When working with very large numbers, you may not always have enough space to write out the number in full. Scientific notation is a style of writing numbers that lets you show very large or very small numbers using a small amount of space. It is used frequently in the sciences because it can show numbers that would normally be too long to write out, such as the mass of a cell or the number of atoms in a star.
Powers in Scientific Notation
A number raised to a power is equal to itself multiplied by itself that many times. For example, 10 to the third power, or 10^3, means 10 x 10 x 10, or 1,000. Scientific notation uses exponents of 10 to shorten numbers. For example:
10^2 = 10 x 10, or 100 -- one hundred
10^3 = 10 x 10 x 10, or 1000 -- one thousand
10^6 = 10 x 10 x 10 x 10 x 10 x 10, or 1,000,000 -- one million
Shortening a Number in Scientific Notation
When you raise 10 to a power, the number it multiplies to always has a number of zeros equal to the power. Scientific notation uses this to shorten a number into a decimal. For example, 75 million, or 75,000,000 is written in scientific notation as 7.5 x 10^7, because 7.5 times 10,000,000 is equal to 75,000,000.
Converting a Number Using Scientific Notation
You can convert any large number to scientific notation by placing a decimal between the first two digits and counting the number of digits to the right of the decimal. The number in scientific notation will be the number converted to decimal form, multiplied by 10 to a power equal to the number of digits you counted. For example, say you want to convert 425,000 into scientific notation.
Place a decimal between the first two digits:
Count the number of digits to the right of the decimal; there are five. So the number in scientific notation is
4.25000 x 10^5
4.25 x 10^5.
You can remove the zeros at the end because they do not change the number's value.
You can also use scientific notation to abbreviate a number with a very small value. For instance, to abbreviate 0.00000567, you would place the decimal point between 5 and 6: 5.67. You'd then count the the number of places that the decimal point shifted to the right. The exponent of 10 for a number whose decimal point shifts to the right is negative in scientific notation. Since you shifted the decimal six points to the right, 0.00000567 in scientific notation is
5.67 x 10^-6.
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