# decimal

1. ### How to mod a decimal

After decrypting an affine cypher I was left with the inverse encoder of \frac{i - 2}{5} with i being the particular letter of the alphabet with a:=0 up to z:=25 Take S for example, which decodes to Y, but \frac{18-2}{5} = 3.2 = 24 mod 26 My work around. 18 + 4\times 26 = 122 122 - 2 =...
2. ### How many decimal digits to expect in the number 2^40?

ln2=.7 and ln10=2.3 Use these approximations and a indirect argument using only arithmetic to explain how many decimal digits to expect in the number 2^40. Are you correct?
3. ### Stuck on a weird step when trying to find two decimal place accuracy for a series!

The question along with its solution are attached. I'm stuck on the step where it compares the sum to the integral with the <= sign. I don't understand how someone can infer the truth of this in a way that requires no additional steps. Basically, how can I show this to be true without...
4. ### Area - whole and decimal numbers

Hi, I hope this is in the right post ... I am trying to work out a simple spread sheet for pricing, based on AREA, like this: If it costs $50 to paint 1m2 (one meter sq) then: 1m x 1m x$50 : $50 2m x 2m x$50 : $200 1.8m x 1.2m x$50 : \$108 etc. This is all good, except when I go into...
5. ### What digit is immediately on the right of the decimal point?

What digit is immediately on the right of the decimal point in (\sqrt{3}+\sqrt{2})^{2002}?
6. ### Need help with explaining a fraction to decimal and vice versa

We are learning how to convert fractions into decimals and then into percents. Ok well our teacher had us draw out a line and make 25,50,75,100% on this line and then had us underneath it say what the fraction of it would be. Ok so here is where i am stuck (so to speak) he said to get half of...
7. ### Converting a Repeating Decimal to a Fraction

Having no guidance but my textbook, which explains basic concepts, but leaves to more in depth stuff to the teacher (of which I have none), I turn yet again to the forums to help me with the following problem. 1.1{\overline{9}} converted to a fraction. Now, knowing how to convert a decimal if...
8. ### Decimal search for roots

I'm really stuck on the following question so please help... a) show praphically that the equation 3cos(x) = x^2+1 has exactly one positive real root the problem here is that I have no idea how to draw the graph etc. b) find an interval for this root in the form (a/10 , (a+1)/10 ) where a is...
9. ### Infinite periodic decimal.

Guys chill, I know this is probably the dummest question that have been ever uploaded in this forum, but I have to know that answer! So if 1/3=0.3333333(and so on) then how can 1/3 *3 = 0.33333333333 *3 = 1 why isn't it 0.9999999(and so on) since 3*3=9, not 10. I know that if we do it in...
10. ### Finding the last two decimal places.....

Finding the last two decimal digits of this number, we know before that the order of mod43 is 42. As a result i was thinking it may be linked in with this with applying the fact that ^42 mod 43=1mod 43 , then simplifying the (9^9) from this fact, on the other hand it may not have anything...
11. ### Convert decimal to fraction of an inch

I am puzzled by this small problem I used to know how to do it but I forgot. For example I have 2.12 inch. I aready know that the number 2 has a value of 2 inches but how about the decimal part? How can I find the nearest fraction of an in. (1/4 of an inch, 1/16 of an in, 1/5 of an inch and so...
12. ### Calculate power of negative decimal number

Hello I am new in this forum (Happy) I try to calculate {-10}^{ 2.6} using the calculator I get an error but i write that way {-10}^{ 2.6} = {-10}^{ 2+ 6/10} = {-10}^{ 2+ 3/5} = {-10}^{2 } * {-10}^{3/5 } = 100 * {{-10}^{ 3} }^{1/ 5} = 100*{-1000}^{ 1/5} \approx -398.107 i don't know if...
13. ### decimal expansion of 7^999,999

I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem. Find the decimal expansion of {7}^{999999}. Thanks for the help.
14. ### Expected value and decimal odds

Hi guys In a game of chance where the player knows the expected value (say -0.37), how do you work out what the decimal odds should be in order to break even in long run? (Decimal odds 2.0 = 1/1) Any help much appreciated :) Mike
15. ### Decimal Equation help please

2+0.1(5 - x) = 1.3x - (0.4x - 2.5) 2+0.5-0.1x = 1.3x-0.4x + 2.5 10(2+0.5-0.1x) = 10(1.3x=0.4x+2.5) 20+50-x = 13-4x + 25 70-x = -4x+38 32-x=-4x 32 = -3x 32/-3 = -3x/-3 In the back of the book it says the answer is x= 0 but get 32/-3? what am I doing wrong...
16. ### Equation with decimal problem

0.05x-2 = 0.3(x-5) 5x-2=3x-15 5x=3x-13 2x/2=-13/2 x=-13/2 I keep getting this answer, but in the book states its x=-2 which is correct but I can't figure how? Thank you
17. ### Leading digit in decimal notation

Hello! I have this problem: How many of the numbers 2^m, for 0<=m<=M, have leading digit 1 in decimal notation?
18. ### Correcting to 3 decimal places (3 d.p) and to 3 significant figures (3 s.f)

In correcting this number: "0.39" to 3 d.p and 3 s.f, would it be as follows? 3 d.p --> 0.390 3 s.f --> 0.390 Thanks.
19. ### How to work a fractional exponent? Need non decimal answer!

So on a recent test I ran into this, I wasnt sure how to work the first part because I couldnt figure out the fraction for it. The question said to PI((4/5(4)^5/4)-(16/3)) My first instinct is to solve the first, then subtract the second from it then multiply it by PI, however I couldnt...
20. ### First 25 digits after decimal point of (sqrt(10)+5)^100?

How would you go about finding the first 25 digits after decimal point of (\sqrt{10}+5)^{100}? (without using calculator)