Verified answer

Answer: 71/90, or maybe 78/99

Do you mean (a) 0.78888888... or (b) 0.7878787878...?

You can work this out on a calculator, a graphing calculator makes it easier to see.

If your calculator has a button that says [->Frac] or [D->F], the calculator will give you the answer right away. Otherwise, here is a way to do it yourself:

(a) Let x = 0.78888888... Since there is 1 digit that repeats, multiply by 10:

10x = 7.888888..

Now subtract :

10x-9x = 7.888888... - 0.7888888... {just put the '8' into the calculator about 10 times}

9x = 7.1

x = 7.1/9 = 71/90

Check: 71/90 = 0.788888888...

(b) Let x = 0.7878787878 ... Since 2 digits repeat, multiply by 100:

100x = 78.78787878...

100x - x = 78.78787878... - 0.7878787878...

99x = 78

x=78/99

Check: 78/99 = 0.7878787878...

More answers

Lvl 2

The answer is 71/90.

Lvl 1

Ch

Lvl 1

Chd

Lvl 1

0.78

Lvl 1

9.5

Lvl 1

39/50

Lvl 1

554

Lvl 1

5

Lvl 1

Dd

Still have questions?

Continue Learning about Other Math

.12

104 - 26 _____ 078

There are two methods here. The essential elements appear to be the same. Repeating decimals can be converted into fractions by the use of simultaneous equations. The trick is to identify how many numbers or decimal places are involved in the "repeating part" of the repeating decimal. Let's do one, and let's make it a familiar one. We'll take 0.3333333... which is 1/3 as you already know. First, there is only one digit that repeats. It's the 3. So we'll need to set up two equations, and the first one is that X = 0.3333333... In that equation, "X" is the decimal equivalent of the number. Now we'll create a second equation to do the simultaneous equation thing. Since there is only one digit that repeats, we're going to move the decimal one place by multiplying that whole equation by 101 which is 10. [X = 0.3333333...] x 10 = 10X = 3.333333... Notice that both sides of the equation were multiplied by 101 here. This is key. We are going to have to multiply our repeating decimal by a factor of 10 that shifts all of the repeating sequence to the left of the decimal. If we'd had 0.47474747.... for our fraction, we'd have had to multiply the equation by 102 because the "repeating part" there, which is '47' is two digits long. If it had been 0.5678567856785678.... we'd be stuck multiplying by 104 because the "repeating part" there, which is '5678' is four digits long. Back to our problem at hand. The 10 times "X" equals 10X and the 0.3333333 times 101 = 3.333333... Now we have two equations, and we're going to subject one from the other. So let's do that. 10X = 3.333333... X = 0.3333333... 10X - X = 9X, and 3.333333... - 0.3333333... = 3 Notice how the "repeating part" of the decimal "dropped out" or "disappeared" there? That's why we built two equations and subtracted one from another. We need to get the "repeating part" to get lost. Look at what's left. It this equation: 9X = 3 Can you handle that? Sure you can. Divide both sides by 9 and you'll have X = 3/9 which reduces to 1/3 and presto! Problem solved. If we'd done 0.474747474747... it would look like this: X = 0.474747474747... 100X = 47.4747474747... Note that we multiplied by a factor of 10 enough to shift a "whole block" of the repeating part to the left of the decimal. Now subtract the top equation from the bottom one. 100X = 47.4747474747... X = 0.474747474747... 100X - X = 99X and 47.47474747... - 47.4747474747... = 47 99X = 47 and X = 47/99 As 47 is a prime number, we can't reduce this fraction. There are some simple rules that apply when converting any repeating decimal to a fraction. First we'll perform the "construction" of an initial equation where we set the fraction ("X") equal to the repeating decimal. Then we'll "manufacture" a second equation from the first by multiplying the first equation by 10n where n = the number of digits in the "repeating part" of the repeating decimal so they all kick over to the left of the decimal. Then we solve the simultaneous equations, and lastly reduce our fraction. Try a few and you'll be able to slam dunk this bad boy every time you see it. This is made quite easy with the following observations:5/9 = 0.55557/9 = 0.777712/99 = 0.12121223/99 = 0.232323456/999 = 0.45645645678/999 = 078/999 = 0.078078078So we can see that fractions with a denominator of 9, 99, 999, 9999, are pretty useful for making repeating decimals. All we have to do is to reduce the fraction to its lowest terms. For example, let's take the repeating decimal 0.027027027...Clearly this is 27/999 = 1/37 (having divided top and bottom of the fraction by 27)Now let's try something more tricky. Take a look at 0.4588888888...This isn't simply something divided by 99.. since the 45 bit doesn't repeat. What we need to do is move the decimal point over to the start of the repeating bit. In this case we multiply by 100 to get 45.888888...Now we know the fraction part is 8/9. In total we have 45 + 8/9 = 413/9 (changing into a top-heavy fraction will make things easier for us).So 45.88888... = 413/9Now just divide both sides by 100 to get:0.458888... = 413/900

