Question

How to write $3.67$ multiplied by 10 to the ninth power. Write that distance in standard form?

Answer 1

Hint: We first explain the purpose of scientific notation and its standard form of expression. Then we explain the process. We use the decimal point and move it rightwards to multiply the decimal with 10. The multiplied form is the scientific form and multiplied number is the standard form.

Complete step by step answer:
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
That’s why we use as many powers or indices of 10.
The expression of 10 to the ninth power can be written algebraically as ${{10}^{9}}$.
The given expression is $3.67$ multiplied by 10 to the ninth power.
This can be written as $3.67\times {{10}^{9}}$. This is the scientific notation.
Now we find the standard form the notation.
For the given number we move a decimal place to the right one position. The decimal starts from its actual position. The more we move to the right, the more we multiply with 10.
If there is no digit left for the decimal to cross then we add more zeroes for that.
In the first step $3.67\times {{10}^{9}}$ becomes $36.7\times {{10}^{8}}$.
Then it changes to $367.0\times {{10}^{7}}$. Now we bring one zero as there is no digit to cross for the decimal.
$367.0\times {{10}^{7}}$ becomes $3670.0\times {{10}^{6}}$. The final answer will be $3670000000$. It’s the standard form.

Note: We also can ignore the notation as $3.670000000\times {{10}^{9}}$ for the simplicity and mathematical use. The use of zeroes is necessary. But in no case we can use digits other than 0 after decimal.