It can be just as important to appreciate that an answer is in the tens versus in the millions, as it is to know the exact amount. Alongside precision you need to develop an appreciation of the magnitude of numbers. You do this by considering the nearest power of ten. For example, 340 m is closer to 100 m (102 m) than it is to 1000 m (103 m). Hence its nearest order of magnitude is 102.
An example of when the magnitude of a number is useful is if someone has over 10 million followers on Twitter. Knowing there are roughly 107 people potentially reading their tweets may be more important than knowing exactly how many there are at a given minute. Using another Twitter example, someone with 83 839 followers has closer to 100 000 followers than 10 000 followers, hence the magnitude or power of ten that best describes their following is 105.
Using the magnitude, you can then easily compare between these two examples:
Note that ~ means ‘approximately equal to’, and applies only to the first step in the expression above because the exact numbers of followers has been rounded to provide these values. The three parts thereafter are exactly equal to one another, which is why the equals symbol (=) has been used.
Ten million (107) is one hundred (102) times larger than one hundred thousand (105), or two orders of magnitude greater. It is therefore easy to see that Person 1 has 100 times more followers than Person 2.
Note also that the order of magnitude quoted is the power of ten difference between the two numbers, in this example, 2. It is important to appreciate that if A is two orders of magnitude larger than B, then A is 100 times larger, not twice as large.
You might already be familiar with the concepts of magnitude. A question is provided below for you to test your knowledge.
Express the number 9.2499 × 103 to the nearest order of magnitude.
9.2499 × 103 is approximately 104 to the nearest order of magnitude, because 9.2499 × 103 is closer to 104 than 103. That is, 9249.9 is closer to 10 000 than 1000.
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