Question

How do you write $72\times {{10}^{4}}$ in scientific notation.

Answer 1

Hint: Now we know that any number in scientific notation is written as $x\times {{10}^{n}}$ where x is any number less than 10 and n is any integer. Hence we will try to write the number in the form by multiplying required power of 10 and simplify.

Complete step by step answer:
Now consider the number $72\times {{10}^{4}}$
Now we want to write the number in scientific notation. Hence we want to write the number in the form $x\times {{10}^{n}}$ where x is number less than 10 and n is any integer.
Now first we will try to write 72 as a number which is positive and less than 10 multiplied with power of 10.
Hence we can write 72 as $7.2\times 10$ where the power of 10 is 1.
Hence we have $72\times {{10}^{4}}=7.2\times 10\times {{10}^{4}}$
Now we know that ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$ .
Hence using this we get the number as,
$72\times {{10}^{4}}=7.2\times {{10}^{5}}$
Now we know that $7.2\times {{10}^{5}}$ is a number of the form $x\times {{10}^{n}}$ where x is number less than 10 and n is any integer

Note:
Now note that if the given number contains decimal then we will shift the decimal such that the number obtained finally is less than 10. To shift the decimal to left we will multiply by negative powers of 10 and to shift the decimal to right we will multiply with positive power of 10. For example if we have 46.3 then we will shift the decimal to left and multiply by ${{10}^{-1}}$ Hence we get $4.63\times {{10}^{-1}}$