Question

How do you write $420,000$ in scientific notation?

Answer 1

Hint: We know that when we multiply ten thousand to a number, the leftmost digits of the product will be the number to which we multiplied ten thousand and the rightmost digits will be the zeros of ten thousand. We know the fact that is given by $10,000={{10}^{4}}.$

Complete step by step answer:
Let us consider the number $420,000.$
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, $420,000=42\times 10,000.$ Because, when we multiply $42$ and $1,$ we will get $42.$ 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 $420,000=42\times 10000=42\times {{10}^{4}}.$
We know that $42=4.2\times 10.$ So, we will get $420,000=4.2\times 10\times {{10}^{4}}.$
That is, $420,000=4.2\times {{10}^{5}}.$
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 $4.2\times {{10}^{5}}.$

Note: The given form of the number is its standard form. Remember that the given number and its scientific notation are the same but we are just expressing the given number written in the standard form in the exponential form.