10 × 10 × 10 is written 10³. The small 3 counts how many tens are multiplied.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
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 2: Try It Yourself
Tap and try it out.
Hundreds
1
Tens
0
Ones
0
1 hundred, 0 tens and 0 ones is 100.
Step 3: 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 4: Watch an Example
One step at a time.
Watch Leo Work Out 6 × 10⁴
Leo multiplies by a power of ten.
- Step 1
He reads 10⁴ as four tens multiplied together, which is 10,000.
Step 5: Your Turn
Practice makes it stick.
The Short Way
Problem 1 of 2
What is 10³ written out in full?
The Big One
Problem 2 of 2
What is 4 × 10³?
Powers and Zeros
1 of 4
What is 10² ?
2 of 4
What is 10⁵ ?
3 of 4
How many zeros does 10⁴ have?
4 of 4
Is 10³ the same as 30?
Find It on the Chart
Build it, then check.
Find 100 on the chart.
Step 6: Quick Check
Show what you know.
Question 1 of 2
What is 7 × 10² ?
Question 2 of 2
What does the exponent count?
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.
Watch for the decimal point being treated as a separator between two whole numbers. It is a marker for where the ones place ends, nothing more.
Say the place names aloud: three and four tenths, not three point four. The words carry the structure that the notation hides.
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