Question

How do you write $3.75\times {{10}^{-2}}$ in standard notation?

Answer 1

Hint: To simplify the given form into standard notation ${{10}^{-2}}$ can be written as $\dfrac{1}{100}$ and therefore the power will be positive, count the digit from the left and number of zero in the $100$ for putting the decimal part , counting, start from the left as no of zeros in $100$ is $2$ and decimal no $3.75$ is $2$
As you count the digits from the left.
Place the decimal point at the digit $4$ from the left.
If the number of digits are less place zero’s from the right

Complete step by step solution:As per given,
$3.75\times {{10}^{-2}}$
So here you have to convert this equation into standard notation:
$3.75\times {{10}^{-2}}$
Here ${{10}^{-2}}$ m multiplication converted into division,
And the sign $\left( - \right)$ will be get $\left( + \right)$ addition sign as per the rule.
Therefore, the modified equation will be,
$\Rightarrow \dfrac{3.75}{{{10}^{2}}}$
Here we can ${{10}^{2}}$ as $100$ because $\left( \text{square}\ \text{of}\ \text{two} \right)$ ${{10}^{2}}=100$
$\Rightarrow \dfrac{3.75}{100}$
Now, at last as you know that $'100'$ m division has two zeros m it. It replace to by placing the decimal after two digits in $3.75$ as it is seen than decimal point is after two digits as count it from left so you have to put two zero before $3.$
Therefore the standard notation will be
$\Rightarrow 0.0375$

Additional Information:
Scientific notation is defined as expressing very large or small numbers by powers of ten so that the values are more easily understood.
Current scientific notation to standard notation, First observe what happen when a particular number is multiplied or divided by multiples of $10.$
Eg.$1.$ $123.45\times 10=1234.5$ Decimal place moved by $1$ place to the right.
$\left( 2 \right).$ $67.89\times 1=6.789$ decimal place moved by $1$ place to the left.
Remember that numbers multiples can also be expressed in exponential form:-
$\begin{align}
  & 1={{10}^{0}} \\
 & 10={{10}^{1}} \\
 & 1={{10}^{-2}} \\
 & 100 \\
 & \\
\end{align}$
A number in scientific notation form is in the form
$\left( \text{A} \right)\times {{10}^{\text{b}}}$
Where A is the rational number in decimal form. To convert to a number is scientific notation from more the decimal place by $\text{ }\!\!'\!\!\text{ b }\!\!'\!\!\text{ }$ is Pointe more to the right.

Note:
Convert ${{10}^{-2}}$ in multiplication into division and do not forget to change the sign $\left( - \right)$ by $\left( + \right)$
Remember the number’s multiples expressed in exponential form and vice rears
${{10}^{2}}=100$
In $\dfrac{3.75}{100}$ the decimal place is moved by $2$ from left as $100$ contains two zero.