1. 10.7 Operations with Scientific Notation

2. Multiplication of Numbers in Scientific Notation
Computing with numbers in scientific notation uses the properties of powers: Multiplication
Multiplication of Numbers in Scientific Notation
When you look at the original problem you are being asked to multiply two numbers that are each written in scientific notation.
One way to solve this problem would be to find the standard from of each number, then multiply those together, then make sure the product is written in scientific notation.
Although this works, it is not the most efficient way to solve problems. Also, you need to understand how to apply mathematical properties in solutions.

3. Computing with numbers in scientific notation uses the properties of powers: Multiplication
These properties allow you to regroup and move your numbers within parentheses so that you can have your powers of ten and their exponents in one set of parentheses and the other factors in the other set of parentheses.
Since you now had (3.4 x 2.3) you can simply multiply a pair of two digit numbers. Don’t forget that when you multiply decimals, your product needs to have the number of decimal places as the sum of decimal places in the factors.
Since you now had (105 x 103) where you had the same bases being multiplied together, you can use the Product of Powers property for which you add the exponents.

4. Multiplication of Numbers in Scientific Notation
Computing with numbers in scientific notation uses the properties of powers: Multiplication
Multiplication of Numbers in Scientific Notation
When you look at the original problem you are being asked to multiply two numbers that are each written in scientific notation.
One way to solve this problem would be to find the standard from of each number, then multiply those together, then make sure the product is written in scientific notation.

5. Division of Numbers in Scientific Notation
Computing with numbers in scientific notation uses the properties of powers: Division
Division of Numbers in Scientific Notation
When you look at the original problem you are being asked to divide two numbers that are each written in scientific notation.
One way to solve this problem would be to find the standard from of each number, then divide those numbers, then make sure the quotient is written in scientific notation.
Although this works, it is not the most efficient way to solve problems. Also, you need to understand how to apply mathematical properties in solutions.

6. Computing with numbers in scientific notation uses the properties of powers: Division
This property allow you to regroup your numbers into parentheses so that you can have your powers of ten and their exponents in one set of parentheses and the other factors in the other set of parentheses.
Since you now had (2.325 ÷ 3.1) you can simply divide those decimals in that set of parentheses. Then regroup the powers of 10 in the other set.
The Quotient of Powers Property allows you to just subtract your exponents since both numerator and denominator had 10 as a base.
For numbers to be correctly written in scientific notation, you can only have a single digit from 1-9 in front of the decimal point

7. Computing with numbers in scientific notation uses the properties of powers: Addition
When you look at the original problem you are being asked to add two numbers that are each written in scientific notation.
One way to solve this problem would be to find the standard from of each number, then add those numbers, then make sure the sum is written in scientific notation.
Although this works, it is not the most efficient way to solve problems. Also, you need to understand how to apply mathematical properties in solutions.

8. Computing with numbers in scientific notation uses the properties of powers: Addition
In order for you to be able to add numbers in scientific notation the exponent on the power of 10 must be the same. Rewrite the the larger number so that it has the same exponent as the smaller number
The distributive property is written as a(b+c) = ab+ac. It allows you to pull out the factors that are being multiplied by the same number and added together first. In this problem a would be 105 since it is the number that is a factor in both quantities. b would equal 5.24 and c would equal 86.5
Find the sum of b & c by adding , then rewrite the x105. Finally, make sure that your answer is written in scientific notation with a single number in front of the decimal point and the appropriate exponent of the 10.