Patterns with Powers of Ten
Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)
What a learner can do afterwards
- Write 10⁴ = 10,000 and explain the exponent means four factors of 10
- Explain why 3.4 × 10² = 340 by describing the decimal shift
- Predict 2.56 × 10³ without calculating and explain the pattern
The lesson
You already know that multiplying by 10 shifts every digit one place to the left. A power of ten is a short way to write repeated tens. 10³ means three factors of 10 multiplied together: 10 × 10 × 10.
3.4 × 10² has an exponent of 2, so the decimal point moves two places to the right: 3.4 becomes 340.
Count the exponent to know how many places to move the decimal point, or how many zeros a whole number gets. 10⁵ means five places, or five zeros.
The exponent on a power of ten tells you how many places the decimal point moves, or how many zeros the number gets.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.