The extended form is a way to rewrite a number by breaking it down into separate digits, showing what place value each digit represents. Writing numbers in extended form is pretty straightforward once you understand what it is.
Steps
Part 1 of 5: Transforming the Standard Form into the Extended Form
Step 1. Look at the number written in standard form
Read the number and see how many digits make it up.
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Example: Write 5827 in extended form.
- Read the number mentally or aloud: five thousand eight hundred twenty-seven.
- Note that this number consists of four digits. As a result, the extended form will consist of four parts.
Do Expanded Form Step 2 Step 2. Separate the digits
Rewrite the number so that all its digits are separated by the + sign. Leave some space between each digit and the + that follows it. You will have to write more.
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Example: The number 5827 for now becomes:
5 + 8 + 2 + 7
Do Expanded Form Step 3 Step 3. Identify each place value
Each digit of the original number corresponds to a specific position value. Starting with the rightmost digit, name each digit with the appropriate place value.
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Example: Since this number consists of four digits, you will need to identify four positional values.
- The rightmost digit is 7 and represents units (1).
- The next digit is 2 and represents the tens (10).
- The third digit is 8 and represents hundreds (100).
- The fourth and final digit is 5 and represents thousands (1000).
Do Expanded Form Step 4 Step 4. Multiply each digit by the correct place value
Multiply each single digit by the number that represents the positional value the digit occupies in the original number.
Example: [5 * 1000] + [8 * 100] + [2 * 10] + [7 * 1]
Do Expanded Form Step 5 Step 5. Write the final answer
When you have multiplied all the digits, you will get the extended form of the original number.
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Example: The extended form of 5827 is:
5000 + 800 + 20 + 7
Part 2 of 5: Transform the Written Form into the Extended Form
Do Expanded Form Step 6 Step 1. Look at the number in writing
Read the number. When a number is expressed in this form, you should be able to identify the full value of each individual digit.
Example: Write in extended form: seven thousand two hundred eighty-nine
Do Expanded Form Step 7 Step 2. Identify all positional values
Write each digit separately, inserting the correct place value after it. This value is simply the one already indicated next to the number. Insert the + sign between the various values.
- Note that you will not find explicitly written "tens" and "units", but you will have to understand that they are there. You can indicate that you understand this by writing the name of the place value in parentheses, but this is not strictly necessary.
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Example: The number seven thousand two hundred eighty-nine becomes:
- seven thousands + two hundred + eighty (dozens) + nine (unit)
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- seven thousand + two hundred + eighty + nine
Do Expanded Form Step 8 Step 3. Rewrite in numerical form each positional value expressed in word
Look at each part separately. Rewrite each value you read in numbers.
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Example: Seven thousand + two hundred + eighty + nine:
- Seven thousand = 7000
- Two hundred = 200
- Eighty = 80
- Nine = 9
Do Expanded Form Step 9 Step 4. Write the final answer
You now have all the data you need to rewrite the number in extended form.
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Example: The extended form of seven thousand two hundred eighty-nine is:
7000 + 200 + 80 + 9
Part 3 of 5: Extended Form with Decimals
Do Expanded Form Step 10 Step 1. Look at the number in standard form
Read the number and count how many digits it consists of, paying particular attention to the digits written after the comma (to its right).
- Example: Rewrite 531, 94 in extended form.
- Read the number: five hundred thirty-one point ninety-four.
- Note that there are three digits before the comma (or decimal point) and two digits after the comma. So there will be five numbers making up the extended form.
Do Expanded Form Step 11 Step 2. Separate the digits
Rewrite the number by separating all digits with the + sign. For now, write the comma too.
- Note that the comma will be deleted eventually, but you may want to keep it for now to avoid getting confused as you troubleshoot the problem.
- Leave some space between each digit and the + that follows it. You will have to write more.
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Example: The number 531, 94 for now becomes:
5 + 3 + 1 +, + 9 + 4
Do Expanded Form Step 12 Step 3. Identify the name of each place value
Give each digit the name of the place value that corresponds to its position in the original number.
- When dealing with the numbers before the comma (to the left of it), start with the one closest to it.
- When dealing with the numbers after the decimal point (to the right of it), start with the one closest to it.
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Example: You will need to identify three positional values to the left and two to the right of the comma.
- For the values on the left:
- The number closest to the comma is 1, which corresponds to the units (1).
- The next number is 3, which corresponds to the tens (10).
- The third number is 5, which corresponds to hundreds (100).
- For the values on the right:
- The number closest to the decimal point is 9, which corresponds to tenths (10).
- the second number is 4, which corresponds to cents (100).
