**The Standard Form of a number with examples**: Standard form is an important topic in mathematics that all students MUST understand. In mathematics, you might be given a question and finally be requested to leave your answer in standard form. This article will explain ineptly everything you need to know on this topic.

###### STANDARD FORM DEFINITION

Standard form is used to express very large and very small numbers. Examples of such numbers are , . The standard form is written as

Where, is a number between 1 and 10, and, can be a positive (+Ve) or negative (-Ve) integer.

In the next two paragraphs, we will consider examples of large and small numbers expressed in standard form.

RECOMMENDED: Logarithm of Numbers and Permutation and Combination.

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###### STANDARD FORM OF LARGE NUMBERS

The number can be expressed as which will be equal to . These value is its standard form, that is in the format .

Where which lies between and as defined above and which is a positive (+ve) integer.

Sometimes we can easily get the standard form of large value like the above, by simply counting the number of digits from the RIGHT to LEFT up to the point (at blue arrow) the decimal point will be placed. For example, the number is

The digit count is digit from the right to left. So we will have .

###### STANDARD FORM OF SMALL NUMBERS

Numbers that are very small are better expressed in standard form. Consider the number, . This number is equal to . That is

However, we can easily get the standard form of very small values by simply counting the number of digits from the decimal point in the left to the point between the first two real numbers.

Counting from the left to the right (negative counting), we get .

Any number can be expressed in its standard form. But in most instances, it is usually more convenient to use the standard form for very large or very small numbers.

Astronomers use the standard form of number extensively because they use very large numbers and very small numbers in calculations. For example, the average distance between the Earth and the Sun is about 93 million miles (150 million kilometers).

Let us consider some examples on the standard form of large and small numbers as real examples and see the solutions to such questions.

###### STANDARD FORM EXAMPLES WITH REAL SOLUTIONS

Write in standard form the numbers: i. and ii.

- Count the number from the right to the left (+ve counting), we will have . Note, this can also be , it all depends on where you place the decimal point.
- Counting the number from the decimal point to the right (the point between the first two real numbers), we get

Recall that

Also Read: Surds

In some instances, you might be given a question that will require you to add and subtract or multiply and divide two numbers in standard forms. In the next two paragraphs, we will learn how to solve such questions.

###### ADDITION AND SUBTRACTION IN STANDARD FORM

In order to add or subtract expressions in standard form, the powers of of the two numbers must be made equal. See the examples below:

- Add

In the above example, we have to make have by moving the decimal point. This will become .

∴

- Subtract.

Considering the two values, let’s make have same power as . We will have .

∴

###### MULTIPLICATION AND DIVISION OF STANDARD FORM

The process of multiplication and division follows a similar rule as in the operation of **indices. **For example, if and

∴ , which will further be

Also in the division,

∴

Furthermore, the practical examples below will explain how to carry out this operation.

- Simplify in standard form.

From the above,

- Evaluate ÷

The above will give, , simplifying these will give,

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