10 × 10 × 10 is written 10³. The small 3 counts how many tens are multiplied.
Step 1: Picture It
Start with something you already know.
Packs inside crates
- A pack holds 10 stickers.
- A box holds 10 packs, and a carton holds 10 boxes.
- A crate holds 10 cartons.
- Each layer of packing multiplies by ten again.
The small raised 4 in 10⁴ counts the layers of ten.
Four layers of ten is not 10 + 10 + 10 + 10.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
10 × 10 = 100. What is 10 × 10 × 10?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
The small raised number has a name.
Exponent says how many times a number is multiplied by itself.
Counting the zeros
10³ is 1,000, which has 3 zeros. The exponent and the zeros always match.
A warning
10³ is not 30. It is 10 multiplied three times, not 10 added three times.
Step 3: Try It Yourself
Tap and try it out.
Hundreds
1
Tens
0
Ones
0
1 hundred, 0 tens and 0 ones is 100.
Step 4: In Real Life
Computer storage
A kilobyte is 10³ bytes, a megabyte 10⁶, a gigabyte 10⁹. Engineers write the power instead of the zeros. Nobody wants to count nine zeros twice.
Step 5: Watch an Example
One step at a time.
Watch Leo Work Out 6 × 10⁴
Leo multiplies 6 by a power of ten.
- Step 1
10⁴ means four tens multiplied together.
The powers of ten so far
- 110¹ = 10
- 210² = 100
- 310³ = 1,000
- 410⁴ = 10,000
Watch Ana Write 80,000 the Short Way
Ana writes 80,000 as a digit times a power of ten. She starts. You finish.
- Step 1
80,000 is an 8 with zeros after it. The power counts those zeros.
Step 6: Your Turn
Practice makes it stick.
The Fun Run
Problem 1 of 11
Room A raises 10³ dollars. Room B raises 3 × 10³ dollars. How much do they raise in all?
dollars
The Coin Rolls
Problem 2 of 11
A box holds 4 rolls. Each roll holds 10² pennies. How many pennies fill the box?
pennies
Powers and Zeros
Read the power first. Then answer.
Problem 3 of 11
What is 10² ?
Problem 4 of 11
How many zeros does 10⁶ have?
Problem 5 of 11
What is 5 × 10³ ?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 11
Dev works out 10⁵. One line is a slip. Which?
Dev's answer for 10⁵
- 110⁵
- 210⁵ = 10 + 10 + 10 + 10 + 10
- Answer10⁵ = 50
Problem 7 of 11
What is 10⁵ ?
Problem 8 of 11
Maya writes 2,000 the short way. One line is a slip. Which?
Maya's short way for 2,000
- 12,000 the short way
- 22,000 has 4 digits, so the power is 4
- Answer2,000 = 2 × 10⁴
Problem 9 of 11
How should Maya write 2,000?
Same Number?
Tick every match. Then build a power with blocks.
Problem 10 of 11
Tick every way of writing 1,000.
Problem 11 of 11
Show 3 × 10² with the blocks.
Nothing.
Hundreds
0
Tens
0
Ones
0
0 hundreds, 0 tens and 0 ones is 0.
Step 7: Quick Check
Show what you know.
Question 1 of 2
What is 7 × 10² ?
Question 2 of 2
What does the exponent count?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Which is bigger, 2 × 10⁴ or 9 × 10³ ?
Stretch 2 of 2
One sign says 3 × 10⁴ dollars. Another says 30 × 10³ dollars. Do they match?
What You Learned
- 10³ means three tens multiplied together.
- The exponent matches the number of zeros.
- A power of ten is a multiplication, not a repeated addition.
For the grown-up
This lesson is where the child uses whole-number exponents to write powers of ten and explains the pattern of zeros. The pattern that built whole numbers continues to the right of the decimal point without changing. Each place is a tenth of the one before, which is the same rule read the other way.
Ask what 10⁴ means before asking what it equals. The meaning is four tens multiplied.
A child who reads 10³ as 30 will read 10⁶ as 60. Check the small number, not the answer.
The slip this lesson targets is reading 10³ as 30. The exponent counts tens multiplied, not tens added, so 10³ is 1,000 — that is Dev's slip, written out with 10⁵. Maya's slip is the other one: she counts every digit of 2,000 instead of only its zeros. Ask how many tens were multiplied, rather than how long the number looks.
What the small raised number means — 10³ means 10 × 10 × 10 = 1,000. The raised number, called the exponent, counts how many tens are multiplied together — not what to multiply by. So 10⁵ is 100,000, a 1 followed by five zeros. The exponent and the zero count match for powers of ten, which is a useful coincidence but only a coincidence.
Why a shorthand is worth having — Writing 1,000,000,000 is error-prone; writing 10⁹ is not. Scientists dealing with distances between stars or the size of atoms would be lost without it. The notation also makes patterns visible: multiplying 10³ by 10² gives 10⁵, because you are simply multiplying five tens together.
Expanded form with powers — 3,406 can be written (3 × 10³) + (4 × 10²) + (0 × 10¹) + (6 × 10⁰). This says exactly what place value has always said, in a notation that scales to any size of number. And 10⁰ = 1, which follows from the pattern: each step down divides by ten, and 10¹ = 10 divided by ten is 1.
Multiplying and dividing by powers of ten — Multiplying by 10² shifts every digit two places left; dividing by 10² shifts them two places right. Thinking of it as digits moving rather than zeros being added is what keeps the rule working once decimals are involved, where "add a zero" fails outright.
The exponent counts the zeros — 10 to the power 1 is 10. Power 2 is 100. Power 3 is 1,000. The power counts how many times you multiplied by ten. So it also counts the zeros. 4 × 10³ = 4,000 And dividing by 10³ moves three places the other way: 4 ÷ 10³ = 0.004