Powers of 10

A power of 10 is 10 multiplied by itself. The exponent tells you how many zeros: 10⁴ = 10,000. Quiz for kids, parent help below.

🧒 Kids: count the zeros!

10³ means 10 × 10 × 10 = 1,000. There are three 10s and three zeros. Easy! Then try the quiz.

▶ Quiz 🔢 More practice 🧮 Calculator

Each step down: ÷ 1010⁴=10,000÷ 1010³=1,000÷ 1010²=100÷ 1010¹=10÷ 1010⁰=1

💡 Trick: 10⁵ has a 5 on top, so write a 1 and five zeros: 100,000!

More on exponents: What are exponents · Square numbers · Square roots · Cube numbers and cube roots · Powers of 10

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: the exponent counts the zeros

For a power of 10, write a 1 and then as many zeros as the exponent. To multiply a number by a power of 10, move every digit that many places to the left, filling the gaps with zeros. Dividing moves the digits to the right.

Patterns to spot

Key words

Why it matters: Our number system is built on powers of 10: every place is 10 times the one to its right. Powers of 10 make multiplying by 10, 100 and 1,000 easy, and they lead to scientific notation in grade 8.

See it: pictures to draw with your child

Draw these on paper, or build them with tiles and blocks. Seeing the shape makes the numbers easy to remember.

10⁶1,000,0006 zerosmillion10⁵100,0005 zeroshundred thousand10⁴10,0004 zerosten thousand10³1,0003 zerosthousand10²1002 zeroshundred10¹101 zeroten10⁰10 zerosone
Powers of 10 from 10⁰ to 10⁶. The exponent counts the zeros and names the place.
Each step down: ÷ 1010³=1,000÷ 1010²=100÷ 1010¹=10÷ 1010⁰=1÷ 1010⁻¹=1/10÷ 1010⁻²=1/100
Each step down the ladder divides by 10, so 10⁰ = 1 and 10⁻¹ = 1/10.
103baseexponent10 × 10 × 10 = 1,00010 is used as a factor 3 times
10³: three 10s multiplied make 1,000.

What your child already knows

Children already know place value: ones, tens, hundreds and thousands. They also know that multiplying by 10 adds a zero to a whole number. Powers of 10 give those ideas a short way to write.

In real life: A kilometre is 10³ metres, and a kilogram is 10³ grams. India counts 1 lakh as 10⁵ and 1 crore as 10⁷. Scientists write the age of the universe as about 1.4 × 10¹⁰ years.

Powers of 10 below 1

Keep going down the ladder and keep dividing by 10. 10⁰ = 1, 10⁻¹ = 0.1 (a tenth) and 10⁻² = 0.01 (a hundredth).

So the exponent also counts decimal places: 10⁻³ = 0.001 has its 1 in the third place after the point. This idea is used for tiny numbers in science and is taught in grade 8.

Worked examples

Example 1: Write a power of 10

  1. Write 10⁵ as a number.
  2. The exponent is 5, so write a 1 and five zeros: 100,000.

Example 2: Multiply

  1. Work out 3.2 × 10².
  2. Move every digit 2 places to the left: 3.2 becomes 320.

Example 3: Find the exponent

  1. Write 1,000,000 as a power of 10.
  2. Count the zeros: there are six.
  3. So 1,000,000 = 10⁶.

Common mistakes

Multiplying 10 by the exponentWorks out 10³ as 30.Fix: 10³ = 10 × 10 × 10 = 1,000.
Adding a zero to decimalsWorks out 2.5 × 10 as 2.50.Fix: move the digits one place left: 25.
Miscounting zerosWrites 10⁴ as 1,000.Fix: four zeros: 10,000. Count the zeros, not the commas.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

  1. “What does 10³ mean?” (10 × 10 × 10.)
  2. “How many zeros?” (3, so 1,000.)
  3. “What is 10⁶?” (1,000,000, a million.)
  4. “What is 7 × 10²?” (700.)
  5. “What power of 10 is 10,000?” (10⁴.)

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

  1. 10²
  2. 10⁴
  3. 10¹
  4. 10⁰
  5. 6 × 10³
  6. 45 × 10²
  7. Write 100,000 as a power of 10.
  8. How many zeros in 10⁹?
  9. Stretch: 3,400 ÷ 10²
Show the answers
  1. 100
  2. 10,000
  3. 10
  4. 1
  5. 6,000
  6. 4,500
  7. 10⁵
  8. 9
  9. 34

Games to play at home

Zero count

Say a power of 10 like 10⁴. Your child writes it with the right number of zeros.

Money ladder

Show ₹1 or $1, then 10, 100 and 1,000. Each note is 10 times the one before.

Place value slide

Write 3.5 on paper. Slide it one, two and three places to the left to show × 10, × 100 and × 1,000.

Big number hunt

Look up the population of your city or the distance to the Moon. Round it, then write it as a number times a power of 10.

A 5-day plan for powers of 10

Ten minutes a day is enough. Short, regular practice works far better than one long session.

By grade

Grade 5 (Common Core 5.NBT.A.2) explains patterns of zeros when multiplying by powers of 10 and uses exponents to write them. Grade 8 uses powers of 10 in scientific notation (8.EE.A.3). In India, powers of 10 appear in the class 8 chapter “Power Play”.

CBSE families: see the class 8 parent guides for A Square and a Cube and Power Play.

What comes next

Next, practice with multiplying by 10, 100 and 1,000 and the powers of 10 practice. For very big and very small numbers, learn scientific notation.

Worksheet and more practice

Print a free worksheet with an answer key, or keep practicing online with exponents practice.

Printable worksheets: powers of 10 worksheet · exponents worksheet · exponent rules worksheet · make a fresh exponents test

← Cube numbers and cube rootsExponents practice →

More: exponents for kids · exponent calculator · practice · order of operations with exponents · negative numbers and powers

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Questions parents ask

What are powers of 10?

Numbers you get by multiplying 10 by itself: 10, 100, 1,000, 10,000 and so on. They are written 10¹, 10², 10³, 10⁴.

Why does the exponent count the zeros?

Each extra 10 in the multiplication moves the 1 one place to the left, adding one zero.

What is 10 to the power of 0?

1. Each step down divides by 10: 10² = 100, 10¹ = 10, 10⁰ = 1.

How do you multiply by a power of 10?

Move every digit as many places to the left as the exponent. 4.7 × 10² = 470.

What grade learns powers of 10?

Grade 5 under Common Core 5.NBT.A.2. Grade 8 uses them for scientific notation.