Scientific Notation Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scientific Notation.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A way of writing very large or very small numbers as a \times 10^n, where 1 \leq |a| < 10 and n is an integer.
Instead of writing out all the zeros in 93,000,000 or 0.000042, you slide the decimal point and count how many places it moved. The exponent on 10 keeps track of the shift.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Scientific notation uses powers of 10 to express any number compactly, making it easy to see its size at a glance.
Common stuck point: Determining the sign of the exponent: moving the decimal left gives a positive exponent (big numbers), right gives negative (small numbers).
Sense of Study hint: Place the decimal after the first nonzero digit, then count how many places you moved it. That count is the exponent — positive if the original number was big, negative if small.
Worked Examples
Example 1
easySolution
- 1 Move the decimal point right until we have a number between 1 and 10: 4.7.
- 2 Count the places moved: 4 places to the right, so the exponent is -4.
- 3 Result: 4.7 \times 10^{-4}.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
easyBackground Knowledge
These ideas may be useful before you work through the harder examples.