Understanding how difficult and complex calculations are carried out is important for understanding the concepts of math. The standard form of numbers is one of the valuable concepts for these kinds of computations. To apprehend very large or very small numbers needs to be proficient in the concept of the standard form of numbers.

Scientists can easily present long measurements and quantities using the concept of the standard form of numbers. Even though it is more common in technical fields, the standard form can be used in everyday interactions involving important values.

In this article, we will cover the topic of the standard form of numbers. We will discuss its definition and important steps that are very useful to represent numbers in the standard form as well as we will be expanding numbers from the standard form with solved examples. We will also discuss its useful applications.

## Standard Form of Numbers:

A number in standard form has the general form:

**Q x 10 ^{r}** and

**1 ≤ Q < 10**and

**r Є Z**(a +ve or -ve integer) is the power of

**10**.

This form simplifies calculations and representation of numbers that may involve extensive digits. So, the standard form of a number comprises the product of two factors:

- A decimal number greater than or equal to 1 and less than 10 (the coefficient).
- A power of 10 (the exponent).

## Important Steps for Writing Numbers in Standard Form:

An ordinary number is written in standard form by following the important steps explained in the following.

**Identify the Coefficient:**Write down the significant digits of the original number and it will be the coefficient (Q).**Determine the Exponent:**Find out the exponent of 10 that is required to bring the coefficient back to the original number. The exponent of 10 will be a positive integer if the decimal point is shifted to the left. The exponent of 10 will be a negative integer if the decimal point is shifted to the right.**Write the Standard Form:**Write the coefficient followed by**x 10^**and then the exponent. For example, if you moved the decimal point 4 places to the right and the significant digits were 1.23 and thus the standard form of the number in this case would be 1.23 x 10^{-4}

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## Examples:

**Example 1:**

Determine what will be the standard notation of the number 47,781, 000, 000, 000, 000.

**Solution:**

**Step 1:** Given data:

Number: 47, 781, 000, 000, 000, 000, 000, 000 (which is an ordinary number)

**Step 2:** Note the significant digits of the given number.

47781

**Step 3:** After the first two digits, place the decimal point.

4.7781

**Step 4:** Find out the power of **10** that is necessary to write the coefficient back to the original number and the decimal point will jump 22 places from right to left to reach the standard position. It is the power of 10.

**7.7781 x 10 ^{22}**

**Example 2:**

Determine what will be the scientific form of the number 0.000000000003492.

**Solution:**

**Step 1:** Given data:

Number: 0.0000000000000000002392

**Step 2:** Note the significant digits of the given number.

2392

**Step 3:** After the first two digits, place the decimal point.

2.392

**Step 4:** Find out the power of **10** that is required to write the coefficient back to the original number and the decimal point will jump 19 digits from left to right to reach the standard position. It is the power of 10.

**2.392 x 10 ^{19}**

**Example 3:**

Determine what will be the standard form for the given number.

0.000000693 x 10^{18}

**Solution:**

**Step 1:** Given data:

Number: 0.0000006935 x 10^{18}

**Step 2:** Note the significant digits of the given number.

6935

**Step 3:** After the first two digits, place the decimal point.

6.935

**Step 4:** Determine how much the number that the decimal number will move from left to right to be on its standard position and in this case, it will move 7 places. Subtract it from the power of the 10.

6.935 x 10^{18-7} = **6.935 x 10 ^{11}**

You can also use a standard form calculator to convert number in standard notation or to verify your results.

## Standard Form of Numbers Applications:

The standard form finds its applications and utility in various scientific and everyday scenarios, such as:

**Science and Engineering:**

The Standard form of numbers is generally used in scientific research and engineering to indicate very large or very small measurements such as the size of atoms or the distance between celestial objects.

It simplifies expressing incredibly large or small measurements, like the distance between planets or the size of atoms. Engineers to express measurements in physics, electronics, and other fields use the standard form.

**Astronomy:**

When dealing with astronomical distances, masses, and other quantities, standard form simplifies the representation of such large numbers. Expressing astronomical distances and sizes of celestial bodies.

**Financial Notation:**

In finance, the standard form can be used to express large amounts of money in a concise way, such as the national debt or company revenues.

**Technology:**

Computer science and electronics often deal with very large and very small numbers, making standard form useful for expressing data sizes, computing power, and other metrics displaying the volume of data stored and the speed of processing.

**Economics:**

The standard form is used in economics to depict large numbers in financial statements and reports. Representing GDP figures, national debts, and market values.

**Chemistry:**

Standard form is used to represent the masses of atoms and molecules, especially in chemical equations. Describing extremely large or small atomic masses and quantities.

**Education:**

Standard form is taught in schools as part of mathematics education to help students understand and work with numbers of varying magnitudes.

## Wrap Up:

We can conclude that the standard form of numbers is a universal notation that helps in the representation of extremely large or small numbers. We have discussed the concept of the standard form of numbers in detail in this article. We have covered its definition as well as essential steps for obtaining numbers in scientific form and important applications with some examples.

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