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Power of ten definition how to#

When we multiply two powers we add their exponents. If two powers have the same base then we can multiply the powers. Write these multiplications like exponents

The exponent corresponds to the number of times the base is used as a factor. The number 5 is called the base, and the number 2 is called the exponent. This expression can be written in a shorter way using something called exponents.Īn expression that represents repeated multiplication of the same factor is called a power.

Power of ten definition how to#

Any number raised to the n th power is equal to the product of the number used as a factor n times.We know how to calculate the expression 5 x 5.Ten to the second power is a 1 followed by two zeroes, or 100. Ten to the zero power is 10 divided by 10, or 1 with no zeroes behind it, which equals one. Any number raised to the power of one is equal to itself. Ten is an easy number to visualize with powers, as you can think of the exponent number as being the number of zeros to put behind the one.Any number raised to the power of zero is one.The process of calculating scientific notation comes from the rules of exponents. POWERS, EXPONENTS, AND SCIENTIFIC NOTATION Oxford, U.K.: Oxford University Press, 2001. The meaning of SCIENTIFIC NOTATION is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10. Wonders of Numbers: Adventures in Math, Mind, and Meaning. New York: Scientific American Library, 1994. Powers of Ten: A Book About the Relative Size of Things in the Universe and the Effect of Adding Another Zero. New York: Scientific American Library, 1997. Mathematics, the Science of Patterns: The Search for Order in Life, Mind, and the Universe. See also Measurement, Metric System of Numbers, Massive Powers and Exponents.ĭevlin, Keith J.

In scientific notation the example would be written 7.21 × 10 −20 Along the same lines the weight of a particular chemical may be 0.0000000000000000000721 grams. Using three significant figures the number is written 1.10 × 10 27. If a chemist is trying to discuss the number of electrons expected in a sample of atoms, the number may be 1,100,000,000,000,000,000,000,000,000. Power of any number is an expression that represents repeated multiplication of the number. Conversely, if the number is small and you moved the decimal point to the right, the exponent is negative. If the number is large and you moved the decimal point to the left, the exponent is positive. Raise the 10 to the exponent that represents the number of places you moved the decimal point. Then, following the number, write a multiplication sign and the number 10. Rewrite the number with the new decimal place and include only the identified significant digits. First, identify the significant digits and move the decimal place to the right or left so that only one integer is on the left side of the decimal. A nanosecond is 0.000000001 seconds, or 1.0 × 10 −9 seconds.Ĭonverting Numbers into Scientific NotationĬomplete the following steps to convert large and small numbers into scientific notation.

Computer calculation speeds are often measured in nanoseconds.

A computer hard disk could hold 4 gigabytes (about 4,000,000,000 bytes) of information.

The weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is 0.000,000,000,000,000,000,000,000,006,645 kilograms (6.645 × 10 −27 kilograms). A million monetary units, such as dollars: made a million in the stock market.

One black hole was measured as 10,000,000 or 1.0 × 10 7 solar masses. According to mathematics, the power of ten is any of the integers powers of the number multiplied by 10.

Some black holes are measured by the amount of solar masses they could contain.

The wavelength for violet light is 40-millionths of a centimeter 4 × 10 −5cm.

Some examples of measurements where scientific notation becomes useful follow. This type of notation is also used for very small numbers such as 0.0000000072, which, in scientific notation, is rewritten as 7.2 × 10 −9. Mathematically, writing a number in scientific notation is the expression of the number in the form n × 10 x where n is a number greater than 1 but less than 10 and x is an exponent of 10. The first part is a number between 1 and 10, and the second part is a power of ten.

Since many large and small numbers have a few integers with many zeros, the power of ten can be used to shorten the length of the written number.Ī number written in scientific notation has two parts. The basis of scientific notation is the power of ten. Ordinary numbers are useful for everyday measurement, such as daily temperatures and automobile speeds, but for large measurements like astronomical distances, scientific notation provides a way to express these numbers in a short and concise way. Scientific notation is a method of writing very large and very small numbers.