The standard form, or standard index form, is a number writing system that can be particularly useful for working with very large or very small numbers. It is based on the use of powers of 10 to express how big or small a number is.
They are formed when working with the speed of light and the distances between galaxies, which can be enormous. The size of bacteria or atoms can also be referred to in standard form, as they are very tiny. The standard form is also sometimes known as scientific notation.
Equations in the standard form for linear equations in two variables is Ax + By = C. For example, 2x + 3y = 5 is a linear equation in standard form When an equation is given in this form, it is quite easy to find both intersections (x and y). This form is also very useful for solving systems of two linear equations.
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A Rational Number in Standard Form?
A rational number is in its standard form when its denominator is a positive integer and the numerator and denominator have no common factor other than 1. Two rational numbers with the same denominator can be added by adding their numerators with the same denominator.
Procedure to convert rational numbers in standard form
Whenever we have a rational number, first, we will find the H. of the numerator and denominator, if it is 1 i. If the numerator and denominator of the rational number are coprime numbers, then the given rational number is in its standard form.
If the numerator and denominator are not coprime, then we start dividing both the numerator and denominator by the common factor of both of them. We keep dividing the numerator and denominator with the common factors unless we get a numerator. and denominator with H. equal to 1.
How do you express fractions in standard form?
Standard Form of Fractions: If the numerator and denominator are co-prime numbers, the fraction is given in standard form. Two numbers are co-prime if they have no common factor other than 1.40 a4
How to write numbers in standard form:
Example1:-
Write 81 900 000 000 000 in standard form:
81 900 000 000 000 = 8.19 × 1013. It is 1013 because the decimal point has been moved 13 places to the left to get the number in 8.19.
Example 2:-
Write 0.000 001 2 in standard form:
0.000 001 2 = 1.2 × 10-6
This is 10-6 because the decimal point has been moved 6 places to the right so that the number is 1.2
On a calculator, you generally enter a number in standard form as follows:
Enter the first number (the between 1 and 10) Press EXP. Enter the power that 10 is raised to.