Question

How do you write $9.24\times {{10}^{-3}}$ in standard form?

Answer 1

Hint: To solve this question, we have to first define the standard form and scientific form of a number. After that, we will understand what 10 to the power positive and negative numbers indicate. Then, we will use it to express ${{10}^{-3}}=\dfrac{1}{1000}$ . Now, we can multiply 9.24 with it and remove the decimal from the number. This will give us the standard form of the number $9.24\times {{10}^{-3}}$ .

Complete step by step answer:
We can start by defining the terms – standard form and scientific form of a number. So, if we have a number, then we can represent it in multiple forms like decimals, fractions, percentages, exponents, etc…
We do come across some numbers that are too big or too small and it becomes difficult to express them using any form. So, we have to make use of the scientific form. When we make use of decimals and multiply that decimal number with a power of 10, then we can identify that number as the scientific form. We must note that the number in the decimal form must be less than 10 and more than 1.
We can have both positive and negative powers of 10. Let us consider examples to understand it.
So, if we have the number as $2.98\times {{10}^{4}}$, then we will have to express it such that there are no decimals or we can say that the power of 10 is removed. Since we have 10 to the power 4, it means that we have four zeroes - 10000. So, we can rewrite it as $2.98\times 10000$ . Now, we can shift the decimal point to the right by 4 places. Finally, the standard form of $2.98\times {{10}^{4}}$ would be 29800.
Let us take another example as $5\times {{10}^{-3}}$. Here, the power is negative, so it means that it has to be divided. We can express ${{10}^{-3}}=\dfrac{1}{1000}$ . So I can rewrite the number as $5\times \dfrac{1}{1000}$, which is the same as $5.0\times \dfrac{1}{1000}$ . We now have to shift the decimal point to the left side by 3 places. We will get the standard form as 0.005.
Now, coming to our question, we have to convert $9.24\times {{10}^{-3}}$ to standard form. The power is negative, so we express it as ${{10}^{-3}}=\dfrac{1}{1000}$.
Rewriting the number, we get $9.24\times \dfrac{1}{1000}$ .
Now, we have to shift the decimal point by 3 places to the left. Doing so, we will get 0.00924.

Hence, we can write $9.24\times {{10}^{-3}}$ in the standard form as 0.00924.

Note: We must know how to convert from standard to scientific form as well. So, let us take the same example and check it. If we have the number as 29800, then we will have to express it such that the decimal is in between 1 and 10. So, we can write it as 2.9800. We can also write 29800 as 29800.0. Now to make 29800.0 as 2.9800, we have to shift decimal to the left by 4 places. So, we can express this shift as ${{10}^{4}}$. Finally, the scientific form of 29800 would be $2.98\times {{10}^{4}}$ .