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Convert between standard and scientific notation
Very large or small numbers may sometimes be written in scientific notation.
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A number in the form a x10n where and n is an integer is said to be in scientific notation
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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:
- Place the decimal point to get a number between 1 and 10.
9.3000000=9.3
- Count the number of places to the right of the decimal point. There are seven places.
- 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:
- Move the decimal point to the right to produce a number from 1 to 10:
0009.45
- Now, count how many places the decimal point in the original number was moved. The decimal point was moved three places to the right.
- Since the original number is less tahn one, the exponent is negative:
0.00945=9.45x10-3
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