TopIn mathematics, scientific notation has an important role. If we want to multiply the two values or Numbers in scientific notation first we have to multiply the number values without exponents after that we have to add the exponents of power of 10 and then we have to place the new power of 10 in scientific notation including the decimal. After multiplication if your decimal is bigger than 10, start counting that how many times the decimal move in left direction and add that number to the exponent. Now we will see how to multiply and divide scientific notation.
Here we have two values which we have to multiply,
(2.6*107) and (6.3*104)
In this we have to first multiply 2.6 and 6.3 and there resulting value is 16.38. After that we add both exponents 7 + 4=11. Then we put the new decimal value with new exponents in scientific notation manner, we get,
16.38 * 1011,
Now we can easily see that decimal number is bigger than 10 so we start counting that how many times the decimal moves in left direction. In this case decimal moves once place to left so the final result is
1.638 * 1012,
If we want to divide the numbers in scientific notation than first we have to divide the decimal numbers and after that we have to subtract the exponents of 10. Then we have to place the new power of 10 with the decimal value in the scientific notation form. If the resulting decimal number isless than one, then move the decimal Point to the right direction and decrease the exponent number from the number of places that decimal point has moved. Let's take an example:
Here we have two values (1.23*1011) and (2.4*104) where we apply division operation,
So in this case first we divide decimal numbers,
Now we subtract exponents which contain power of 10,
Then we place both new decimal number and exponent in scientific notation manner
.5125 * 107
At last we move decimal point one place to right and decrease the exponent by 1 so finallythe resulting value is
(1.23 * 1011) / (2.4 * 104) = 5.125 * 106.