Question

How do you write \[2.2\times {{10}^{6}}\] in standard notation?

Answer 1

Hint: To convert the given scientific notation to standard notation we should have to eliminate the term \[\times {{10}^{n}}\] . For this first of all we have to consider the given equation as equation (1) and then by eliminating the term a \[\times {{10}^{n}}\] we will get the given number in standard notation.

Complete step-by-step solution:
To write \[2.2\times {{10}^{6}}\] the number into a standard notation, we have to assume the equation with S and consider the equation as equation (1).
\[S=2.2\times {{10}^{6}}...................\left( 1 \right)\]
As we know that given equation is in scientific notation which means it has a single digit to the left of the decimal sign and is multiplied with power of 10.
In other words we can write scientific formulas as \[a\times {{10}^{n}}\]. Where a is lies between 1 and 10 and n is an integer.
To write a number in standard notation we just need to multiply. This means moving decimal \[n\] digits to right if multiplying by \[{{10}^{n}}\] and moving decimal \[n\] digits to right if multiplying by \[{{10}^{n}}\].
In this case we have equation (1), we need to move decimal points to the right by 6 points.
For this, let us write \[2.2\] as \[2200000\] by moving decimal to the write as six points.
Let us consider the above number equation as equation (2).
\[S=2200000..........\left( 2 \right)\]
Therefore equation (2) i.e. \[S=2200000\] is the solution for the solution for equation (1) i.e. \[S=2.2\times {{10}^{6}}\].

Note: The most important thing while doing this problem is there should be no number in the right side of the decimal. If the power is negative like \[2.2\times {{10}^{-6}}\] then we have to divide \[2.2\] with \[{{10}^{-6}}\]. Because as we know \[{{a}^{-n}}=\dfrac{1}{{{a}^{n}}}\]. The key point of this type of problems is if we multiply a decimal with \[{{10}^{n}}\] then the decimal will move n times to the right.