Do Expanded Form Step 13 Step 4. Multiply the digits to the left of the comma by the place value
All digits to the left of the decimal point must be multiplied by the corresponding position value. Do it now.
Example: [5 * 100] + [3 * 10] + [1 * 1] = 500 + 30 + 1
Do Expanded Form Step 14 Step 5. Divide the digits to the right of the comma by the place value
All digits to the right of the comma must be divided by the corresponding place value. Do it now.
Example: [9/10] + [4/100] = 0, 9 + 0, 04
Do Expanded Form Step 15 Step 6. Write the final answer
Write all the values you found separating them with the + sign. Delete the comma. This will be the final answer.
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Example: The extended form of 531, 94 is:
500 + 30 + 1 + 0, 9 + 0, 04
Part 4 of 5: Adding Numbers in Extended Form
Do Expanded Form Step 16 Step 1. Look at the problem
Verify that you need to add the extended forms of two or more numbers. If the problem is expressed in both numbers and words rather than just numbers, find the matching numbers and write them in extended form.
- If you are given numbers in written or standard form, but need to calculate with numbers in extended form, rewrite all numbers in extended form before proceeding.
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Example: Add [500 + 30 + 6] and [80 + 2].
Rewrite the problem like this: 500 + 30 + 6 + 80 + 2
Do Expanded Form Step 17 Step 2. Separate numbers by place value
Identify all the numbers that represent the units, then all the tens, all the hundreds, etc. Continue like this to identify all the numbers present. Rewrite the calculation so that all numbers belonging to the same place value are grouped together.
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Example: For 500 + 30 + 6 + 80 + 2:
- Hundreds: 500
- Tens: 30 + 80
- Units: 6 + 2
Do Expanded Form Step 18 Step 3. Add each group of positional values separately
Add up all the numbers in each group. Start with the units and work your way up to the highest place value in order.
- Note that if the sum of a place value exceeds the number of digits that place value is made up of, you will need to add one digit to the next category.
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Example: Start with the units, then proceed with the tens and then with the hundreds.
- 6 + 2 = 8
- 30 + 80 = 110; since this value exceeds the category of tens, you must separate it into 100 + 10; the 10 stays here, while you have to add the 100 to the next category as follows:
- 500 + 100 = 600
Do Expanded Form Step 19 Step 4. Write the final answer
Reorder the totals of each category by separating them with the + sign. This is the extended form of the result.
- If you want to write the result in standard form, all you have to do is add all the digits.
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Example: 500 + 30 + 6 + 80 + 2 = 600 + 10 + 8
In standard form, the result would be 618
Part 5 of 5: Subtracting Numbers in Extended Form
Do Expanded Form Step 20 Step 1. Look at the problem
Make sure you are told to subtract the extended forms of two numbers. If the numbers are expressed in written form, find the matching numbers and write the subtraction in extended form.
- Note that you must rewrite all numbers expressed in standard or written form if the problem explicitly asks you to provide the answer in extended form.
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Example: Subtract [500 + 70 + 1] from [800 + 10 + 4].
- Rewrite as: [800 + 10 + 4] - [500 + 70 + 1]
- O: 800 + 10 + 4 - 500 - 70 - 1
Do Expanded Form Step 21 Step 2. Separate numbers by place value
Identify all the numbers belonging to the different categories (units, tens, hundreds, thousands, etc.). Rewrite the calculation so that all numbers belonging to the same place value are grouped together.
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Example: For [800 + 10 + 4] - [500 + 70 + 1]:
- Hundreds: 800 - 500
- Tens: 10 - 70
- Units: 4 - 1
Do Expanded Form Step 22 Step 3. Subtract each group separately
Subtract the numbers of each place value. Start with the lowest category (the units) and work your way up to the highest one.
- If the minuend is less than the subtract, you will need to take out a loan from the next category. For example, take "10" from the tens if the numbers in the units cannot be subtracted without taking out a loan.
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Example: Start with the units, then proceed with the tens, then with the hundreds.
- 4 – 1 = 3
- 10 - 70; since "70" is greater than "10," you will have to take "100" from "800" and add it to "10," transforming the calculation into: 110 - 70 = 40
- 700 - 500 = 200; "800" became "700" as you borrowed "100" to add to the tens.
Do Expanded Form Step 23 Step 4. Write the final answer
Reorder the results of each category by separating them with the + sign. This is the extended form of the result.
- To find the standard form of the result, all you have to do is add up all the digits that make up the extended form.
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Example: [800 + 10 + 4] - [500 + 70 + 1] = 200 + 40 + 3
In standard form, the result would be 243
