Scientific notation

Scientific notation writes very big or very small numbers as a number between 1 and 10 times a power of 10, like 4.5 × 10⁴.

The idea: a short way to write long numbers

150,000,000 km, the distance to the Sun, has a lot of zeros to count. In scientific notation it is 1.5 × 10⁸ km.

Every number in scientific notation has two parts: a number from 1 up to (but not including) 10, and a power of 10. The power says how far the decimal point moved.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

450004 places left4.5 × 10⁴
A big number: the point hops 4 places left, so the power is 4.
0.00453 places right4.5 × 10⁻³
A small number: the point hops 3 places right, so the power is −3.
32000006 places left3.2 × 10⁶
3,200,000: six hops, so 3.2 × 10⁶.

Writing a big number

Put the decimal point after the first digit: 45,000 becomes 4.5. Then count how many places the point moved to get there: 4 places.

So 45,000 = 4.5 × 10⁴. For a big number, the power of 10 is positive.

Writing a small number

For 0.0045, move the point to just after the first non-zero digit: 4.5. It moved 3 places to the right.

So 0.0045 = 4.5 × 10⁻³. For a number smaller than 1, the power is negative. The negative exponents lesson explains why.

Converting back to an ordinary number

Move the point the other way. 3.2 × 10⁵ means move the point 5 places to the right: 320,000.

2.1 × 10⁻³ means move it 3 places to the left: 0.0021. Fill any gaps with zeros.

Big powers of 10

Try base 10 with a big or negative exponent. Then try 9 with exponent 20 to see a big answer in scientific notation.

Comparing numbers in scientific notation

Compare the powers of 10 first. 3 × 10⁵ is bigger than 9 × 10⁴, because 10⁵ is ten times 10⁴.

Only when the powers are the same do you compare the first numbers. 7.2 × 10⁶ is bigger than 6.9 × 10⁶.

Scientific notation on a calculator

Calculators show very big answers with an E: 1.5E8 means 1.5 × 10⁸. Some show “×10” with small digits instead.

Children sometimes copy 1.5E8 as 1.58, which is a very different number. Teach them to read the E as “times ten to the”.

Key words

Teaching tip: hop the point

Write the number on squared paper with one digit per box. Draw the decimal point, then draw a small hop for every place it moves, as in the pictures.

The number of hops is the power of 10. Hops to the left make a positive power, and hops to the right make a negative power.

Real data makes it stick. Look up the population of India (about 1.4 × 10⁹) or the size of a red blood cell (about 8 × 10⁻⁶ m).

A week of practice

Ten minutes a day is plenty. Short, regular practice beats one long session at the weekend.

If one day goes badly, repeat it rather than moving on. Each day builds on the one before.

Quiz: scientific notation

Type the number and the power of 10.

Where this fits: exponents step by step

  1. What are exponents
  2. Square numbers
  3. Square roots
  4. Estimating square roots
  5. Cube numbers and cube roots
  6. Powers of 10
  7. Exponent rules
  8. Zero and negative exponents
  9. Scientific notation (this page)
  10. Operations with scientific notation

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “What does 10⁴ equal?” (10,000.)
  2. “So what is 4.5 × 10⁴?” (45,000.)
  3. “How do we write 600 in scientific notation?” (6 × 10².)
  4. “Is 12 × 10³ in scientific notation?” (No, 12 is bigger than 10. It is 1.2 × 10⁴.)
  5. “What about 0.07?” (7 × 10⁻².)

More worked examples

Example 1: big number

3,500,000 = 3.5 × 10⁶.

Example 2: small number

0.00072 = 7.2 × 10⁻⁴.

Example 3: back to standard form

6 × 10⁵ = 600,000.

Example 4: fixing the form

12 × 10⁵ = 1.2 × 10⁶, because 12 = 1.2 × 10.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 45,000
  2. 7,000,000
  3. 0.003
  4. 0.000052
  5. 2.4 × 10³ as a number
  6. 9.1 × 10⁻² as a number
  7. Which is bigger, 3 × 10⁴ or 8 × 10³?
  8. Write 12 × 10⁵ correctly.
  9. Write 0.5 × 10³ correctly.
  10. Stretch: how many digits does 6.02 × 10²³ have when written out?
Show the answers
  1. 4.5 × 10⁴
  2. 7 × 10⁶
  3. 3 × 10⁻³
  4. 5.2 × 10⁻⁵
  5. 2,400
  6. 0.091
  7. 3 × 10⁴
  8. 1.2 × 10⁶
  9. 5 × 10²
  10. 24

Common mistakes

Too many digits before the pointWrites 45,000 as 45 × 10³.Fix: the first number must be between 1 and 10: 4.5 × 10⁴.
Wrong sign on the powerWrites 0.003 as 3 × 10³.Fix: numbers smaller than 1 have a negative power: 3 × 10⁻³.
Counting zeros, not placesWrites 4,500 as 4.5 × 10².Fix: count the places the point moves: 3, so 4.5 × 10³.

How to teach it at home

Big number hunt

Find big numbers in the news or on food labels and write them in scientific notation together.

Space facts

The Moon is about 384,000 km away. Ask your child to write it as 3.84 × 10⁵.

Tiny things

A human hair is about 0.00008 m wide. Write it as 8 × 10⁻⁵ m.

By grade

More for each grade: Grade 8 math and the CBSE class 8 maths guide.

Worksheets and practice

Scientific notation worksheet, page 1

Scientific notation worksheet: printable PDF with an answer key. · Make a fresh test

Exponents practice · exponent calculator · exponents for kids · exponent rules worksheet · scientific notation worksheet · order of operations with exponents

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Questions parents ask

What is scientific notation?

A way to write a number as a number from 1 up to 10, times a power of 10. 45,000 = 4.5 × 10⁴.

How do you write a small number in scientific notation?

Move the point to just after the first non-zero digit and count the places. 0.0045 = 4.5 × 10⁻³.

Why must the first number be less than 10?

So every number has only one way to be written, which makes comparing easy.

What does E mean on a calculator?

Times ten to the power of. 2.5E6 means 2.5 × 10⁶ = 2,500,000.

What grade learns scientific notation?

Grade 8 under Common Core 8.EE.A.3 and 8.EE.A.4.