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Introduction to Decimal Number System
In mathematics, the decimal number system is the system in which every real number is represented by a unique sequence of digits, beginning with 0. The decimal number system is also called base 10 because it uses 10 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Expanded Form with Decimals – Definition Applications and Examples.
The number 26.789 can be represented in the decimal number system as 2,679. The number 26.789 can also be represented in the binary number system as 11011.001. The number 26.789 can also be represented in the octal number system as 377.621. The number 26.789 can also be represented in the hexadecimal number system as 1a.bcd.
The Expanded Form of Decimal Numbers
The expanded form of decimal numbers is a way to show a decimal number as a sum of its individual digits multiplied by their respective place values. For example, the number 123.456 can be written as 1 × 10^2 + 2 × 10^1 + 3 × 10^0 + 4 × 10^-1 + 5 × 10^-2.
Decimal Expansion Definition
A decimal expansion is a sequence of digits representing a real number that is written as a decimal. The decimal expansion of a number starts with the number’s digits to the left of the decimal point and continues with 0s to the right of the decimal point if necessary. For example, the decimal expansion of the number 2.3456 is 2.3456, 2.34, 2.3, 2.2, 2.1, 2.0, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0.
How to Write Decimals in Expanded Form?
To write decimals in expanded form, divide the number by 10 and write the remainder above the decimal point. If there is no remainder, write a 0.
Applications of Expanded Form with Decimals
There are a few different ways that expanded form with decimals can be used in the real world. One way is to use it to help with math operations. For example, if a student is trying to subtract two numbers and one of the numbers is in expanded form, the student can use the expanded form to help them solve the problem. Another way to use expanded form with decimals is to help students understand how decimals work. For example, a student might be learning about place value and how to read and write decimals in standard form. Expanded form can be a helpful tool for students as they learn these concepts.
Decimal Expansion Example
To understand the decimal expansion of a number, let’s look at the number 123.
The number 123 can be written as 1.23 × 10^2. This means that the number 123 is equal to 1.23 multiplied by 100, or 1,230.
The number 123 can also be written as 1.23 × 10^1. This means that the number 123 is equal to 1.23 multiplied by 10, or 123.
The number 123 can also be written as 1.23 × 10^0. This means that the number 123 is equal to 1.23 multiplied by 1, or 123.
The number 123 can also be written as 1.23 × 10^-1. This means that the number 123 is equal to 1.23 multiplied by 0.1, or 12.3.
The number 123 can also be written as 1.23 × 10^-2. This means that the number 123 is equal to 1.23 multiplied by 0.01, or 1.23.
Expanded Form with Decimals – Definition Applications and Examples.
