Question

How do you simplify and write $0.0007\times 190$ in scientific notation?

Answer 1

Hint: In this question, we have to convert a decimal notation into scientific notation. As we know, a decimal notation is a number that has a decimal point, which means the decimal can be removed by placing the numbers after the decimal in the denominator. Also, a scientific notation is either a very large number or a small number; it is represented when a number lies between 1 to 10 is multiplied by a power, which implies $a\times {{10}^{b}}$ where a is the number between 1 and 10 and b is either negative for small numbers. So, in this problem, we first count the total numbers of 0 after a decimal point that is where the number 7 appeared, and then write it in the form of scientific notation by using exponent and mathematical rules, which is our required solution to the problem.

Complete step by step solution:
According to the question, we have to find the scientific notation from a decimal notation.
The decimal notation given to us is $0.0007\times 190$ -------- (1)
So, we first count the total number of zeros after the decimal point, we have
$\begin{align}
  & \text{ }0.0007 \\
 & \text{ }\uparrow \uparrow \uparrow \\
\end{align}$
So, we get 3 zeroes after a decimal point and before 7.
Also, we have to count the decimal point as a zero; therefore in total, we get 4 zeroes before a decimal point, thus we get the value of b for a scientific notation is,
$b=-4$
Therefore, we can write it as $7\times {{10}^{-4}}\times 190$
Now, we will split 190 as a product of 19 and 10, we get
$7\times {{10}^{-4}}\times 19\times 10$
On further simplification, we get
$133\times {{10}^{-4}}\times 10$
Now, we can write 133 as a $1.33\times {{10}^{2}}$ , thus we get
$1.33\times {{10}^{2}}\times {{10}^{-4}}\times 10$
Now, we will apply the exponent rule ${{a}^{b}}{{a}^{c}}={{a}^{b+c}}$ in the above expression, we get
$1.33\times {{10}^{2-4+1}}$
On further solving, we get
$1.33\times {{10}^{-1}}$

Therefore, for the decimal notation $0.0007\times 190$, its scientific notation is equal to $1.33\times {{10}^{-1}}$

Note: While solving this problem, do mention all the steps properly to avoid mathematical errors. Keep in mind the difference between scientific notation and decimal notation. Also, a scientific notation is only represented for decimal numbers.