Assuming the digits can be used again, there are 10*10*10 or 1000 three digit combinations.IF YOUR LOOKING FOR 3 DIGIT LOTTERY ANSWERS HERE THEY ARE!Of the 1000 3-digit numbers 720 are non-repeating, 270 one-repeating, and 10 triples. Since a non-repeating number has 5 more siblings, we can divide 720 by 6 to obtain 120 distinct non-repeating-digit numbers which are listed below.3-digit, non-repeating combinations (6-way)012, 013, 014, 015, 016, 017, 018, 019, 023, 024, 025, 026, 027, 028, 029, 034, 035, 036, 037, 038, 039, 045, 046, 047, 048, 049, 056, 057, 058, 059, 067, 068, 069, 078, 079, 089, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168, 169, 178, 179, 189, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 256, 257, 258, 259, 267, 268, 269, 278, 279, 289, 345, 346, 347, 348, 349, 356, 357, 358, 359, 367, 368, 369, 378, 379, 389, 456, 457, 458, 459, 467, 468, 469, 478, 479, 489, 567, 568, 569, 578, 579, 589, 678, 679, 689, 789Similarly, since three one-repeating numbers can be represented by one number, there are 270/3=90 distinct one-repeating numbers (doubles) as listed below.3-digit, one-repeating combinations (Doubles) (3-way)001, 002, 003, 004, 005, 006, 007, 008, 009, 011, 022, 033, 044, 055, 066, 077, 088, 099, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 334, 335, 336, 337, 338, 339, 344, 355, 366, 377, 388, 399, 445, 446, 447, 448, 449, 455, 466, 477, 488, 499, 556, 557, 558, 559, 566, 577, 588, 599, 667, 668, 669, 677, 688, 699, 778, 779, 788, 799, 889, 899The following table and figures summarize the foregoing facts and the probability of winning with any order arrangement of 3-digit games.Group name and aliasesHow many 3-dig Numbers fall into this groupHow many distinct members of the groupodds of winning with a number in the groupProbability of a number drawn to be in the groupNon-repeat (6-way)7201201:16772%One-repeat (3-way) (Doubles)270901:33327%Triples10101:10001%One thousand if you allow repeating digits.

Related questions

0.78 = 39⁄50

13 + .078

078

.078 of 50000.00 is 3900.00.

078 percent

This is made quite easy with the following observations: 5/9 = 0.5555... 7/9 = 0.7777... 12/99 = 0.121212... 23/99 = 0.232323... 456/999 = 0.456456456... 78/999 = 078/999 = 0.078078078... So we can see that fractions with a denominator of 9, 99, 999, 9999, ... are pretty useful for making repeating decimals. All we have to do is to reduce the fraction to its lowest terms. For example, let's take the repeating decimal 0.027027027... Clearly this is 27/999 = 1/37 (having divided top and bottom of the fraction by 27) Now let's try something more tricky. Take a look at 0.4588888888... This isn't simply something divided by 99.. since the 45 bit doesn't repeat. What we need to do is move the decimal point over to the start of the repeating bit. In this case we multiply by 100 to get 45.888888... Now we know the fraction part is 8/9. In total we have 45 + 8/9 = 413/9 (changing into a top-heavy fraction will make things easier for us). So 45.88888... = 413/9 Now just divide both sides by 100 to get: 0.458888... = 413/900

7.8%

The value was in 2011: 63 078 000 000 US $.The value was 63 078 000 000 US $ in 2011.

.12

079

104 - 26 _____ 078

78 is less than 313.