Let's begin by listing the first few multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44. So, between 1 and 37 there are 9 such multiples: {4, 8, 12, 16, 20, 24, 28, 32, 36}. Note that 4 divided into 36 is 9.
Let's experiment by modifying the given problem a bit, for the purpose of discovering any pattern that may exist:
<span>How many multiples of 4 are there in {n; 37< n <101}? We could list and then count them: {40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100}; there are 16 such multiples in that particular interval. Try subtracting 40 from 100; we get 60. Dividing 60 by 4, we get 15, which is 1 less than 16. So it seems that if we subtract 40 from 1000 and divide the result by 4, and then add 1, we get the number of multiples of 4 between 37 and 1001:
1000 -40 ------- 960
Dividing this by 4, we get 240. Adding 1, we get 241.
Finally, subtract 9 from 241: We get 232.
There are 232 multiples of 4 between 37 and 1001.
Can you think of a more straightforward method of determining this number? </span>
If the number of hours in school each week is somewhere between 20 and 40, then it can be written in scientific notation as 2.0×10¹ to 4.0×10¹
The exponent of 10 in each case is 1, so we can say the Order of Magnitude is 1. TRUE
_____ In Engineering terms, the order of magnitude is sometimes considered to be the integer part of the base-10 logarithm of the number. log(20) ≈ 1.3010 log(40) ≈ 1.6021 If we round these numbers to integers, we find the order of magnitude of the first is 1; the order of magnitude of the second is 2. Thus a student who spends 6 hours per day for 5 weekdays in class will have hours with an order of magnitude of 1, while a student who spends 7 hours per day for 5 days each week will have hours with an order of magnitude of 2. This question is best answered by considering "order of magnitude" in the simplistic terms of the answer above: the exponent of 10 in scientific notation.
