Scientific Notation
Scientific notation is a way to write very large or very small numbers more simply. We use powers of ten to do this.
- Choose the first digit
- Write the number so there is one nonzero digit before the decimal point.
- This gives a new number between 1 and 10.
- Count the moves
- Count how many places you moved the decimal point. Call this number n.
- Write the power of ten
- If you moved the decimal to the left, n is positive.
- If you moved the decimal to the right, n is negative.
- Combine them
- The result is: \((newNumber) \times 10^n\)
Example 1: A large number
- Original number: 4567834
- Move the decimal point left 6 times: 4.567834
- Exponent: +6 (because we moved left)
- Scientific notation: \(4.567834 \times 10^6\)
Example 2: A very small number
- Original number: 0.00000000000235
- Move the decimal point right 12 times: 2.35
- Exponent: −12 (because we moved right)
- Scientific notation: \(2.35 \times 10^{-12}\)
A number is written in scientific notation if it has the form \(a\times 10^n\) where \(1\le a < 10\)