Concepts of Standard Form

Introduction

Standard form is a simple way to write very large (e.g 230,000,00) or and very small (e.g. 0.000,000,006) numbers.


It is commonly used in scientific calculator when the number to be displayed is too large to be shown on the screen.



General form of standard form
A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is said to be written in standard form.

$$\pm A\times {10}^n$$

Noted,$1\le A\prec 10$ and n is a power in positive or negative whole number.

Example of Number in Standard Form

1. $-5\underset{\begin{array}{c}4decimal\\ places\\ toleft\end{array}}{\underbrace{8370}}$ in standard form is $-5.837\times {10}^4$
2. $0\underset{\begin{array}{c}3decimal\\ places\\ toright\end{array}}{\underbrace{.004}}15$ in standard form is $4.15\times {10}^{-3}$

As shown above for $-58370$, it is because the decimal point has been moved 4 places to the left side to get the number to be $-5.837$.

Note using the scientific calculator
Your calculator will have a key ${10}^x$ and EXP  for entering numbers in standard form.