What Is Scientific Notation? Definition and Importance

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

Math Antics – Scientific Notation

Why is scientific notation important?

The primary reason why scientific notation is important is that it allows us to convert very large or very small numbers into much more manageable sizes. When these numbers are in scientific notation, it is much easier to work with them. Scientific notation is also important because it ensures calculations that involve large numbers are still accurate, as its often easy to lose track of counting extremely large numbers successfully. For example, someone will likely be much better able to work with 10^10 than 10,000,000,000.

In short, this mathematical form of writing makes it easy to represent large or small numbers in a way thats easily understood and more manageable to work with.

What is scientific notation?

Scientific notation is a way to express numbers that are too big or little to write in basic decimal form. Scientific notation is also referred to as standard form, scientific form or standard index form in some settings. Most frequently used by scientists, mathematicians and engineers, scientific notation allows professionals and others to write very long numbers in a much easier-to-understand manner. When using a scientific calculator, the scientific notation can be implemented by selecting the “SCI” display mode.

Engineering notation, not to be confused with normalized scientific notation, is another type of scientific notation that restricts exponents to multiples of three, whereas normalized scientific notation uses a value to denote any number from one to ten. On scientific calculators, scientific notation is often denoted by the symbol “ENG.”

How does scientific notation work?

The following are several ways in which scientific notation work based on how its being used:

General scientific notation

When simply writing a number in scientific notation to make it easier to read and understand, you would consider the following:

Each exponent, or the number of zeros in a number, represents a “1” in scientific notation. For example, 1,000 has three zeros, so there are three exponents in this number and it would be written as 10^3 in scientific notation. Similarly, 10^0 is equal to one, as it is the equivalent to 10 times 0 which equals one.

When writing in scientific notation for negative numbers, youll use the same method except with a negative exponent. So, .001 would be 10^-2 in scientific notation.

Scientific notation for addition and subtraction

When using scientific notation to perform subtraction or addition, its important to make sure all of the exponents in the equation are the same. For example, 10^3 + 9^3 is an appropriate way to use scientific notation for addition. In this equation, you would simply add together the two base numbers, 9 and 10, to get 19^3.

If you have two numbers that dont have the same exponents, youll need to make them the same before performing addition or subtraction. For example, (3 + 10^3) + (2 + 10^2) would need to be changed to (0.2 + 10^3) + (3 + 10^3). This will answer 3.2 x 10^3, or 3,200.

Scientific notation for multiplication

When using scientific notation in multiplication, the exponents do not need to be the same as they do for addition and subtraction. Rather, youll simply add the exponents to get the correct answer.

For example, 10^3 x 10^2 = 10^5 which equals 100,000.

Another example is as follows: (4 x 10^2) x (3 = 10^3) = 12 x 10^5, or 12 x 100,000, which gives you 1,200,000.

Scientific notation for division

When using scientific notation in division, youll need to subtract the exponents from each other for each representative number. For example, 10^8 / 10^ 5 = 10^3, or 1,000.

Another example of using scientific notation in division is as follows: (4 x 10^5) / (2 x 10^3) = 4/2 = 2 x 10^5 x 10^3 = 2 x 10^2 = 2 x 100 = 200.

Different types of scientific notation

There are two primary types of scientific notation: normalized notation and engineering notation. For normalized notation, you can use any real number and transform it into scientific notation. For example, 300 can be written as 3 x 10^2 or 30 x 10^1 or 300 X 10^0. In normalized scientific notation, “n” stands for the exponent and is the absolute value of “m”, which must equal one or more. This type of notation is frequently used in common algorithm tables and is seen in most settings.

Engineering notation is different from normalized notation in that the exponent “n” can only represent multiples of three. This type of notation enables the numbers to specifically math the corresponding SI prefixes, or a metric prefix that is standardized for use in the International System of Units (SI) as created by the International Bureau of Weights and Measures. SI prefixes are now a component of the International System of Quantities and are used in the Unified Code of Units of Measure (UCUM).

For example, 10^9 could be used in engineering notation, whereas 10^8 could not because eight is not a multiple of three.

Benefits of scientific notation

The following are the key advantages of writing in scientific notation:

FAQ

How do I convert a number to scientific notation?

The format for scientific notation appears like this: Using scientific notation, the number 300 can be written as 3 × 10 2 which means. The 100 is written as a power of ten. The number 0.07 can be written as 7 × 10 − 2 which means 7 × 1 100 .

How do you write 2300000000 in scientific notation?

To convert any number into scientific notation, you write the non-zero digits, placing a decimal after the first non-zero digit. Then, you count the number of digits you need to move the beginning decimal to get to where your decimal is now. If you move the decimal to the left, then your power is positive.

How do you write 0.000345 in scientific notation?

Written in scientific notation, 2,300,000,000 is 2.3 x 10.

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