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Convert between standard and scientific notation

Very large or small numbers may sometimes be written in scientific notation.

 A number in the form a x10n where $1\le|a|\le10$ and n is an integer is said to be in scientific notation

Any number written in scientific notation is expressed as a number between 1 and 10 and multiplied by a power of 10.

Convert a number from scientific notation to standard form.

The sign of the exponent n determines which way the decimal point moves. When the exponent on 10 is positive, multiply by 10n, or move the decimal point n places to the right. When the exponent of 10 is negative, multiply by 10-n, or move the decimal point n places to the right.

Positive Powers of 10.
Write 3.8x104 in standard form.

First, remind yourself of the rules for reading numbers in scientific notation. When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The factor must be a number greater than or equal to 1 and less than 10.

If the power of 10 is positive, the decimal point moves to the right the same number of places as the exponent.

3.8x104 = 38,000

Negative Powers of 10.
Write 3.8x10-3 in standard form.

First, remind yourself of the rules for reading numbers in scientific notation. When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The factor must be a number greater than or equal to 1 and less than 10.

If the power of 10 is negative, the decimal point moves to the left the same number of places as the exponent.

3.8x10-3 = 0.0038

Convert a number from standard form to scientific notation.

Positive Powers of 10.
The sun is about 93,000,000 miles from Earth. To write this number in scientific notation, follow these steps:

1. Place the decimal point to get a number between 1 and 10.
9.3000000=9.3
2. Count the number of places to the right of the decimal point. There are seven places.
3. The second part of the number, the power of 10, shows that there are 7 places to the right of the decimal point.

In scientific notation, 93,000,000 is written as 9.3x107

Negative Powers of 10.
To write 0.00945 in scientific notation follow the following steps:

1. Move the decimal point to the right to produce a number from 1 to 10:
0009.45
2. Now, count how many places the decimal point in the original number was moved. The decimal point was moved three places to the right.
3. Since the original number is less tahn one, the exponent is negative:
0.00945=9.45x10-3