Question

How do you write $8,670,000,000$ in scientific notation?

Answer 1

Hint: We will first write all the zeroes of the number in the form of raising powers to $10$and then see what we are left with and then introduce a decimal so that we get only one digit before decimal.

Complete step-by-step answer:We have the number $8,670,000,000$ with us which needs to be written in scientific notation. Now we can clearly see that it has seven zeroes at the end after $867$in it.
We can write $10,000,000$= ${{10}^{7}}$
Now if we multiply both sides with $867$, we will get;
$8,670,000,000$can be written as $867\,\times \,{{10}^{7}}$
Now we know that in scientific notation we need only one digit before the decimal but here we have three which are $867$
So, we can write $867$ as $8.67$ multiplied by $100$
Therefore, $8,670,000,000$ can be written as
$\Rightarrow \,8.67\,\times \,100\,\times \,{{10}^{7}}$ or it can be written as $8.67\,\times \,{{10}^{2}}\,\times \,{{10}^{7}}\,$
Now we know the exponents addition rule as: $\left( {{x}^{a}}\times \,{{x}^{b}} \right)\,=\,{{x}^{a+b}}$ it means if in a multiplication the bases are same then the powers or exponents gets added. Hence for the above expression $2\,and\,7\,$ will add to give $9$
Using this rule in the above expression, we get the standard form as mentioned below;
$8.67\,\times \,{{10}^{9}}$
Hence, we can say that $8,670,000,000$can be written in scientific notation as $8.67\,\times \,{{10}^{9}}$.

Note: Student should note that scientific notation is a method of expressing numbers in terms of a decimal number multiplied by a suitable power of ten. It helps us to get an idea of the number without writing all the zeroes and in an easier form as compared to the actual complex form.