now we will count the number of digits between decimal and carrot. Now here you can see that there are 3 digits between the decimal and carrot. So here in scientific notation will be these number of digits but here the given number is between 0 and 1 so the power of 10 will be a negative integer of 10 in scientific notation may be minus 3. Now as the decimal is to be placed after first non-zero digit so here the coefficient of factor a will be 7.0. In scientific notation the given number can be written as 7.0 into 10 raised to power minus 3. Now to evaluate this given expression now for evaluating this we will use the scientific notation which we have obtained in part 1 and part 2. Now for the first part we have obtained this scientific notation for the second part we have obtained this scientific notation. Now using these scientific notation for 684000 will be equal to 6.84 into 10 raised to power 5 the whole into 1.4 into 10 raised to power minus 2 the whole. This whole again now 0.007 is equal to 7 into 10 raised to power minus 3 further by using the associated property of multiplication this is equal to 6.84 into 1.4 the whole into 10 raised to power 5 into 10 raised to power minus 2 the whole. This whole again 7 into 10 raised to power minus 3 further this is equal to 6.84 into 1.4 this whole again 7 into 10 raised to power minus 2 above 10 raised to power minus is 1.4 and 0.2 into 6.84 is equal to 1.2. Now here we will use the multiplication rule of exponents and according to this rule if bases are same then powers are added so here it will be 10 raised to power 5 plus of minus 2 which will be 10 raised to power 5 minus 2 upon 10 raised to power minus 3 further this is equal to 1.37 into 10 raised to power 3 upon 10 raised to power minus 3 is equal to 1.37 into never and it will be 10 raised to power 3 minus of minus 3 which will be 10 raised to power 3 plus 3 3 7 into 10 raised to power 6 evaluating this expression we obtained 1.37 into 10 raised to power 6. That's all for this session hope you all have enjoyed the session.