Question

How do you write 0.0003 in scientific notation?

Answer 1

Hint: We are given 0.0003 and we are asked to change it and write into scientific notation. We will learn about scientific notation and do various examples and learn tricks to solve this kind of problem. After we learn it, we start our problem, to change 0.0003 into scientific notation, we have to shift the decimal after the first non – zero term. So, we shift and write accordingly as given below.

Complete step by step answer:
We are given a term 0.0003, we are asked to convert this into a scientific notation to solve this problem. We learn about the scientific notation with certain examples and we will start our problem. Now scientific notation is a way of writing very large or very small numbers in an easy way. A number is written in scientific notation when a number between 1 and 10 is multiplied by 10. In scientific notation, the exponent tells us about the extent of the number whether it is small or big. A positive exponent indicates a large number while a negative exponent indicates a small number.
To write any term in scientific notation, we write the term in such a way that the decimal is placed after the first non – zero terms and while doing this we adjust the power of 10. For example, say we have 0.002. So, to make it into scientific notation we will have to place the decimal after non – zero term which is 2 here. So, it means we have to move decimal 3 units to the right. We need to understand that if we move the decimal to the right then we get 10 raise to that power is negative and if we move the decimal to the left then we get 10 raise to that power in positive.
Now, in 0.005, we move 3 units to the right. So, we get \[5.0\times {{10}^{-3}}.\] Similarly, if we have 0.0.58 then we get \[5.8\times {{10}^{-2}}\] as we move decimal 2 unit to the right, i.e, we have \[8\underleftarrow{00.}00\] then in scientific notation we got \[8.00\times {{10}^{2}}\] and as we move the decimal to the left by 2 units.
Now, we will solve our problem. In our problem we have 0.0003 so, the first non – zero terms is 3 we can see that we have to move 4 terms to the right to reach there. So, 10 will be raised by 4. So, we get,
\[0.0003=3\times {{10}^{-4}}\]
Therefore, the scientific notation of 1440000 is \[3\times {{10}^{-4}}.\]

Note:
While changing the power over 10, we need to be very careful as we may make mistakes like \[0.03=3\times {{10}^{-2}}.\] We may put wrong terms on 10. So, we should do it carefully. Also, if our term has no decimal so we should know that decimal is always there after the last term. For example, 400 = 400.00. So, from here, we can now convert \[400=400.00=4.00\times {{10}^{2}}.\] The key point here is to find the non-zero term and the number of terms shifted by a decimal to reach there.