Scientific Notation, Squares and Square Roots, Finding the LCM using Prime Factorization

Scientific Notation 

–          Exponents are used to write very large and very small positive numbers in scientific notation. Scientific notation has two factors and follows the format a x 10ⁿ

The first factor, known as the coefficient, has to be a number that is greater than 1, and less than 10.

The second factor is a base of 10 raised to any power. The power depends on how many decimal places have been jumped.

• The standard form of a number is writing the number out in its entirety. Ex: 6.02 x 10³ is equal to 6020.
• All you are simply doing when multiplying by a base of 10 is moving the decimal point according to the exponent.

Squares & Square Roots

–          a² = squaring

*If a² = b, then a is called the square root of b

*PERFECT SQUARES are called “perfect”, because they have whole numbers as square roots. To find the square root of a number, think about which factor when multiplied by itself will give you that square. Ex: √64 = 8 because 8² = 64

*When finding the square root of a nonperfect square, you can approximate between two numbers. Ex: √28  –  this is between  √25 and √36, so your answer is between 5 and 6.

To find the LCM of two or more numbers:

1. Find the prime factorization of each number.
2. Take the highest valued numbers from each factorized number and multiply them.

*If there are multiple copies of the highest valued number for a factorized number, include only the copy that has the highest exponent.