A Standard Form Calculator is an online tool or application that helps you to convert a decimal number into standard form, also known as scientific notation. Standard form is a way of representing a number as a product of a decimal number between 1 and 10 and a power of 10. For example, the number 3,400,000 can be written in standard form as 3.4 x 10^6.
Enter Information:
The formula to convert a decimal number to standard form, also known as scientific notation, is:
a x 10^n
Where:
"a" is a decimal number between 1 and 10 (excluding 10).
"n" is an integer representing the number of places the decimal point must be moved to obtain the standard form.
To convert a decimal number to standard form using this formula, you should follow these steps:
Determine the decimal number "a" by moving the decimal point to the left or right until the number is between 1 and 10 (excluding 10).
Count the number of places the decimal point was moved. If the decimal point was moved to the left, the exponent is positive, and if it was moved to the right, the exponent is negative.
Write the decimal number "a" followed by the multiplication symbol "x" and the base number 10 raised to the power of the exponent "n" (i.e., 10^n).
What is the standard form?
In mathematics, standard form usually refers to two different concepts depending on the context:
- Standard form of a linear equation: The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and x and y are variables. In this form, the coefficients A and B are usually integers, and A is positive.
- Standard form of a number: The standard form of a number is a way of writing a number using digits and place value. For example, the number 345,678 in standard form is written as 3.45678 x 10^5, where 3 is the digit in the hundred thousands place, 4 is the digit in the ten thousands place, and so on.
In general, standard form is a way of expressing something in a standardized or consistent way, often to make it easier to compare or manipulate.
Standard form format:
The standard form format for a linear equation is:
Ax + By = C
where:
- A, B, and C are constants (numbers)
- x and y are variables
- A and B cannot both be zero
- A must be positive (this convention is not always followed, but it is the most common one)
For example, the standard form of the linear equation y = 2x – 3 is:
-2x + y = -3
Note that we rearranged the terms to put the equation in standard form. Also, we could have multiplied both sides of the equation by -1 to make A positive, but that is not necessary. The important thing is that A, B, and C are constants, and the equation is written in the form Ax + By = C.
How to write in standard form?
To write a linear equation in standard form, follow these steps:
- Rearrange the equation so that the x and y terms are on the left side, and the constant term is on the right side.
- Make sure that the coefficient A of the x term is positive. If it’s negative, multiply both sides of the equation by -1 to make it positive.
- Check that the coefficients A and B are integers. If they are not, multiply both sides of the equation by a common denominator that makes them integers.
- If there are fractions in the equation, clear them by multiplying both sides of the equation by the least common multiple of the denominators.
- Simplify the equation by dividing all the terms by the greatest common factor of the coefficients A, B, and C.
- Write the equation in the form Ax + By = C, where A, B, and C are integers and A is positive.
For example, suppose we have the equation y = -3/4 x + 2. To write it in standard form, we can follow these steps:
- Rearrange the equation: 3/4 x + y = 2
- Make A positive: multiply both sides by -4/3: -x – 4/3 y = -8/3
- Clear the fractions: multiply both sides by 3: -3x – 4y = -8
- Simplify: divide both sides by 1 (the GCF): 3x + 4y = 8
- Write in standard form: 3x + 4y = 8
Note that in step 5, we wrote the equation in the form Ax + By = C, where A, B, and C are integers and A is positive.