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Scientific notation is a system of writing numbers in a way that makes it easier to manage and manipulate numbers that are too large or too small. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by a power of 10. For example, 763 thousandths in scientific notation is 7.63 x 10^-1.

Understanding scientific notation is important in a variety of fields, including Mathematics, Physics, Chemistry, and engineering. It can help simplify complex calculations and make it easier to work with large and small numbers. In this article, we’ll explore scientific notation in more detail, including how to convert numbers to and from scientific notation.

Scientific notation is a way of expressing a number as the product of a number between 1 and 10 and a power of 10. The number between 1 and 10 is known as the coefficient, while the power of 10 is known as the exponent.

For example, the number 763 thousandths can be expressed in scientific notation as 7.63 x 10^-1. The coefficient is 7.63, which is between 1 and 10, and the exponent is -1, which means we move the decimal point one place to the left.

Scientific notation can be used to express both very large and very small numbers. For example, the distance from the Earth to the Sun is approximately 93 million miles, or 9.3 x 10^7 miles in scientific notation. On the other hand, the mass of an electron is approximately 9.11 x 10^-31 kilograms.

There are several reasons why scientific notation is useful. One of the main reasons is that it makes it easier to manage large and small numbers. For example, imagine trying to multiply 2.5 billion by 3.2 billion without a calculator. The result is a number with 19 digits, which is difficult to manage. However, if we express the numbers in scientific notation, we get:

2.5 billion = 2.5 x 10^9

3.2 billion = 3.2 x 10^9

Now, we can easily multiply the coefficients and add the exponents to get:

2.5 x 10^9 x 3.2 x 10^9 = 8 x 10^18

Another reason why scientific notation is useful is that it makes it easier to compare numbers. For example, imagine you have two numbers: 6.75 x 10^8 and 7.12 x 10^7. At first glance, it may be difficult to tell which number is larger. However, if we convert both numbers to the same power of 10, we get:

6.75 x 10^8 = 675 x 10^6

7.12 x 10^7 = 71.2 x 10^6

Now, we can easily see that 6.75 x 10^8 is larger than 7.12 x 10^7.

To convert a number to scientific notation, follow these steps:

Determine the coefficient. The coefficient should be a number between 1 and 10. Move the decimal point in the original number until you get a number between 1 and 10. Count the number of places you moved the decimal point.

Determine the exponent. The exponent should be the number of places you moved the decimal point in step 1, but with a negative sign if you moved the decimal point to the left, and a positive sign if you moved.

To express 763 thousandths in scientific notation, we need to move the decimal point three places to the left and raise 10 to the power of 3, giving:

763 thousandths = 0.763 = 7.63 x 10^-1

Here are a few more examples of numbers in scientific notation:

4.56 x 10^2 = 456 (four hundred and fifty-six)

1.23 x 10^-3 = 0.00123 (one thousand two hundred and thirty)

2.34 x 10^5 = 234,000 (two hundred and thirty-four thousand)

9.87 x 10^-6 = 0.00000987 (nine thousand eight hundred and seventy)

6.78 x 10^4 = 67,800 (sixty-seven thousand eight hundred)

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