Question

How do you simplify and write $\left( {2.5 \times {{10}^{ - 3}}} \right) + \left( {4.6 \times {{10}^{ - 3}}} \right)$ in standard notation?

Answer 1

Hint: The above question is based on the writing of an expression in standard form with writing an exponent in powers of ten.
Standard notation is also called scientific notation in which we use to write any numerical value if it contains decimal value or a large number of zeros, in the powers of ten.
Using the powers of ten we will write the standard form of the given value.

Complete step-by-step solution:
Let’s discuss scientific notation in much more detail.
Scientific notation is a way of expressing numbers that are too large or too small to be expressed in decimal form. It may be referred to as scientific form or standard index form. These base ten notations are commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations.
The scientific notation is written as;
$m \times {10^n}$
In the term written above, n is the exponent and m is called significant or mantissa; m and n are the integers, therefore could be written with negative sign as well.
Now, we will do the calculation part of the problem.
$ \Rightarrow \left( {2.5 \times {{10}^{ - 3}}} \right) + \left( {4.6 \times {{10}^{ - 3}}} \right)$ (We will take out common from the given expression)
$ \Rightarrow \{ {10^{ - 3}} \times (2.5 + 4.6)\} $ (We will add the two terms in bracket)
$ \Rightarrow {10^{ - 3}} \times (7.1)$
$ \Rightarrow 7.1 \times {10^{ - 3}}$ (This is the standard form of the given expression)

Note: Scientific notation is used to write very large or very small numbers using fewer digits. Scientists use scientific notation for representing distance between the planets, astronomical distances or the microscopic distances such as the length of a blood cell. Many engineers use the scientific notation for representing very small current, units of capacitors and many other formulas to ease the lengthy and long written values.