Scientific Notation

Scientific Notation

by JoAnn Bowen

•The first number is called the coefficient. It must be greater than or equal to 1 and less than 10.

•The second number is called the base.

•The base number is always written in exponential form as a power of 10.

•In the number on the base ten is referred to as the exponent or power of ten.

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​Rules for Scientific Notation

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1.Move the decimal point as much as needed to get a number between 1 and 10.

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2.The amount of places the decimal was moved becomes the exponent on the 10 base. If the number is very small, the exponent is negative. If it is very large, the exponent is positive.

​How to Convert a Number from Standard Notation to Scientific Notation

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1.If the exponent is positive, move the decimal point to the right to make a big number.

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2.If the exponent is negative, move the decimal point to the left to make a small number.

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3.Move the decimal point from its current place, the amount and direction specified by the exponent on the 10.

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​How to Convert a Number from Scientific Notation to Standard Form

​Comparing Numbers in Scientific Notation

​The power of ten determines the size of the number.

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​The larger the exponent, the larger the number.

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​If the power of ten is the same, the coefficient determines which number is larger.

​Adding and Subtracting in Scientific Notation

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IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.

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If the exponents are NOT the same, we must move a decimal to make them the same.

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Determine which of the numbers has the smaller exponent.

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Change this number by moving the decimal place to the left and raising the exponent, until the exponents of both numbers agree. Note that this will take the lesser number out of standard scientific notation.

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Add or subtract the coefficients as needed to get the new coefficient.

The exponent will be the exponent that both numbers share.

Put the number in standard scientific notation

​Rules for Multiplying in Scientific Notation

1. ​Multiply the coefficients.

2. ​Add the exponents (base 10 remains).

3. ​Answer must be in scientific notation.

​We must move the decimal point over to the left until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be raised by 1 power of ten.

​What if the answer is NOT in proper scientific notation?

​Rules for Division in Scientific Notation

1. ​Divide the coefficients.

2. ​Subtract the exponents (base 10 remains).

3. ​Answer must be in scientific notation.

​What if the answer is NOT in proper scientific notation?

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We must move the decimal point over to the right until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be lowered by 1 power of ten.