Often, numbers in scientific notation need to be put in integer form.

To convert scientific notation to integers:

Step 1:Write decimal number.

Step 2:Move the decimal the number of places specified by the power of ten: to the right if positive, to the left if negative. Add zeros if necessary.

Step 3:Rewrite the number in integer form.

Example:

Convert 4.4 x 10³ to integer form.

Solution:

Addition

In order to add two or more numbers using scientific notation, the following three steps must be used.

Step 1:Change all addends to have the same power of ten by moving the decimal point (that is, change all lower powers of ten to the highest power).

Step 2:Add the decimal numbers of the addends and keep the common power of ten.

Step 3:If necessary, rewrite the decimal with a single number to the left of the decimal point.

For example, for 3.5 x 10³ + 5 x 10² you are asked to add 3.5 thousands to 5 hundreds. Converting 3.5 thousands to 35 hundreds ( 3.5 x 10³ = 35 x 10²) we obtain 35 hundreds + 5 hundreds = 40 hundreds or 3.5 x 10³ = 35 x 10² + 5 x 10² = 4 x 10³. The student should do the same problem by converting the 5 x 10² to thousands and then adding.

Example:

Solution:

Subtraction

In order to subtract two numbers in scientific notation, the steps listed below must be followed.

Step 1:As in addition, change all addends to have the same power of ten.

Step 2:Subtract one digit from the other and keep the power of ten.

Step 3:If necessary, rewrite the decimal with a single number to the left of the decimal point.

Example:

Solution: