Question

How do you write \[7,500\] in scientific notation?

Answer 1

Hint: We are given a number which we have to write in scientific notation. The scientific notation consists of two parts, which is, the digits with decimal point and the second part with 10 raised to a power. To the number given to us, we will place the decimal point after the first digit, that is after 7 and how many places the decimal has moved will be shown by the power of 10, which is 3. Now, we will substitute the obtained values in the generalized form of a scientific notation is \[a\times {{10}^{b}}\], where \[a\] is the number with the decimal part and \[b\] is the number raised to power of 10.

Complete step by step answer:
According to the given question, we are given a number which we have to write in scientific notation.
Scientific notation refers to the form which is clearly understandable and has the general form as:
\[a\times {{10}^{b}}\]
So, clearly we can see that scientific notation consists of two parts -
First is a number \[a\], which has a decimal point placed just after the first digit, and the second part is the 10 raised to a power which is \[b\].
Here, the number \[a\] has a value greater than or equal to 1 and less than 10, that is, \[1\le a<10\].
Similarly, \[b\] is an integer which is the power raised to 10.
The given number is \[7,500\],
So, placing the decimal point after the first digit 7 and so for that we will be moving 3 places towards the left and then writing the number of places the decimal placed moved as a power of 10, we get,
\[7,500\]
\[\Rightarrow 7.500\times 1000\]
\[\Rightarrow 7.5\times {{10}^{3}}\]
Therefore, the given number in scientific notation is \[7.5\times {{10}^{3}}\].

Note:
The calculation of the decimal place shift should be done correctly else, the obtained scientific notation will not be equivalent to the given question. We have to add a decimal point after the first digit of the given number and then count the number of places required to get the given number. So, here we had 7500, adding decimal point, 7.500 and then we have 3 places, so we have written \[7.5\times {{10}^{3}}\] . This must be followed for such questions.