Question

How do you write $5.64\times {{10}^{-2}}$ in standard notation ?

Answer 1

Hint: Standard form in mathematics is mentioned for basically decimal numbers, equations, polynomials, linear equations and many other things. It’s correct definition could be explained better in terms of decimal numbers and following certain rules. As we know, the decimal numbers are the simplified form of fractions. Some fractions give decimal numbers which have numbers after decimal in thousandths, hundredths or tenths place. But there are some fractions, which gives a big decimal number.

Complete step by step answer:
To represent such big numbers, we use such simpler forms, which is also stated as Scientific notation.
Standard form does not only exist for numbers. It expands to calculus, geometry, algebra. In geometry, we have the standard equation of lines, circles, parabola and many other conics. In calculus we have the standard equation of special kinds of functions.
For example we have $154$ . Let us try to expand it.
Upon expanding we get the following :
$\Rightarrow 154=1\times 100+5\times 10+4\times 1$ .
This is the expanded form where the number we took is in its standard form.
We basically have to shrink the number.
The number we are given is in it’s Scientific Notation.
$\Rightarrow 5.64\times {{10}^{-2}}=0.0564$

$\therefore $ The standard notation of $5.64\times {{10}^{-2}}$is $0.0564$.

Note: We should remember the definitions of all the forms of notations such as standard notation, scientific notation, expanded exponential notation. We should remember all their rules so as to complete a question quickly in the exam. Practice is required to have clarity about all of them. Apart from this, we should also be aware of significant digits concepts as it can be asked along with these concepts.