You will use what you learn about number relationships and the basic properties of operations of numbers in scientific notation to solve problems.
After completing this tutorial, you will be able to complete the following:
Exponents, also called powers, tell how many times to multiply the base number.
Here a is the base and 3 is the exponent.
This expression means that a will be multiplied three times.
If a = 2, then 2 × 2 × 2 = 8.
Scientific notation is a way of using exponents and powers of 10 to write very large or very small numbers. It is the product of two factors: a base number × a power of 10. The base number, a, is a decimal greater than or equal to 1 but less than 10. The exponent can be either positive or negative.
a × 10b
4,000,000 = 4 × 107
0.0057 = 5.7 × 10-3
Professionals in the science, math, and medical fields often find it very useful to write numbers using scientific notation.
9.46 × 1015 meters (the distance light travels in one year)
5.44 × 106 square meters (the area of the Artic Ocean)
7.53 × 10-7 grams (weight of a particle of dust)
Please note that in the Activity Object all numbers except zero
are written in scientific notation.
Laws of Exponents and Properties of Powers to assist in operations.
There are specific rules when performing operations with numbers in scientific notation.
In the following example from the Activity Object, addition, subtraction, and multiplication are modeled:
The problems can be solved using number relationships.
Despite the scientific notation, many of the problems can be by examining the relationships between numbers. Every number can be broken down into smaller numbers. For example, 7 can be created by adding several combinations of numbers - 2 + 5, 3 + 4, and 6 + 1. Students use information about number relationships to determine the placement of the numbers in the problems.
Using numbers 1 through 9, A must be 1, 2, 3, or 4. When each of these numbers is doubled (or added to itself), the sum is less than ten. B must be 2, 4, 6, or 8 as these numbers are the only possible sums of 1, 2, 3 or 4 doubled. Using number relationships to solve this example allows us to narrow the possible options.
When multiple problems are solved in Level 2 and 3, students will be able to eliminate options more easily as they analyze the number relationships.
The Identity Property of Addition states that when any number is added to zero the sum is the number.
Students should be able to quickly recognize this property when solving the problems in this Activity Object.
Algebraically, this can be expressed as: a + 0 = a
Zero is called the Identify Element of Addition.
Using the Identity Property of Addition, we can see that the number added to C must be zero since the sum of the addition problem is C. Therefore, D is zero.
The Identity Property of Multiplication states that when any number is multiplied by one the product is the number.
Again, most students should be able to quickly recognize this property when solving the problems in this Activity Object.
Algebraically, this can be expressed as: a × 1 = a
One is called the Identity Element of Multiplication.
Using the Identity Property of Multiplication, we can see that E must be one since the product of the multiplication problem is F. Therefore, E is one.
The Multiplication Property of Zero states that when any number is multiplied by zero the product is zero.
This property is also easily recognizable when solving problems.
Algebraically, this can be expressed as: a x 0=0
Using the Multiplication Property of Multiplication, we can see that H must be zero, since the product of the multiplication is H. Therefore, H is zero.
|Approximate Time||10 Minutes|
|Pre-requisite Concepts||Students should understand the concept of number sense.|
|Type of Tutorial||Skills Application|
|Key Vocabulary||numbers in scientific notation, operations, properties|