Scientific Notation Rules

Scientific Notation

A way to write a number that includes a base 10 exponent. The first number of scientific notation must be greater than or equal to 1 and less than 10.

See example below:

Standard Notation

The "normal" way of writing a number.

See example below:

Changing Standard Notation to Scientific Notation

• Change number (move decimal) so that the number is less than 10 but greater than (or equal to) 1.

• The number of times that the decimal is moved become the exponent with a base 10. If the standard notation was larger than 10, the exponent will be positive. If the standard notation was less than 1, the exponent will be negative.

Changing Scientific Notation to Standard Notation

• Move the decimal however many times the exponent says.

• Positive Exponent means the number is large so move decimal to right.

• Negative Exponent means the number is small so move the decimal to left.

• The two numbers that are being added must have the same exponent.

• If they are different, change the smaller exponent to match the larger exponent.

• If you make the exponent larger, you must make the first number smaller (by moving the decimal place) the same amount of places that you added/subtracted from the exponent.

• If you make the exponent smaller, you must make the first number larger(by moving the decimal place) the same amount of places that you added/subtracted from the exponent.

• Keep exponents the same.

• Express answer in scientific notation (first number between 1 and 10)

• If you have to make the first number smaller (by moving decimal places) then make the exponent bigger (by the same amount that you moved the decimal place).

• If you have to make the first number bigger(by moving decimal places) then make the exponent smaller(by the same amount that you moved the decimal place).

Subtracting Numbers in Scientific Notation

• The two numbers that are being subtracted must have the same exponent.

• If they are different, change the smaller exponent to match the larger exponent.

• If you make the exponent larger, you must make the first number smaller (by moving the decimal place) the same amount of places that you added/subtracted from the exponent.

• If you make the exponent smaller, you must make the first number larger(by moving the decimal place) the same amount of places that you added/subtracted from the exponent.

• Subtract first numbers

• Keep exponents the same.

• Express answer in scientific notation (first number between 1 and 10)

• If you have to make the first number smaller (by moving decimal places) then make the exponent bigger (by the same amount that you moved the decimal place).

• If you have to make the first number bigger(by moving decimal places) then make the exponent smaller(by the same amount that you moved the decimal place).

Multiplying Numbers in Scientific Notation

• Multiply first numbers

• Express answer in scientific notation (first number between 1 and 10)

• If you have to make the first number smaller (by moving decimal places) then make the exponent bigger (by the same amount that you moved the decimal place).

• If you have to make the first number bigger(by moving decimal places) then make the exponent smaller(by the same amount that you moved the decimal place).

Dividing Numbers in Scientific Notation

• Divide first numbers

• Subtract exponents.

• Express answer in scientific notation (first number between 1 and 10)

• If you have to make the first number smaller (by moving decimal places) then make the exponent bigger (by the same amount that you moved the decimal place).

• If you have to make the first number bigger(by moving decimal places) then make the exponent smaller(by the same amount that you moved the decimal place).

Raising Numbers in Scientific Notation to Powers

• Raise first number to outside power.

• Multiply exponents.

• Express answer in scientific notation (first number between 1 and 10)

• If you have to make the first number smaller (by moving decimal places) then make the exponent bigger (by the same amount that you moved the decimal place).

• If you have to make the first number bigger(by moving decimal places) then make the exponent smaller(by the same amount that you moved the decimal place).