Lesson

Scientific notation is used to abbreviate numbers that are quite large or small to make them easier to write. A number in scientific notation will follow the form:

B x 10ⁿ

where B is a number that is equal to or greater than 1 and less than 10. The n is a positive or negative whole number. The n cannot have decimals but could be zero.

Expressing a Number in Scientific Notation

Sort the numbers out in front of you making a pile of numbers greater than one and a pile of numbers less than one. Using the stack of numbers that is less than one, take the number that is on top. Place a button on the decimal point. Move the button to the right until it is one place to the right of the first nonzero digit. Count the number of places that you moved the button from its original position. This number is the n value in scientific notation. It is negative because you moved the button to the right. The number to the left of the button and its significant digits to the right of the button becomes the B in scientific notation. In the space below, write the original number and then the number in scientific notation.

Repeat this for all of the other numbers that are less than one and write the original number and then the number in scientific notation.

For the numbers that are greater than one, choose the number that is one top of the pile. For a number that is one or greater and doesn’t have an obvious decimal point, the decimal point is located all the way to the right after the last number. Using the number greater than one that you chose, place the button where the decimal point would be. Move the button left until there is only one nonzero digit to the left of it. Count the number of decimal places that you moved the button from the original position. This value is the n value in scientific notation and it is positive because you moved the decimal point to the left. The digit to the left of the button and the significant digits to the right of the button become the B value in scientific notation. In the space below, write the original number and then the number in scientific notation.

Repeat this for all of the other numbers in the space below writing the original number and then the number in scientific notation.

Now, write the rules for writing number in scientific notation. Make sure you have a rule that explains how to do it for numbers less than AND numbers greater than one.

Taking Numbers Out of Scientific Notation

Go back to the first number that you put into scientific notation that was less than one. Rewrite the number in scientific notation here:

For numbers less than one, the exponent again tells you how many places that you have to move the decimal place. But when you take a number out of scientific notation, if it has a negative exponent, you move the decimal to the left that many places and substitute zeros as placeholders but keep all the significant digits. Rewrite the other numbers less than one that are in scientific notation here, then take the numbers out of scientific notation.

For numbers that are greater than one, again the exponent tells you how many places to move the decimal point. However, for numbers that are greater than one in scientific notation, the exponent will be positive so you have to move the decimal that many places to the right substituting zeros as placeholders but keeping all the significant digits.

Copy all the numbers greater than one in scientific notation here and then take them out of scientific notation: