Fifth Grade · Math · week 6

Powers of 10 notation

Use whole-number exponents to denote powers of 10, and connect exponents to the digit-shifting patterns from earlier this unit.

An exponent tells you how many times to multiply 10 by itself. We write 10 x 10 as 10^2 (say "10 to the second power"), and 10 x 10 x 10 as 10^3 ("10 to the third power").

Powers of 10 connect straight back to the shifting pattern from week 1: multiplying by 10^3 shifts every digit three places left, exactly the same as multiplying by 1,000. The exponent tells you exactly how many places to shift.

📋 For the teacher
Teach it (10–15 min):
  • Show the repeated-multiplication meaning first (10 x 10 x 10) before introducing the compact exponent notation.
  • Connect directly to last week: the exponent tells exactly how many places the digits will shift.
  • Build a quick table together -- 10^1, 10^2, 10^3, 10^4 next to their standard forms -- and notice the zero-count pattern.
  • Keep exponents to a base of 10 for now; this is not yet the general exponent rules used with other bases.
Talk about it:
  • What does the exponent in 10^3 tell you to do?
  • How many zeros does 10^5 have, without multiplying it out?
  • How does 10^2 connect to shifting digits two places?

Mastery looks like: They can write and evaluate powers of 10 using exponents, and use them to multiply decimals and whole numbers by shifting digits.

Common stumbles: Confusing the exponent with the answer, such as thinking 10^3 equals 30; miscounting zeros when the exponent is large.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

ExponentsRepeated multiplication and how fast powers grow.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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