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Explain Decimal Point Shifts When Multiplying or Dividing by Powers of 10

Students explain and apply the pattern that multiplying a decimal by a power of 10 moves the decimal point to the right (making the number larger), and dividing moves it to the left (making the number smaller). They use exponent notation for powers of 10.

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Explain Decimal Point Shifts When Multiplying or Dividing by Powers of 10

Grade 5 · Powers of 10 and Decimal Patterns · question 1 of 3

0 of 20

20 rungs. A star at the top.

1.7 × 10^1 =

How it is taught

0:00 of 3:40

A power of ten hops the decimal point.

Dividing hops left and makes the number smaller.

Read it: Powers of ten: multiply and divide

0.36 × 10^2: 10^2 is 10 × 10, so every digit is worth 100 times as much. The digits slide 2 places left: 0.36 × 10^2 = 36. Dividing slides them right: 36 ÷ 10^2 = 0.36.

  1. Count the places: one place for each 10, so 10^2 or 100 is 2 places.
  2. Multiplying slides every digit left; dividing slides it right.
  3. Write in any zeros the places need, and keep the point where it stands.

Each place is worth 10 times the place to its right, so × 10 moves a digit one place left.

10^2 is 10 × 10, and 100 has 2 zeros: both are 2 places.

The point does not move: the digits move past it.

× 10^n slides every digit n places left; ÷ 10^n slides it n places right.

Writing two zeros on the end: 0.3600.

Slide the digits 2 places left instead: 0.36 × 10^2 = 36.

0.67 × 10^2 = ___ — 67. 10^2 slides every digit 2 places left: 67.

5.6 × 10² = 560

Powers of ten can stretch or shrink a decimal in a snap. Let's see how!

We'll work out five point six times ten to the second power.

The little exponent two tells us how many places the decimal will hop.

First hop! The decimal point moves one place to the right. Now it reads fifty-six.

Second hop! There's no digit there, so we fill the spot with a zero. Now it reads five hundred sixty.

So five point six times ten squared equals five hundred sixty.

Powers of 10 move the decimal5.6 × 10² = ?5.6×102=?560exponent 2 = TWO decimal hops56..= 56.0.fill empty spot with 0= 560Dividing? Decimal hops LEFT560 ÷ 10² = 5.6decimal jumps 2 places to the LEFT× 10ⁿ → decimal moves n places RIGHT÷ 10ⁿ → decimal moves n places LEFTThe Power-of-10 RuleANSWER5605.6 × 10²
Grade 5 · Multiplying and dividing decimals by powers of 10

What if we divide instead? The decimal flips direction and hops to the LEFT.

The rule: multiply by ten to the n, shift n places right; divide by ten to the n, shift n places left.

Five point six times ten squared is five hundred sixty. The exponent shows the hops!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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