What is a standard form?
The standard form is a technique representing very large or very small numbers in an easily readable format. For example, if you have a 5000, you can write it as 5 x 10³.
This idea is known as the standard form. You can use this same technique to write Small numbers as well. However, in the case of small numbers index will be negative. In the example of 5 x 10³, the index is 3.
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Rule to express numbers in standard form:
- The rule to write any number in a standard form is that you have to write down a number between 1 and 10, then you write × 10(to the power of a number).
- According to the United Kingdom rules, the standard form of a number is also known as scientific notation.
- In the united states, the standard form is the normal way of writing numbers in decimal representation. For example, if we have the number 975. We can expand it: 900 + 70 +5
- written form = nine hundred seventy-five.
A standard form is a crucial form of representing numbers when scientists work with the speed of light and distances among various galaxies. In microbiology, the size of bacteria can be expressed in a standard form as they are so minute.
How to write numbers in standard form in mathematics?
There are various ways to express numbers in standard form. Some of them are given below:
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Use a standard form calculator
The easiest and the simplest way to express numbers in standard form is to use an online tool. This standard form converter is one of the best solutions to converts any number in the following standard form:
- Scientific notation
- Real number or general equation
- Engineering notation
This online converter is functioned to accept the values in exponential as well as decimal form. It performs the conversion of all the given numbers to a standard form in a fraction of seconds.
- You have to Enter the given number in the input box.
- Get on the Convert button and let the process begin.
- This standard form calculator will convert the entered number into Scientific Notation, Real Number, E-Notation, and Engineering notation after few seconds.
Standard forms and power of 10
To write the numbers in standard form, we use the decimal place value system. This system is based on powers of 10 and has the following possible forms:
- 100 = 1
- 101 = 10
- 102 = 100
- 103 = 1000
- 109 = 1000000000
- And goes on……
The standard form of large numbers
If you have a certain number, let’s suppose you have: 91 900 000 000 000 how can you express, it is a standard form?
Follow a set of rules to express it in a standard form:
- First of all, Write the first number, which is:
- In the second step, add the decimal it: 9.
- Now count the total number of digits that are present after 9. There is a total of thirteen digits after 8.
- Write it in the exponential form with raised to the power of 10: 9.19 x 10¹³.
- Hence the standard form of 91 900 000 000 000 is 9.19 x 10¹³.
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The standard form of smaller numbers
If you have a very small number like 0.000 0019, how will you write it in a standard form?
- First of all, filter out the first non-zero digit that is 1
- Now add the decimal point to the first non-zero digit: 1.
- Note that the initial position of the decimal point. Count the numbers between the initial and final place of the decimal.
- In this case, there are six digits.
- Consequently, the standard form will be: 0.000 0019 is 1.9 ×10ˉ⁶ for smaller values; we use negative signs with exponents’ power.
The standard form of decimal numbers
If you have any decimal number such as 8999.9, then it can be expressed in standard form as follow:
- First of all, move the decimal to the desire position. So 8999.9 will become 8.999.
- In this example, we have moved it to 3 points. So standard form of this decimal number will be 8.999 × 103
The standard form of an equation
To represent the equation in the standard form, its right side should be equal to zero.
- (any expression) = 0
- So if we have x2 = 10 then its standard form will be x2 − 10 = 0.
The standard form of a linear equation
Standard form of Linear equation is = Ax + By = C.
If we have y = 3x + 1, how will it be expressed in a standard form?
- We will move 3 to the left side of the equation: −3x + y = 1
- Now we will multiply both sides by -1: 3x − y = −1
The standard form of a quadratic equation
Standard form of Quadratic equation is ax2 + bx + c = 0
If the given equation is: x(x−1) = 6, then it can be converted into standard form as follow:
- First of all, we will expand the equation by simplifying it: x2 − x = 6
- Now we will move the 6 to the left side of the equation. This displacement will change the sign of 6: x2 − x − 6 = 0
- So the standard form of quadratic equation is: x2 − x − 6 = 0.
The standard form of one million
- We write one million as 1000000
- There are a total of 6 zero and one non-zero digit.
- Hence, we will express it: 1 x 10 610 is exponent 1 is the base number, and 6 is the exponent power representing the zeros of one million.
- To represent the fraction to a standard form, you have to multiply it to eliminate fractions.
- The numerator and denominator of a fraction should be co-prime to express it in a standard form.
- Additionally, there must be a common factor as well in numerator and denominator.
A standard form is the flawless demonstration of mathematical numbers. It follows precise rules to make the complex numbers easy to read.
Though it takes in some difficulties to write complex numbers into standard form, and for that reason, you can use a standard form calculator for quick and accurate results.