Question

How do you write \[60,000\] in scientific notation?

Answer 1

Hint: To write the given number in scientific notation, we will be using decimal and we will place it after the first digit and put the number of zeroes that the decimal had to skip as the power of 10 and convert large number as this given into something which is convenient to read and understand. For example – if we have a number like \[4,800,000,000\], then we can use decimal and powers of 10 as follows:
\[4,800,000,000=4.8\times {{10}^{9}}\]
This way we have a standard way of writing pretty large numbers in a convenient and easy way.

Complete step-by-step solution:
There are two parts to the scientific notation which can be seen above. The digit’s part and the part having powers of 10. There are some guidelines to be followed:
1. In the digit’s part, the decimal is placed after the first number and also the value of the decimal part should always be in the range \[[1,10)\], this means that the decimal part can be 1 and greater than 1, but should always be less than 10(excluding 10).
2. The power on 10 is determined by the position of decimal.
According to the question we have, we have to write the scientific notation for \[60,000\]
So we will first solve the digit’s part, the decimal is placed after the first digit. So it will be \[6.0\].
And also the powers of 10 will be \[{{10}^{4}}\], since we moved the decimal four places towards the left.
So, the scientific notation for \[60,000\] is \[6.0\times {{10}^{4}}\].
Therefore, \[60,000=6.0\times {{10}^{4}}\]

Note: While writing the digit’s part, the decimal should be positioned in the proper place (that is after the first digit). And while writing the power of 10, if the number is greater than 10, then the decimal is moved towards the left side and we get the positive powers on the power of 10. If the number is less than 1, then the decimal is moved towards the right side and we have the negative powers on the power of 10.