In mathematics, numbers hold significant importance. Numbers can be difficult to read and understand if they have several digits. Mathematicians introduced the standard form of a number to overcome this problem. The standard form is the method of expressing numbers that makes them easier to write and read.
In this blog, we will explore the concept of standard form with its mathematical repression. We will learn how to write fractions, expanded forms, and ordinary numbers into standard forms. In the example section, we will solve some examples for our readers.
In mathematics, the standard form is a way of representing numbers in a concise and standardized format. The standard form is also known as scientific notation or exponential notation. Standard form is very helpful when dealing with extremely large or extremely small numbers.
The general format of a number in standard form is a × 10n
The number 5,000,000 can be expressed in standard form as 5 × 106. The number 0.000045 can be written as 4.5 × 10-5. The numbers become more manageable and easier to compare using the standard form.
You can follow the following steps to convert whole numbers into standard form.
Let's learn these steps by example.
Example: Convert the whole number 3,250,000 to standard form.
Step 1: Write the first digit from the left, which is 3.
Step 2: Put the decimal point after 3.
Step 3: Count how many numbers of digits after the first digit. Here are 6 digits after 3.
Therefore, the standard form 3,250,000 is 3.25 × 106.
A standard form calculator is an online tool that is used to convert numbers in standard notation according to the above-mentioned steps.
Follow these steps to write a decimal number in standard form.
Example: let's convert the decimal number 0.0000000000893 in standard form.
Step 1: The first non-zero digit is 5.
Step 2: Place the decimal point after 5.
Step 3: The decimal point moves 11 places to the right to obtain the original number.
Step 4: Since the decimal point moves to the right, we write a negative sign on the exponent of 10.
Thus, the standard form of 0.0000000000893 is 8.93 × 1011.
Steps are given in the following to write the expanded form in standard form.
Example: 4 × 105 + 2 × 103 + 7 × 10-2
Example: 4 × 100000 + 2 × 1000 + 7 × 0.01
Example: 400000 + 2000 + 0.07
A rational number p/q is expressed in its standard form when
To convert a given rational number into its standard form, follow these steps
Example: Write the standard form of the rational number 14/21.
Step 1: Identify the given rational number 14/21.
Step 2: The GCD of 14 and 21 is 7.
Step 3: Divide the numerator and the denominator by 7.
(14 ÷ 7) / (21 ÷ 7) = 2/3
Thus, the standard form of 14/21 is 2/3.
Let's go through some examples of standard form and scientific notation.
Represent the distance from the Earth to the Sun in scientific notation.
The distance from the Earth to the Sun is about 93000000 miles.
93,000,000 miles = 9.3 × 107 miles
Write the mass of an electron in standard form.
The mass of an electron is approximately 0.00000000000000000000000000000091 kilograms
0.00000000000000000000000000000091 kg = 9.1 × 10-31 kilograms
Hence, the mass of an electron in standard form is 9.1 × 10-31 kilograms
In this article, we examined the standard form in detail. We learned how to write any form of a number in its standard form. Different solved examples have been provided for you for mastering the standard form. After reading this article, you will be able to represent any number in standard form and understand its significance.