A free online calculator that displays standard form numbers is called the Standard Form Calculator. A number can either be expressed as an integer or as a decimal. With STUDYQUERIES’s online standard form calculator tool, the conversion is faster and easier, and it displays the standard form of the number in a fraction of a second.

How to Use Standard Form Calculator?

Here are the steps for using the standard form calculator:

  • Step 1: Enter the number as an integer or decimal into the input box
  • Step 2: After clicking “Convert,” the conversion process will begin
  • Step 3: In the output field, the number is displayed in its standard form.

Standard Form Calculator

What is Standard Form?

A standard form is a way to write a mathematical concept, like an equation, a number, or an expression in a way that follows certain rules.

4.5 billion years is written as 4,500,000,000 years

As you can see, writing a large number like 4.5 billion in its number form is not only ambiguous but also time-consuming, and there is a possibility that we might write a few 0’s less or more while writing it. We use the standard form to represent extremely large or extremely small numbers efficiently.

Standard Form Rules

It follows certain rules to write a mathematical concept such as an equation, number, or expression in the standard form.

In standard form, the formula varies based on what kind of concept it refers to.

For example, the standard form of 4,500,000,000=4.5×1094,500,000,000=4.5×109

What about the fractions 14/22 and 13/6? Are these standard forms of fractions?

To ensure that fractions are in the standard form, the numerator and denominator must be prime.

The standard form or the simplest form of the fraction 14/22 has no common factors other than 1. Therefore, the fraction has a standard form of 7/11.

As 13 and 6 are co-primes, 13/6 already has its simplest form in mind.

The above examples illustrate the standard way of writing decimal numbers and fractions.

How do we write in Standard Form?

Depending on where you live, the standard form has different meanings. Standard form is another name for the scientific notation in the United Kingdom and other countries that use UK conventions.

3890=3.89×10³

In the United States and countries using US conventions, the standard form is the usual way of writing numbers in decimal notation.

Standard form =3890

Expanded form =3000+800+90=3000+800+90

Written form = Three thousand eight hundred and ninety

The next step is to study the standard form in algebra. There are several topics covered in standard algebra form, such as polynomials, linear and quadratic equations. Let’s start with polynomials.

Standard Form of a Polynomial

Consider the algebraic expressions:

Polynomial
Polynomial

Can you identify the correlation between all these expressions?

Each of these is a polynomial. Unlike the last two examples, the first two are written in standard form.

Polynomials are written in standard form by following a few simple rules.

  • Put the terms in descending order of their powers (also known as exponents).
  • Do not include terms that are similar in the polynomial.

The standard form is:

Standard Form of a Polynomial
Standard Form of a Polynomial
Standard Form of Polynomial
Standard Form of Polynomial

How to Write Polynomials In Standard Form?

In the standard form of a polynomial, terms are grouped, added, subtracted, and rearranged with decreasing exponents.

Here are the steps to write a polynomial in standard form:

  • You need to write down the terms.
  • Organize all the similar terms.
  • Calculate the exponent.
  • The term with the highest exponent should be written first.
  • In decreasing order, write the remaining terms with lower exponents
  • Put a constant (a number without variables) at the end.

Standard Form of a Linear Equation

The “Standard Form” for writing down a Linear Equation is Ax + By = C

A shouldn’t be negative, A and B shouldn’t both be zero, and A, B, and C should be integers.

Example: Put this in Standard Form: y = 3x + 2

Bring 3x to the left: −3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

This form: Ax + By + C = 0

is sometimes called “Standard Form”, but is more properly called the “General Form”.

Standard Form of a Quadratic Equation

The “Standard Form” for writing down a Quadratic Equation is ax² + bx + c = 0, (a not equal to zero)

Example: Put this in Standard Form: x(x−1) = 3

Expand “x(x-1)”: x2 − x = 3

Bring 3 to left: x2 − x − 3 = 0

Note: a = 1, b = −1, c = −3

Standard Form of a Parabola

A parabola is the graph of a quadratic function. The standard form of the parabola is: f(x)=ax²+bx+c

Standard Form of a Parabola
Standard Form of a Parabola

Note: It contains only one squared term.

The word parabola comes from para meaning “beside” and bol meaning “throw” (from the verb ballein). Graphs of two typical parabolas are shown below; their x and y-intercepts are marked by green dots, and their vertex is marked by blue dots.

For any quadratic polynomial ax²+bx+c=y where a≠0, the graph will have one of the two shapes as shown above.

  • When a > 0, it represents the first parabola (figure 1) which opens upward (U-shaped).
  • When a < 0, we obtain a parabola that opens downward (inverted U-shaped) as shown in figure 2

When we put y = 0 in the above equation, we get the x-intercept, which can also be called the root of the equation: ax2+bx+c=0

Axis of Symmetry In a Parabola
Axis of Symmetry In a Parabola

Finding the roots provides us with the turning point of the parabola.

The vertical line which is drawn from the turning point is called the axis of symmetry. It is calculated using the formula: x=−b/2a

Example: For the equation x²+3x−4=0, the equation of the axis of symmetry is x=−b/2a=−3/2.

Frequently Asked Questions About Standard Form Calculator

What is a standard form calculator?

The Standard Form Calculator is a free online tool that displays the number in standard form. Integer numbers or decimal numbers can be used. Using STUDYQUERIES’s online standard form calculator tool, you can convert numbers faster and easier, and it displays the standard form of the number in a fraction of a second.

How do you write 3000000 in standard form?

To get to “standard” scientific notation, we move the decimal point so there is only one non-zero digit in front of the decimal point. So, 3,000,000 becomes 3.000,000 .

How do you write 0.00147 in standard form?

It can be written as 1.47×10-³.

What are standard form numbers?

We call a number that can be written as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, a standard number. 1.98 ✕ 10¹³; 0.76 ✕ 10¹³ are examples of numbers in standard form.

What is the standard form of -1?

The standard form of -1 is 1.