Cogito
Grade 8 Math · Chapter 7 · Lesson 4
Calculating in Scientific Notation
Multiplying and dividing very large and very small numbers.
10 problems · about 20 minutes · 8.EE.A.4
What this lesson teaches
The child multiplies and divides numbers written in scientific notation.
- Handle the number parts and the powers of ten separately.
- Multiplying adds the exponents; dividing subtracts them.
- Renormalise so the number part sits between 1 and 10.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Zero and Negative Exponents: What is 10⁻²? Give it as a decimal.
Answer 0.01
Why 0.01.
Review — Scientific Notation: 3 × 10⁴ written out. What is it?
Answer 30000
Why 30,000.
Review — Laws of Exponents: 3⁵ × 3² = 3 to what power?
Answer 7
Why 3⁷.
Warm Up
Straightforward practice. Get the method working first.
3 problems(4 × 10⁵) × (2 × 10³). What is the exponent?
Answer 8
Why 8.
(3 × 10²) × (3 × 10⁴). What is the exponent?
Answer 6
Why 2 + 4.
(8 × 10⁶) ÷ (2 × 10²). What is the number part?
Answer 4
Why 8 ÷ 2.
Build It Up
The same ideas with more to keep track of.
2 problemsSame division. What is the exponent?
Answer 4
Why 6 − 2.
60 × 10³ rewritten properly. What is the exponent?
Answer 4
Why 6 × 10⁴.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Product: (2 × 10³) × (4 × 10²). What is the number part?
Answer 8
Why 8 × 10⁵.
The Exponent: Same product. What is the exponent?
Answer 5
Why 5.