What Is Scientific Notation?
In science, we often deal with numbers that are incredibly large (like the distance to the Sun: 149,600,000,000 m) or incredibly small (like the size of a bacterium: 0.000001 m). Writing all those zeros is tedious and error-prone. That's where scientific notation comes in.
A way of expressing numbers as a product of a coefficient (a number between 1 and 10) and a power of 10. The general form is , where and is an integer.
For example:
The exponent tells you how many places the decimal point has moved:
- A positive exponent means the number is large (decimal moves right).
- A negative exponent means the number is small (decimal moves left).
Think of scientific notation like a zoom lens on a camera. The coefficient () tells you what you're looking at, while the power of 10 () tells you how far zoomed in or out you are. A big positive exponent means you're zoomed way out (huge distances), while a big negative exponent means you're zoomed way in (tiny particles).
Quick Review: Converting to and from Scientific Notation
Before we do operations, let's make sure we're confident converting numbers.
Converting a large number to scientific notation:
- Move the decimal point left until you have a number between 1 and 10.
- Count how many places you moved — that's your positive exponent.
Convert to scientific notation.
- Move the decimal:
- We moved 5 places to the left.
- Answer:
Converting a small number to scientific notation:
- Move the decimal point right until you have a number between 1 and 10.
- Count how many places you moved — that's your negative exponent.
Convert to scientific notation.
- Move the decimal:
- We moved 4 places to the right.
- Answer:
A common mistake is getting the sign of the exponent wrong. Remember: big numbers = positive exponents, small numbers (less than 1) = negative exponents.
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