Question

How do you write \[88900MHz\] 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, 8 and how many places the decimal has moved will be shown by the power of 10, which is 4. 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 \[88900MHz\],
So, placing the decimal point after the first point and then writing the number of places the decimal placed moved as a power of 10, we get,
\[88900MHz\]
\[\Rightarrow 8.8900\times 10000MHz\]
\[\Rightarrow 8.89\times {{10}^{4}}MHz\]

Therefore, the given number in scientific notation is \[8.89\times {{10}^{4}}MHz\].

Note: Scientific notation is very helpful when dealing with large numbers. Using scientific notation, the calculation of large numbers can be easily carried out which otherwise could take a lot of time. Also, \[MHz\] refers to megahertz and is equal to \[{{10}^{6}}Hz\]. So, if we want to simplify further, that is, writing in terms of hertz, \[Hz\], we will have,
\[8.89\times {{10}^{4}}MHz\]
\[\Rightarrow 8.89\times {{10}^{4}}\times {{10}^{6}}Hz\]
\[\Rightarrow 8.89\times {{10}^{10}}Hz\]