Comparing Quantities by Dividing
Comparing Quantities by Dividing is a skill on Pengi from Lesson 57: Operations with Small Numbers in Scientific Notation in Saxon Math, Course 3.
Key Concepts
Property To estimate how many times larger one quantity is than another, divide their estimated values in scientific notation. Divide the coefficients and subtract the exponents of 10:$$\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m n}$$.
Examples Example 1: Compare 9 x 10^ 7 and 3 x 10^ 3. (9 x 10^ 7) / (3 x 10^ 3) = (9 / 3) x 10^( 7 ( 3)) = 3 x 10^ 4 Example 2: A large city has a budget of about 7.5 x 10^5 dollars for parks, and a small town has 3 x 10^2 dollars. How many times larger is the city's budget? (7.5 x 10^5) / (3 x 10^2) = (7.5 / 3) x 10^(5 2) = 2.5 x 10^3 The city's budget is 2.5 x 10^3 (or 2,500) times larger.
Explanation Often in science and finance, we don't just want to know a number; we want to compare it to something else! To find out "how many times bigger" something is, we use division. This is a simple two part process. First, divide the front numbers (the coefficients). Then, use your Quotient of Powers property to subtract the bottom exponent from the top exponent.
Common Questions
What is Comparing Quantities by Dividing?
Comparing Quantities by Dividing is a skill on Pengi from Lesson 57: Operations with Small Numbers in Scientific Notation in Saxon Math, Course 3.
What grade level is Comparing Quantities by Dividing for?
Comparing Quantities by Dividing is part of the Grade 8 Math curriculum, covered in Saxon Math, Course 3. It is designed for students studying Math at the Grade 8 level.
How can I learn Comparing Quantities by Dividing?
Pengi offers an AI-guided lesson for Comparing Quantities by Dividing that walks you through the key concepts step by step. The lesson is aligned to Saxon Math, Course 3 so the content matches what you see in class.
How do I practice Comparing Quantities by Dividing?
After learning the concept, use the Practice mode to work through targeted exercises on Comparing Quantities by Dividing. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Comparing Quantities by Dividing?
Comparing Quantities by Dividing is covered in Saxon Math, Course 3, specifically in Chapter 6: Number & Operations • Data Analysis & Probability under Lesson 57: Operations with Small Numbers in Scientific Notation. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Comparing Quantities by Dividing free to study on Pengi?
Yes, the core Learn and Practice modes for Comparing Quantities by Dividing are available for free on Pengi. No credit card is required to start studying.