There are many number formats which are referred to as the “standard form”. The method used to write numbers in standard form varies according to the type of standard form they are referring to.
Steps
Method 1 of 4: Extended Form to Standard Form
Step 1. Look at the problem
A number written in extended form will be very similar to an addition problem. Each value is rewritten separately, but all must be joined by the plus sign.
Example: Write the following number in standard form: 3000 + 500 + 20 + 9 + 0, 8 + 0, 01
Step 2. Add the numbers
Since the extended form looks like an addition, the simplest way to rewrite the number in standard form is to simply add all the digits.
- Essentially, you will remove all zeroes (0) and combine the remaining digits.
- Example: 3000 + 500 + 20 + 9 + 0, 8 + 0, 01 = 3529, 81
Step 3. Write the final answer
You should have obtained the standard form of the number previously written in extended form, which represents the final answer to this type of problem.
Example: The standard form of the given number is: 3529, 81.
Method 2 of 4: from Written Form to Standard Form
Step 1. Look at the problem
Instead of being written in numbers, the number is written in word.
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Example: Write in standard form seven thousand nine hundred forty-three comma two.
The number "seven thousand nine hundred and forty-three comma two" is expressed in word and you have to rewrite it in standard form. You will need to rewrite the number in digits before turning it into standard form for the final answer
Step 2. Write each part numerically
Look at each value written in word separately. Considering them one at a time, write all the mentioned numerical values separately, separating them with the plus sign.
- When you have completed this step, you will have the number expressed in extended form.
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Example: seven thousand nine hundred forty-three point two
- Separate each value: seven thousand / nine hundred / forty / three / two tenths
- Write them all in numbers:
- Seven thousand: 7000
- Twentieth century: 900
- Forty: 40
- Three: 3
- Two tenths: 0, 2
- Combine them all in the extended form of the number: 7000 + 900 + 40 + 3 + 0, 2
Write Numbers in Standard Form Step 6 Step 3. Add the numbers
Convert the extended form you just found to the standard form by adding all the numbers.
Example: 7000 + 900 + 40 + 3 + 0, 2 = 7943, 2
Write Numbers in Standard Form Step 7 Step 4. Write the final answer
At this point, you will have obtained the number written in standard form. This is the final answer to this type of problem.
Example: The standard form of the given number is: 7943, 2.
Method 3 of 4: Scientific Notation
Write Numbers in Standard Form Step 8 Step 1. Look at the number
While this is not always the case, most numbers that need to be rewritten with scientific notation are either very large or very small. The original number must already be expressed in numbers.
- This form is called "standard form" in the UK, while in other countries it is referred to as "scientific notation".
- The general purpose of this notation is to write very large or very small numbers in an abbreviated, easy-to-write format. However, technically it is possible to rewrite any number with more than one digit in scientific notation.
- Example A: Write the following number in standard form: 8230000000000
- Example B: Write the following number in standard form: 0, 0000000000000046
Write Numbers in Standard Form Step 9 Step 2. Move the comma
Move the comma left or right as needed until it is directly after the very first digit of the number.
- When doing this, be sure to pay attention to the original position of the comma. You need to know this information to proceed to the next step.
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Example A: 8230000000000> 8, 23
Even if the comma is not visible, it is implied that there is one at the end of each number
- Example B: 0, 0000000000000046> 4, 6
Write Numbers in Standard Form Step 10 Step 3. Count the spaces
Look at both versions of the number and count how many spaces you moved the comma. This number will be the index in the final answer.
- The "index" is the exponent of the multiplier in the final answer.
- When you move the comma to the left, the index will be positive; when you move it to the right, the index will be negative.
- Example A: The comma has been moved 12 places to the left, so the index will be 12.
- Example B: The comma has been shifted 15 places to the right, so the index will be -15.
Write Numbers in Standard Form Step 11 Step 4. Write the final answer
Include the rewritten number and index multiplier when writing the final answer in standard form.
- The multiplier is always 10 for numbers expressed in scientific notation. The calculated index is always placed to the right of 10 as an exponent in the final answer.
- Example A: The standard form of the given number is: 8, 23 * 1012
- Example B: The standard form of the given number is: 4, 6 * 10-15
Method 4 of 4: Standard Form of Complex Numbers
Write Numbers in Standard Form Step 12 Step 1. Look at the problem
This must include at least two numeric values. One will be a real integer, while the other will be a negative number under the root (square root symbol).
- Keep in mind that two negative numbers give a positive result when multiplied together, as do two positive numbers. For this reason, any number squared (that is, multiplied by itself) will give a positive result, regardless of whether it is a positive or negative number. Therefore, in "real" terms it is not possible for the number under the square root to be negative, since that number should, it is supposed, be produced by squaring a smaller number. When a negative value that is considered impossible occurs, as in this case, you have to handle it in terms of imaginary numbers.
- Example: Write the following number in standard form: √ (-64) + 27
Write Numbers in Standard Form Step 13 Step 2. Separate the real number
This must be placed at the beginning of the final answer.
Example: The real number included in this value is 27 ', since it is the only part that is not under the square root
Write Numbers in Standard Form Step 14 Step 3. Find the square root of the integer
Look at the number under the square root. While it is not possible to calculate the square root of a negative number, you should be able to calculate the square root of the number as if it were positive rather than negative. Find that value and write it down.
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Example: The number under the square root symbol is -64. If the integer were positive rather than negative, the square root of 64 would be 8.
- Writing it another way, we could say:
- √(-64) = √[(64) * (-1)] = √(64) * √(-1) = 8 * √(-1)
Write Numbers in Standard Form Step 15 Step 4. Write the imaginary part of the number
Combine the newly calculated value with the imaginary number indicator i. When written together, these two elements make up the part consisting of an imaginary number in the standard form.
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Example: √ (-64) = 8 i
- The i is another way of writing √ (-1)
- If you consider that √ (-64) = 8 * √ (-1), you can see that this becomes 8 * i or 8i.
Write Numbers in Standard Form Step 16 Step 5. Write the final answer
At this point you should have all the necessary data. First write the part made up of the real number and then the part made up of the imaginary number. Separate them with a plus.
Example: The standard form of the given number is: 27 + 8 i
