Scientific Notation
Scientific notation writes very large or small numbers as a × 10ⁿ.
About this topic
Scientific notation writes very large or very small numbers as a number between 1 and 10 multiplied by a power of ten. The distance to the Sun, about 150,000,000 km, becomes 1.5 × 10⁸ km, and the width of a hair, 0.00007 m, becomes 7 × 10⁻⁵ m.
A positive exponent means moving the decimal point right, and a negative exponent means moving it left. This notation makes comparing magnitudes easy and avoids counting zeros. Scientists and calculators use it constantly. To multiply, multiply the front numbers and add the exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. To divide, divide the front numbers and subtract the exponents.
Consider the mass of the Earth, roughly 6 × 10²⁴ kg, and the mass of a proton, about 1.7 × 10⁻²⁷ kg. Writing them out in full would take dozens of zeros, but with powers of ten you can see at a glance that the Earth is about 10⁵¹ times heavier. Astronomy, chemistry, biology and computing all use this notation.
A common error is leaving the front number outside the range, such as 15 × 10⁶, which should be 1.5 × 10⁷. Another is mixing up the sign of the exponent: tiny numbers have negative exponents, not negative values. When adding numbers in scientific notation, first make the powers of ten match.
Key ideas
- 1 ≤ a < 10
- Positive n for large, negative n for small
- Multiply by adding exponents
Quick check
Use cases: where Scientific Notation helps
- Homework: review the key idea behind Scientific Notation before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Scientific Notation without notes.
- Visual learning: play with the interactive lab to see how Scientific Notation changes when you adjust its inputs.
- Teaching a friend: explain Scientific Notation in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Scientific Notation?
Scientific notation writes very large or small numbers as a × 10ⁿ.
What will I learn in Scientific Notation?
1 ≤ a < 10. Positive n for large, negative n for small. Multiply by adding exponents.
Is Scientific Notation part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Scientific Notation lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Scientific Notation?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.