Question

How do you write $450,000$ in scientific notation?

Answer 1

Hint: We know that we use the scientific notation of a number to make the large numbers short in order to make it easy to use or apply wherever it is needed. First, we will write the first digit. Then we will put a decimal point and we will write the rest of the digits after the decimal points. We will multiply the number with $10$ to the power of a number that is equal to the number of the digits after the decimal point. We will use the fact that is given by $10,000={{10}^{4}}.$

Complete step by step answer:
Let us consider the number $450,000.$
We need to write this number in the scientific notation. That means, we need to write the exponential form of the given number.
Let us consider the fact that we multiply the nonzero digits first and then write as many zeros as the two numbers contain at the right end of the product when two numbers are multiplied.
From this we get, $450,000=45\times 10,000.$ Because, when we multiply $45$ and $1,$ we will get $45.$ Then we add four zeros at the right end.
Now, we are going to recollect another fact. That is, $10,000$ can be written as the fourth power of $10.$ That is, $10,000={{10}^{4}}.$ Because the product of four tens is ten thousand. That is, $10\times 10\times 10\times 10=10,000.$
So, we will get $450,000=45\times 10000=45\times {{10}^{4}}.$
We know that $45=4.5\times 10.$ So, we will get $450,000=4.5\times 10\times {{10}^{4}}.$
That is, $450,000=4.5\times {{10}^{5}}.$
The above obtained is the exponential form of the given number. We know that the scientific notation of a number is its exponential form.
Hence the scientific notation of the given number is given by $4.5\times {{10}^{5}}.$

Note:
When we have to deal with higher calculations including large numbers, it will be easy to use the scientific notation of the numbers. Because, by writing the numbers in their scientific form, we make them short. We just have to focus on the number of digits after the decimal point and the exponent of $10.$