To understand the concept of Multiplying Scientific notation, we should first know what scientific notation is. Scientific notation is expressing numbers in powers of base 10. Scientific Notation is useful because it allows us to track really large and really small numbers in ways that are easy for our brains to write down and to understand. Let us understand by some numbers like 7.102 times 10^2.It is already written in scientific notation already as it is written as a product with a power of ten. So how do we write it just as numeral?
How to Multiply Scientific Notation – We can Multiply Scientific Notation in two ways, there is a slow way and there is a fast way to solve it. The slow way is by simply multiplying, for example if we have 7.102 times 100. That means when we multiply 7.102 with 100 will be 710.200, here firstly we shall multiply the numbers then we shall add the remaining decimal points which gives the correct answer as 710.2.
Now a faster way of Multiplying Scientific Notation is as we see we have only three decimal points and 7.102 times 10 to the 2nd power and when we shift the decimal points by two. Thus the answer would be 710.2. Every time we multiply it by ten, we shift the decimal to the right by one. Let us take another example to understand it better.
Let us say we have 4.5 time 10^4 and this time let us do it in the fast way method. So 4.5 times 10 ^4, here we will shift to the right side after every tenth, so 10^ 4 is nothing but 10000, four times the decimal point will get shifted. So our solution will be 45000.
Let us solve an example with negative exponent to understand the concept in a better way. We have 1.75 times 10 ^-3, this is in scientific notation, and we have to write the numerical value of this. So when we take negative power times ten then should shift the decimal to the left. So this will be 0.00175. We can also call it as the same thing, 1.75 times 10^-3 is equal to 0.00175. Another way to check that we got the right answer is if we count here 1 including the zeros to the right of the decimal should be the same as the negative exponent given.
How to Multiply Scientific Notation – We can Multiply Scientific Notation in two ways, there is a slow way and there is a fast way to solve it. The slow way is by simply multiplying, for example if we have 7.102 times 100. That means when we multiply 7.102 with 100 will be 710.200, here firstly we shall multiply the numbers then we shall add the remaining decimal points which gives the correct answer as 710.2.
Now a faster way of Multiplying Scientific Notation is as we see we have only three decimal points and 7.102 times 10 to the 2nd power and when we shift the decimal points by two. Thus the answer would be 710.2. Every time we multiply it by ten, we shift the decimal to the right by one. Let us take another example to understand it better.
Let us say we have 4.5 time 10^4 and this time let us do it in the fast way method. So 4.5 times 10 ^4, here we will shift to the right side after every tenth, so 10^ 4 is nothing but 10000, four times the decimal point will get shifted. So our solution will be 45000.
Let us solve an example with negative exponent to understand the concept in a better way. We have 1.75 times 10 ^-3, this is in scientific notation, and we have to write the numerical value of this. So when we take negative power times ten then should shift the decimal to the left. So this will be 0.00175. We can also call it as the same thing, 1.75 times 10^-3 is equal to 0.00175. Another way to check that we got the right answer is if we count here 1 including the zeros to the right of the decimal should be the same as the negative exponent given.
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