# Scientific Notation

on . Posted in Algebra

Scientific notation, also called standard form or exponential notation, is a way to express very large or very small numbers in a concise and easily readable format.  It is commonly used in science, mathematics, engineering, and other fields where dealing with numbers of varying magnitudes is common.  In scientific notation, a number is expressed as the product of a coefficient (a decimal number greater than or equal to 1 and less than 10) and a power of 10. The power of 10 represents the magnitude of the number.

### To convert a number to scientific notation

• Identify the coefficient by moving the decimal point so that there is only one non-zero digit to the left of the decimal point.
• Count the number of places the decimal point was moved. This count becomes the exponent.
• If the decimal point was moved to the left, the exponent is positive.  If it was moved to the right, the exponent is negative.

To convert from scientific notation back to standard notation, you simply reverse the process.

• The number  $$\large{123,000,000 }$$  can be expressed in different ways:
• $$\large{\;1.23\times 10^8 }$$
• $$\large{\;1.23\times e^8 }$$
• $$\large{\;1.23\times e8 }$$
• $$\large{\;1.23e+8 }$$
• $$\large{\;123\times 10^6 }$$  engineering notification

• The number  $$\large{0.000000123 }$$  can be expressed in different ways:
• $$\large{\;1.23\times 10^{-7} }$$
• $$\large{\;1.23\times e^{-7} }$$
• $$\large{\;1.23\times e-7 }$$
• $$\large{\;1.23e-7 }$$
• $$\large{\;123\times 10^{-6} }$$  engineering notification

Multiply:  $$\large{\; \left(3\times 10^8\right) \times \left(2\times 10^4\right) = 6\times 10^{12} }$$

Divide:  $$\large{\; \left(3\times 10^8\right) \div \left(2\times 10^4\right) = 1.5\times 10^4 }$$

 Number Scientific Notification 1 $$1.0\times 10^0$$ 10 $$1.0\times 10^1$$ 100 $$1.0\times 10^2$$ 1,000 $$1.0\times 10^3$$ 10,000 $$1.0\times 10^4$$ 0.1 $$1.0\times 10^{-1}$$ 0.01 $$1.0\times 10^{-2}$$ 0.001 $$1.0\times 10^{-3}$$ 0.0001 $$1.0\times 10^{-4}$$