1. ORDERS of MAGNITUDE
THE power of ten

2. The order of magnitude…
… of an event or object’s property is the power of ten that best represents that number. For example, a kilogram is 3 orders of magnitude larger than a gram (103 as compared to 100).

3. Finding Orders of Magnitude
To find the order of magnitude of a number, DO:
Write the number in proper scientific notation.
Round the numerical part to either 10 or 1.
Rewrite it in proper scientific notation (if needed). The resulting exponent of ten is the order of magnitude of the number.
Ex: 5.6 × 103 has order of magnitude “4”, and has order of magnitude “-3”.

4. Answer: order of magnitude is 4
EXAMPLE
What is the order of magnitude of 8000?
8000 = 8 × 103
8 is closer to 10 than to 1, so replace 8 by 10:
8 × 103 ≈ 10 × 103
Putting in proper scientific notation:
10 × 103 = 104
Answer: order of magnitude is 4

5. WHAT DO WE DO WITH A 5? FOLLOW THE ROUNDING RULES! So… 5 × 103 = 104
and
5.0 × 103 = 104 ,
but
4.9 × 103 = 103

6. What you are really doing…
… is “locating” the number on a scale that goes more or less like this:
these two are “closer” to 101
“0” “1” “1” “2”

7. THE END
Lilian Wehner ©