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Identify Patterns When Multiplying by Powers of 10

Students explore patterns in products when whole numbers and decimals are multiplied by 10, 100, 1,000, and other powers of 10. They recognize that each multiplication by 10 shifts every digit one place to the left and explain why in terms of place value.

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Identify Patterns When Multiplying 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.

7 × 10 =

How it is taught

0:00 of 3:47

A power of ten is ten multiplied by itself some number of times.

Each extra factor of ten shifts every digit one place left.

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.

2.45 × 10 = ___ — 24.5. 10 slides every digit 1 place left: 24.5.

4 × 10, 4 × 100, 4 × 1,000

What happens when we multiply 4 by ten, then by one hundred, then by one thousand? Let's hunt for a pattern!

We start with the number 4, all by itself in the ones place.

We'll track our number on a place-value chart. Each column is ten times bigger than the one to its right.

Multiply by ten. The 4 jumps one place to the left into the tens column, and a zero slides in to fill the ones place. Forty!

Multiply by one hundred. The 4 jumps two places to the left, and two zeros fill in behind it. Four hundred!

Multiply by one thousand. The 4 jumps three places to the left, and three zeros fill in. Four thousand!

Look at the pattern! Every time we multiplied by ten, the 4 marched one more step to the left.

That works because each place value is exactly ten times bigger than the place to its right.

So multiplying by ten to the n shifts every digit exactly n places to the left.

Multiplying by Powers of 10Let's spot a pattern!4 × 10 = ?4 × 100 = ?4 × 1,000 = ?ThousandsHundredsTensOnes× 14× 1040= 40× 100400= 400× 1,0004000= 4,000The 4 shifts one place left each step!× 10 →× 10 →× 10 →Each place is 10× the place to its right.× 10ⁿ shifts every digit n places left.PATTERN× 10ⁿshift n left
Grade 5 · Spotting the place-value shift

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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