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## Question:

Express 763 Thousandths In Scientific Notation

## Introduction:

In mathematics and science, scientific notation is a way of expressing large or small numbers in a concise and standardized form. It is also known as exponential notation or standard form. Scientific notation consists of a number between 1 and 10, multiplied by a power of 10. In this way, very large or very small numbers can be expressed using fewer digits and with greater precision. In this article, we will learn how to express 763 thousandths in scientific notation.

## Expressing 763 Thousandths In Scientific Notation:

The first step in expressing 763 thousandths in scientific notation is to move the decimal point to the left until the number is between 1 and 10. To do this, we need to divide 763 by 1000: 763 / 1000 = 0.763

Now we have a number between 1 and 10, but we need to express it in scientific notation. To do this, we need to write it as a product of a number between 1 and 10 and a power of 10. The power of 10 is determined by the number of times we moved the decimal point to the left.

In this case, we moved the decimal point three places to the left, so the power of 10 is 3. Therefore, we can express 763 thousandths in scientific notation as: 0.763 x 10^-3

This is the scientific notation of 763 thousandths.

## Explanation Of Scientific Notation:

Scientific notation is a convenient way of expressing very large or very small numbers. It is based on the concept of powers of 10. In scientific notation, a number is written as a product of a number between 1 and 10 and a power of 10.

For example, the number 123,000,000 can be written in scientific notation as: 1.23 x 10^8

Here, the number between 1 and 10 is 1.23, and the power of 10 is 8. This means that 123,000,000 can be written as 1.23 multiplied by 10 to the power of 8.

Similarly, the number 0.000000045 can be written in scientific notation as: 4.5 x 10^-8

Here, the number between 1 and 10 is 4.5, and the power of 10 is -8. This means that 0.000000045 can be written as 4.5 multiplied by 10 to the power of -8.

Scientific notation is particularly useful when dealing with very large or very small numbers. For example, the mass of the Earth is approximately 5.97 x 10^24 kilograms, and the diameter of a hydrogen atom is approximately 1.06 x 10^-10 meters. In both cases, writing these numbers in standard form would require many digits and would be unwieldy. However, expressing them in scientific notation makes them much easier to work with.

There are several advantages of using scientific notation, especially when dealing with very large or very small numbers:

Conciseness: Scientific notation allows us to express large or small numbers using fewer digits. This makes it easier to write, read, and compare numbers.

Standardization: Scientific notation provides a standardized way of writing numbers, which is particularly important in scientific and engineering contexts.

Precision: Scientific notation allows us to express very large or very small numbers with greater precision than standard notation.

Flexibility: Scientific notation can be used with both positive and negative powers of 10, making it versatile and flexible.

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