What Is Standard Form and Expanded Form
Decimal numbers can also be written in extended notation using exponential powers of ten. The following are the above examples of converting the extended shape of numbers to standard form. For more examples of the advanced form, see the following table. The extended form can be written for multiples of 10 such as 40, 320, 700. The extended numbers for these numbers are 40 = 4 × 10 + 0 × 1 = 40 + 0, 320 = 3 × 100 + 2 × 10 + 0 × 1 = 300 + 20 + 0, 700 = 7 × 100 + 0 × 10 + 0 × 1 = 700. The standard form has a slightly different meaning in algebra. When it comes to basic equations, the standard form refers to an equation equal to zero. When it comes to polynomials, the standard form refers to the arrangement of terms from the highest to the lowest degree. To add the extended form, the individual numbers must be written in extended form and adding similar terms will result in the final response being added. Let`s understand this by adding two numbers 4896 + 3284 = (4000 + 800 + 90 + 6) + (3000 + 200 + 80 + 4) = (4000 + 3000) + (800 + 20) + (90 + 80) + (6 + 4) = 7000 + 1000 + 170 + 10 = 8000 + 170 + 10 = 8180. To write the decimals in extended form, we multiply each of the decimals by increasing the exponent values by (1/10). Let`s try to understand this with the help of a simple example of a decimal number.
The decimal number 0.437 can be written in extended form as 4 × (1/10) + 3 × (1/10)2 + 7 × (1/10)3 = 4 × (1/10) + 3 × (1/100) + 7 × (1/1000) = 0.4 + 0.03 + 0.007. A fraction, a percentage value can be converted to a decimal number and the same can be written in the extended form. A fraction of 1/7 in the decimal form would be 0.1428, 0.1428 in the extended form would be 0.1428 = 1 × (1/10) + 4 × (1/10)2 + 2(1/10)3 + 8(1/10)4. And a percentage of 25% would be 0.25 = 2 × (1/10) + 5 × (1/10)2 To multiply the extended form, we must first write the numbers in the extended form, then multiply each of the components, and then add the numbers together. Let`s understand this with the help of the product of two numbers. 423 × 12 = (400 + 20 + 3) × (10 + 2) = 400 × 10 + 20 × 10 + 3 × 10 + 400 × 2 + 20 × 2 + 3 × 2 = 4000 + 200 + 30 + 800 + 40 + 6 = 4000 + (200 + 800) + (30 + 40) + 6 = 4000 + 1000 + 70 + 6 = 5000 + 70 + 6 = 5076. Trying to learn a number with a higher number of digits is very difficult without knowing how to express it in an extended form. The extended form helps us to know the constituent elements of the higher numbers.
Each of the numbers can be written in the different forms of 1, 10, 100, 1000. Now, let`s continue with this understanding to learn more about the extended form. When talking about integers, the standard form refers to an integer written as a number, while the word form describes an integer that is spelled as a word. The extended form uses different numbers in an equation to express the integer. In extended forms, we only use addition between place value numbers and in extended notation, we use addition and multiplication. Every number we read is broken down. This process is called a number extension. After disassembly in the extended form, we interpret the number in its standard form. The following points help us to better understand the extended form. The way the integers are formed defines the number well. The value of each digit in mathematics can be written in extended form.
The indication of the number as the sum of each digit multiplied by its place value is the extended form of a number. Let`s look at the example of the extended form 1,278 = 1,000 + 200 + 70 + 8. 5683 = 5 × 1000 + 6 × 100 + 8 × 10 + 3 × 1 = 5000 + 600 + 80 + 3. Therefore, the extended form is 5000 + 600 + 80 + 3. Decimals also have location values. A decimal number can be extended because the extended form is not the same as the extended notation. The extended notation of a number is represented by the sum of each digit of a number multiplied by its space value. In the worksheet on forming numbers with numbers, the questions help us train to form different types of smaller and larger numbers with different numbers. We know that all numbers are formed with the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. We need an extended form to better understand the given number.
The value of each digit according to its space value can be understood from the extended shape. In the initial phase of learning numbers, the advanced form is very useful to better know each of the digits of the number. The extended form helps us to better understand a given number in mathematics. Let`s take an example of the number 875294831. It is difficult to understand this figure. Here, an advanced form helps us understand each of the numbers based on their space value. Let`s take a simple number 324 and try to find its extended form. 324 is written in extended form as 300 + 20 + 4. This means that in this number there are three hundred, two tens and 4.
We can easily understand the meaning of each digit of a number thanks to its extended shape. The extended form is useful for dividing and representing the upper number of digits in its units, tens, hundreds, thousands. An advanced form allows you to better understand numbers with higher digits and read them correctly. A number of the form 10030 is sometimes difficult to understand directly and can be represented in extended form as 10030 = 10,000 + 30. An extended form is to divide a number and write it in its form thousand, hundred, ten, and unit. An advanced form is useful for knowing the space value of each of the digits. To understand the extended form, we check with a simple form of writing the extended form of the number 6809. Here we write 6859 = 6000 + 800 + 50 + 9 and that means 6 thousand, 8 hundred, 5 dozen and 9 units.
The original form of the number “234” is called the standard form. The number 4,981 can be written in extended form as follows: Here is the list of topics closely related to the extended form. These topics will also give you an overview of how these concepts are handled in Cuemath. In extended notation, a number is represented as the sum of each digit multiplied by its space value, while in extended form, the addition is used only between the place value numbers. For example: Example 3: In the extended form of the number 4569023 the number 9 means 9? Select the correct answer from the following options. Here we will convert the extended form into the standard form of a number. Write the decimal number 536,072 in extended notation. Writing a number in extended notation means displaying the location of a number in exponential powers of ten. The extended expression form is also possible for a decimal number. For a decimal number, each of the decimal places is written as an exponent of one tenth. The decimal number 0.436 can be written in extended form as 0.436 = 4 × (1/10) + 3 × (1/10)2 + 6 ×(1/10)3 = 4 × (1/10) + 3 × (1/100) + 6 ×(1/1000) = 0.4 + 0.03 + 0.006. .