There are many ways of calculating the value of e, but none of them ever give a totally exact answer, because e is irrational and its digits go on forever without repeating. Show
But it is known to over 1 trillion digits of accuracy! For example, the value of (1 + 1/n)n approaches e as n gets bigger and bigger: n(1 + 1/n)n12.0000022.2500052.48832102.593741002.704811,0002.7169210,0002.71815100,0002.71827
Try it! Put "(1 + 1/100000)^100000" into the calculator: (1 + 1/100000)100000 What do you get? Another CalculationThe value of e is also equal to 10! + 11! + 12! + 13! + 14! + 15! + 16! + 17! + ... (etc) (Note: "!" means factorial) The first few terms add up to: 1 + 1 + 12 + 16 + 124 + 1120 = 2.71666... In fact Euler himself used this method to calculate e to 18 decimal places. You can try it yourself at the Sigma Calculator. RememberingTo remember the value of e (to 10 places) just remember this saying (count the letters!):
Or you can remember the curious pattern that after the "2.7" the number "1828" appears TWICE: 2.7 1828 1828 And following THAT are the digits of the angles 45°, 90°, 45° in a Right-Angled Isosceles Triangle (no real reason, just how it is): 2.7 1828 1828 45 90 45 (An instant way to seem really smart!) Growthe is used in the "Natural" Exponential Function: Graph of f(x) = ex It has this wonderful property: "its slope is its value" At any point the slope of ex equals the value of ex : when x=0, the value ex = 1, and the slope = 1 when x=1, the value ex = e, and the slope = e etc... This is true anywhere for ex, and helps us a lot in Calculus when we need to find slopes etc. So e is perfect for natural growth, see exponential growth to learn more. AreaThe area up to any x-value is also equal to ex : An Interesting PropertyJust for fun, try "Cut Up Then Multiply"Let us say that we cut a number into equal parts and then multiply those parts together. Example: Cut 10 into 2 pieces and multiply them:Each "piece" is 10/2 = 5 in size 5×5 = 25 Now, ... how could we get the answer to be as big as possible, what size should each piece be? The answer: make the parts as close as possible to "e" in size. Example: 1010 cut into 2 equal parts is 5:5×5 = 52 = 25 10 cut into 3 equal parts is 313:(313)×(313)×(313) = (313)3 = 37.0... 10 cut into 4 equal parts is 2.5:2.5×2.5×2.5×2.5 = 2.54 = 39.0625 10 cut into 5 equal parts is 2:2×2×2×2×2 = 25 = 32 The winner is the number closest to "e", in this case 2.5. Try it with another number yourself, say 100, ... what do you get? 100 Decimal DigitsHere is e to 100 decimal digits: 2.71828182845904523536028747135266249775724709369995957 Advanced: Use of e in Compound InterestOften the number e appears in unexpected places. Such as in finance. Imagine a wonderful bank that pays 100% interest. In one year you could turn $1000 into $2000. Now imagine the bank pays twice a year, that is 50% and 50% Half-way through the year you have $1500, You got more money, because you reinvested half way through. That is called compound interest. Could we get even more if we broke the year up into months? We can use this formula: (1+r/n)n r = annual interest rate (as a decimal, so 1 not 100%) Our half yearly example is: (1+1/2)2 = 2.25 Let's try it monthly: (1+1/12)12 = 2.613... Let's try it 10,000 times a year: (1+1/10,000)10,000 = 2.718... Yes, it is heading towards e (and is how Jacob Bernoulli first discovered it).
Why does that happen?The answer lies in the similarity between: Compounding Formula: (1 + r/n)nand e (as n approaches infinity): (1 + 1/n)nThe Compounding Formula is very like the formula for e (as n approaches infinity), just with an extra r (the interest rate). How many 100 are in 10000?There are 100 $100 bills in $10,000.
How many 100s makes 1000?The students need to know 10 hundreds make 1 thousand and vice versa, and 10 thousands make 1 ten thousand and vice versa.
How many 10000 is equal to?100=1 hundred , 1000=1 thousand, 10000= ten thousand, 100000= 1lakh, 1000000= 10 lakh, 10000000=1 crore.
How do you write 10000 in digits?Ten Thousand in numerals is written as 10000.
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