Numbers come in various forms and representations in mathematics. One such representation is the standard form of a number. This provides a short uniform way to express numbers; making it easier to compare and perform mathematical operations.
This article aims to cover the concept of the standard form of numbers in math; its significance; and how to write different types of numbers in standard form. So; let’s dive in and unveil the mysteries of the standard form.
Standard Form of Numbers
The Standard Form of a number is a way to express a number using digits and place values. It is also referred to as scientific notation or the exponential Form. In this; the number is shown as a product of a decimal number between 1 to 10 and a power of 10 (A × 10n; n must be an integer).
This notation enables us to represent both very large and very small numbers in a compact and manageable format.
Writing Numbers in Standard Form: A Step-by-Step Guide
The numbers to write in standard Form includes two main steps:
- Determining the decimal part.
- Start From the Given number.
- The decimal point should be moved to the left until there is just one digit remaining. Add up how many decimal places you changed.
- Use a power of 10 to represent the decimal portion.
- The exponent for 10 is determined by the number of decimal places we shifted.
- The usual form of the number is the outcome of this.
Writing Decimal Numbers in Standard Form: A step-by-step guide
The decimal numbers may be written in standard form by using a similar approach.
- Determining the decimal part.
- Start From the Given number.
- When there is just one non-zero digit remaining to the left of the decimal point; move the decimal point to the right. How many decimal places did you move?
Express the decimal part as a power of 10.
- The number of decimal places we moved gives us the exponent for 10.
- After this; the resultant is the standard form of the number.
Steps to convert a Rational number into standard Form:
Converting the rational number into standard form involves simplifying the fraction to its lowest term. Let’s outline the steps for converting a rational number into the standard form:
- Decide The numerator and denominator.
- Discover the GCD (greatest Common divisor) of the numerator and denominator.
- Divide both by their GCD.
- Express the simplified fraction as the standard form.
Examples OF the Standard Form of the numbers:
Let’s explore a few examples of the Standard form to solidify our understanding of this.
Example 1: (Standard Form of Numbers)
Write the numbers 5;432;100 in standard form.
Solution:
To write the Number in Standard Form follow these steps;
Determining the decimal part.
Step 1:
Start from the given number: 5;432;100.
Step 2:
The decimal point should be moved to the left until there is just one digit remaining. Add up how many decimal places you changed.
In this; we move the decimal point 6 places to the left; resulting in the number 5. 4321.
Use a power of 10 to represent the decimal portion.
Step 3:
The decimal part is 5. 4321; which is between 1 and 10.
Step 4:
The number of decimal places we moved gives us the exponent for 10. In this case; we moved six decimal places.
Therefore; we can write the numbers 5;432;100 in standard Form as 5.4321 × 106.
Example 2: (Decimal Numbers)
Write the decimal number 0.0000342 in standard form.
Solution:
To write the decimal number in standard form follow these steps.
Solution:
Determining the decimal part.
Step 1:
Start from the given number: 5;432;100.
Step 2:
When there is just one non-zero digit remaining to the left of the decimal point; move the decimal point to the right. How many decimal places did you move?
In this example; we move the decimal point five places to the right; resulting in the number 3.42
Express the decimal part as a power of 10.
Step 3:
The decimal part is 3.42; which is between 1 and 10.
Step 4:
Since we moved the decimal point five places; the exponent for 10 is -5 (negative exponent denotes moving to the right).
Therefore; we can write the decimal number 0.0000342 in standard form as 3.42 × 10-5.
Example 3: (Rational number)
Convert the rational number 16 / 20 into standard form.
Step 1:
The numerator is 16 and the denominator is 20.
Step 2:
Find the GCD (Greatest Common Divisor):
In this case; the GCD of 16 and 20 is 4.
Step 3:
Divide by the GCD:
16 / 4 = 4
20 / 4 = 5.
Step 4:
Express the simplified fraction in standard form:
The simplified fraction is 5 / 4.
Therefore; the rational number 16 / 20 in standard form is 4 / 5.
Conclusion:
In this article; we explained the concept of the standard form of numbers; which is a way to express numbers using digits and place values. The standard form; also known as scientific notation or exponential form; allows for the representation of both large and small numbers in a compact format.
We provided step-by-step guides on how to write numbers; decimal numbers; and rational numbers in standard form. Several examples were given to illustrate the process. By following these steps; we can easily convert numbers into the standard form and perform comparisons or calculations more professionally.
