# Standard Form of Numbers: A Problem-Solving Approach (Scientific Notation)

A number’s standard form, often known as scientific notation, is a method of representing big or tiny numbers in a succinct and practical style. It is written only between numbers 1 and 10 with power 10.

The “standard form” of a number in number theory often refers to expressing a particular number in a specific canonical or standard format. The particular standard form may vary depending on the context or type of number under consideration.

In this article, we will discuss the concept of standard form, notation of standard form, and way of writing decimal numbers in standard form, and merits and demerits of standard form. In addition, in this article example of standard form will be discussed.

## Standard Form Of A Number – Scientific Notation

The standard form of a number typically refers to expressing a number in a specific format that is widely recognized and used. In general, the standard form of a number is a representation that avoids unnecessary complexity and follows established conventions. In standard form, we use an exponent for representation.

Its other name is Scientific notation. Scientific notation gives the process of writing very large numbers or very small number using the number 1 to 10 and multiplying them with the power of 10. If the number is largest than one, we use positive power if the number is smallest than one, we use negative power of ten.

## Notation Of Standard Form – Representation

The representation of standard form is the place value of notation which complements the decimal number system.

## Way of Writing Decimal Numbers in Standard Form

To write decimal numbers in standard form, multiply the number by a coefficient and a power of ten. The purpose is to portray the number more compactly and consistently, making it easier to read and compare to other numbers.

Step 1: Classify the Coefficient

It is clear that the left side of the decimal contains non-zero digits It must be a single non-zero digit (from 1 to 9).

Step 2: Count the Decimal Places

Count the number of decimal places the decimal point must shift to the right to convert the number to its original form (i.e., the number of places it must shift to the right to have a whole number).

Step 3: Write the Standard Form

Write the coefficient followed by the letter “x” (which represents multiplication) and the power of 10 as a superscript with the exponent being the number of decimal places counted in step 2.

You can also take assistance from a standard form converter for getting the results of converting numbers into standard notation.

## Merits and Demerits of Standard Form (Scientific Notation):

Merits and demerits depend on the contents we used. Here we discuss some merits and demerits of the standard form:

## How to Find the Standard Form of A Number?

Example 1:

Convert 9,990,00 into standard form

Solution:

Step 1: Given the data

9, 990, 00

By rules, we can write them multiplication with a power of 10.

Step 2: Simplify

9, 990, 00 = 9.99 x 105

Example 2:

(1/2x) – x = -5.

Show the given equation in standard form.

Solution:

(1/2x) – x = -5

Step 1:

Multiplying with 2x on both sides,

1 – 2x (x)= -10x

Step 2:

Simplify the equation

2x2 +10 x + 1 = 0

Therefore, the standard form of the given equation is 2x2 +10 x + 1 = 0.

## Summary

In this article, we have discussed the concept of standard form, notation of standard form, and way of writing decimal numbers in standard form, and merits and demerits of standard form.

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