Cogito
Grade 8 Math · Chapter 7 · Lesson 2
Scientific Notation
Very big and very small, written compactly.
10 problems · about 18 minutes · 8.EE.A.3, 8.EE.A.4
What this lesson teaches
The child writes numbers in scientific notation and operates with them.
- Scientific notation is one digit, a decimal part, and a power of ten.
- The first part is at least 1 and less than 10.
- Compare the exponents first when comparing sizes.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Laws of Exponents: 3⁵ × 3² = 3 to what power?
Answer 7
Why 3⁷.
Review — Reading a Graph as a Story: A distance graph falls steadily. Is the person moving away or back? 1 for away, 2 for back.
Answer 2
Why Back towards home.
Warm Up
Straightforward practice. Get the method working first.
4 problems3 × 10⁴ written out. What is it?
Answer 30000
Why 30,000.
What must the first part of a scientific notation number be?
Answer At least 1 and less than 10.
Why Between 1 and 10.
60,000 is 6 × 10 to what power?
Answer 4
Why Four zeros.
2 × 10³ written out. What is it?
Answer 2000
Why 2 × 1,000.
Build It Up
The same ideas with more to keep track of.
2 problems4.5 × 10² written out. What is it?
Answer 450
Why 4.5 × 100.
Which is bigger, 8 × 10² or 2 × 10⁴?
Answer 2 × 10⁴.
Why Exponent first.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Big Number: 7,000 is 7 × 10 to what power?
Answer 3
Why 7 × 10³.
The Comparison: Which is bigger, 3 × 10⁵ or 9 × 10³?
Answer 3 × 10⁵.
Why The bigger exponent wins.