How To Convert Numbers into Standard Notation?

How To Convert Numbers into Standard Notation

The standard form usually refers to the general agreement in a way things are denoted & written. Generally, this term is utilized in scientific and technical areas of study such as physics, chemistry, mathematics, and biology. But it can also be used in economics, business sectors. The basic purpose of using this notation is to express the numbers that are too small or too large. In the United Kingdom, it is also known as standard index form and scientific form. No doubt, conversion of too large & small values is difficult. But you don’t have to worry about the conversion of these types of numbers. Use an online standard form that helps you convert the numbers into standard form within a few seconds.

What is Standard Form or Standard Notation?

Scientific notation is said to be a standard way of representing any sort of number as the product of the real number along with the power of “10”. The standard form is expressed as:

A x 10b

In this form, a is said to be the coefficient, and b would be the exponent. Here the coefficient is known as an integer to the left side of the decimal point plus a mantissa. Here the mantissa represents the significant digits to the right of the decimal point. Below is an example of scientific notation along with the labeling of the important parts:

X = -5.7853 x 105

The conversion of large & small numbers seems to be difficult, but the truth is different from your estimation. The easiest way of converting the larger or smaller number is to make use of a standard notation calculator. Most scientists & mathematicians prefer to use the standard form calculator because it quickly converts the large and small values within a matter of seconds.

Why Scientific Notation?

Consider the following expression as an example to understand why scientific notation is important. By the below-mentioned example, you will understand its importance to physicists and engineers.

Example # 1:

Qe = 0.00000000000000182 c

Now, look at all the “zeros” in this number. Here, this expression is the charge on a single electron, and “C” stands for Coulomb, which is known to be the electrical charge. In its actual form, this number is difficult to deal with, but it may be easier if it is converted in the form mentioned below:

qe = 182 x 10-19

If you find the conversion for these types of expressions, then you can consider using the standard form equation calculator for the conversion. This standard form calculator helps you to write the standard form equation into its ordinary form.

To understand its importance more clearly, have a read to another example, which is mentioned below. Sometimes, the mass of the earth in kg (kilograms) is used to compute the gravitational problems. Below it is in its raw form:

Example # 2:

Mass of the Earth: 5976300000000000000000000000 kg (kilograms).

Again, this number is also an unwieldy number, but you can express it in an easy form as follows:

Earth’s Mass = 5.9763 x 1024 Kg (Kilograms)

By reading these examples, we finally understand that the conversion of hard-to-read values to standard form is the easiest way to remember and write numbers too large and small. The manual procedure of converting numbers to standard notation takes a lot of time because of its complex procedure. Simply try the online standard form calculator to perform these calculations.

A Few Important Rules to Convert the Numbers to Standard Notation

  • The base of the number must be 10 always.
  • The absolute value for the coefficient is greater than and sometimes equal to 1 and strictly less than 10.
  • The exponent of the expression is always a non-zero integer.
  • The coefficient of the number carries positive or negative signs.

The mantissa carries the remaining significant digits.

By following these tips or rules, you can easily convert the hard-to-read and use numbers. For ease, make use of the “convert to standard form calculator” that lets you know how to convert the difficult to use numbers.

How to Convert the Number to Standard Form Manually

The standard form for a number would be as a x 10b, where the alphabet “a” represents a number, which can be 1 ≤ |a| < 10. While “b” is the power of 10 that is required. So that the standard notation is known to be mathematically equivalent to the original number.

  1. Move the decimal point of the number until the non-zero digit is at the left of the decimal point. The resultant figure would represent “a”.
  2. Now, you need to count the number that you move the decimal point. The number you count would be “b”.
  • If you move the decimal to the left to the left of b, it is positive.
  • If you require to move the decimal to the right of the b, then b is said to be negative.
  • If you don’t want to move the decimal, then b would be equal to zero.
  1. By following the above procedure for representing hard-to-read numbers or figures, you can easily write the number you’re working on as a x 10b. You can read this number  as “a time 10 to the power of b”.
  2. Now, remove only the trailing zeros when they were left of the decimal point.

Thankfully, now you know how you can convert the unreadable numbers to standard form. The following procedure seems to be difficult if you don’t follow it correctly. However, if you don’t want to follow this complex procedure, you have the option to use the standard form calculator that simply converts the complex numbers into their standard form.

Final Words

In this guidepost, the focus of the discussion is how to convert the numbers that are a bit difficult to deal with. In the post, we mentioned a few rules that can help you write the numbers into standard notation. We also mentioned the manual procedure for the conversion, which is a bit complex. But no worries, give a try to an online standard form calculator that lets you know how to convert the numbers into standard form.


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