Converting to Standard Form: A Detailed Guide with Examples

The standard form of numbers is considered the building block for understanding the different forms of numbers and calculations in the study of mathematics. The standard form of numbers represents them simply and clearly.

In this article, we will explain the concept of numbers in the standard form. We will discuss its definition, how to represent the numbers in the standard form, and important steps to write ordinary numbers into the standard form.

Numbers in Standard Form:

In standard form, a number is written as a decimal number between 1 and 10 multiplied by a power of 10. The standard form of numbers is a way to represent very small or very large numbers in a simple and easy format. Such as astronomers use standard from of numbers to write very larger distance of other planets and stars from the earth in a simple way.

Similarly, scientists always write in standard form to present complex measurements and values in a straightforward and easily comprehensible manner. The common representation of an ordinary number in standard form is as:

R x 10^k

Here

1 ≤ R < 10 and R represents the coefficient or mantissa.

k Є ℤ is the power or exponent of 10 and it can be both positive or negative.

Representation of Numbers in Standard Form

Here we will elaborate on how to represent different types of numbers in the standard form.

Decimal Form:

In this form, we use a decimal point to separate the whole number part from the fractional part. The fractional part is written with each digit behind the decimal point representing its corresponding place value in the standard form.

Negative Numbers:

Negative numbers are numbers that are less than zero. In Standard Form, we simply add a negative sign (-) in front of the number. For example, the number -7 written in Standard Form would be:

-7 = -7 x 100 + 0 x 10 + 0 x 1

Whole Numbers:

The whole numbers are simple numbers like 1, 2, 3, and so on. In Standard Form, they are written with zeros to the right of the last digit to fill up the empty place values. For example, the number 5 written in Standard Form would be:

5 = 5 x 100 + 0 x 10 + 0 x 1

Steps to Write Numbers in Standard Form:

Here we will explain the important steps that are very useful while writing ordinary numbers in standard form.

• Identify the decimal number: This is part of the number that includes the whole number and any decimals such as the decimal number for the number 520 is 520.
• Count the number of digits to the right of the leading digit: The first non-zero digit in the decimal number is called the leading digit such as the leading digit is 5 in the number 520. Now count the number of digits to the right of 5 which is 2.
• Write the decimal number between 1 and 10: Move the decimal point one position to the left without changing the value of the number such as 520 becomes 5.20.
• Write the power of 10: The power of 10 is the number of times you need to multiply 10 by itself to get the original number. We are to multiply 10 by itself twice to get 520. i.e.

(10 x 10 = 100 and 100 x 10 = 500).

So, the power of 10 is 2.

• Write the complete form: Now combine the decimal number and the power of 10 to get the number in standard form and in this case, the standard form of 520 is 5.20 x 10².

Examples of Writing Numbers in Standard Form

Example 1:

What will be the standard form of the number 82,781, 000, 000, 000,000, 000?

Solution:

Step 1: Given data:

Number: 82,781, 000, 000, 000,000, 000 (It is an ordinary number)

Step 2: Write down the significant digits of the given number.

82781

Step 3: Place the decimal point after the leading digit.

8.2781

Step 4: Find out the exponent of 10 that is required to bring the coefficient back to the original number and the decimal point will move 19 places from right to left to be on the standard position and it will be written as the power of 10.

8.2781 x 10¹⁹

Example 2:

What will be the standard notation of the number 0.000000000000006492?

Solution:

Step 1: Given data:

Number: 0.000000000000006492

Step 2: Write down the significant digits of the given number.

6492

Step 3: Place the decimal point after the leading digit.

6.492

Step 4: Find out the exponent of 10 that is required to bring the coefficient back to the original number and the decimal point will move 15 places from left to right to be on the standard position and it will be the power of 10.

6.492 x 10¹⁵

Wrap Up

We can summarize that the standard form of numbers is a flexible notation that makes it easier to describe very large or very small numbers. We have covered the concept of numbers in standard form in this article. We have talked in a lot of detail about how to write numbers in standard form with solved examples.

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