Reading and Writing Scientific Notation – Practice Problems

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Learning to read and write in scientific notation is important. Scientific notation allows very big and extremely small numbers to be understood and written in an easier form, making it easier for scientists to handle their results.

Scientific notation is of the form n•10^a, where n, the coefficient, is always greater than or equal to 1, but less than 10. The 10 is called the base, and a is the exponent which is an indication of how many times the coefficient must be multiplied (or divided, when a is negative) by 10.

To convert a number into scientific notation, it is important to remember that the coefficient must always be greater than or equal to 1 and less than 10. The number of times we move the decimal point from its original position to the position where the number we are converting is greater than or equal to 1 and less than 10 is the exponent a of our base 10; the exponent is positive if the decimal point moved from the right towards the left and negative if the movement was from left to right. The number resulting from moving the decimal point is our coefficient n.

On the other hand, when we convert from scientific notation, if the exponent of the base 10 is positive, we move the decimal point of n to the right since a positive exponent indicates a very large number. If the exponent of the base 10 is negative, we move the decimal point to the left. In both cases, remember to write zeroes for every movement, or decimals places, where no digits are found. The number resulting from moving the decimal point of n is the number that was being represented by scientific notion.

Expressing and understanding numbers in scientific notation have extensive applications in many fields of Science, like Molecular Biology, Astronomy, and Engineering.

Work with radicals and integer exponents.
CCSS.MATH.CONTENT.8.EE.3

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Exercises in this Practice Problem
Explain how to write numbers in scientific notation.
Write the given numbers in scientific notation.
Examine how the numbers are written in scientific notation.
Write the following numbers in scientific notation.
Describe the definition of scientific notation.
Determine the standard form of the number given in scientific notation.