Will mark branliest. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? ​

Answers

Answer 1

Answer:

Step-by-step explanation:

Let  n=2α⋅5β⋅m , where  gcd(m,10)=1 . Then, the decimal expansion of  1n  is of the form

0.a1…akak+1…ak+ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(1) ,

where  k=max{α,β}  and  ℓ  is the least positive integer for which  m∣(10ℓ−1) . In other words,  ℓ  is the order of  10  in the multiplicative group of units modulo  m . So  ℓ∣ϕ(m)  by Lagrange's theorem.

In particular, if  gcd(n,10)=1 , then  α=β=k=0 ,  m=n , and

1n=0.a1…aℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(2)  

Therefore, we know that

117=0.a1…aℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(3)  

Here  ℓ  is the least positive integer for which  17  divides  9…9ℓtimes , and we know that  ℓ  divides  ϕ(17)=16 .

Successively squaring  10  modulo  17  gives

102≡−2(mod17),104≡4(mod17),108≡−1(mod17),1016≡1(mod17) .

So  ℓ=16  in expansion  (3) .

In fact,

a1…a16×17=1016–1.  

a1…a8+a9…a16=108−1 .

The first fact has nothing to do with the denominator  n  being prime. The second fact has everything to do with  n  being prime, and was discovered by E. Midy in  1836 .


Related Questions

Help plz!!


Ryan worked at a local ice cream shop during the summer. The money he earned for the first six weeks is given below.

$40, $80, $38, $40, $32, $65

Ryan then earned $24 in the seventh week. How were the mean and the median affected?

The mean decreased, and the median remained the same.

The median decreased, and the mean remained the same.

The median and the mean both remained the same.

The mean and the median both decreased.

Answers

Answer:

my answer isn't on the list, but doing the math the median increased from 39 to 40, but the mean decreased from 49.16 to 45.57

Jesse bought a $340$ -gram bag of coffee beans. He uses $18.75$ grams of coffee beans each day. When there are $40$ grams of coffee beans remaining in the bag, Jesse will buy another bag to make sure he doesn't run out of coffee.

Answers

Answer:

I will make sure he doesnt run out for you.

Step-by-step explanation:

2. The mean weight of the students on the

Trail Middle School wrestling team is 150

pounds with a mean absolute deviation of

10 pounds. The mean weight of the

students on the Burlington Middle School

wrestling team is 130 pounds with a mean

absolute deviation of 10 pounds. By how

many pounds is the mean weight of the

students on Trail's team greater than the

mean weight of the students on

Burlington's team?

Answers

Answer:

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Step-by-step explanation:

Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School  wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.

Thus, the difference in mean deviation is [tex]150-130 = 20[/tex]

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Melanie cuts a rectangle out of a piece of scrap paper as shown. She wants to calculate the angle measure of the piece that is left over. What is the measure in degrees?

Answers

Answer: The angle measure of the piece that's left over would be 36°.

Number 7 please help 10 points no links pleAse

Answers

Answer:

Option C : 25

Step-by-step explanation:

Given,

Number of rainy days = 18

Number of cloudy days = 14

Number of sunny days = 29

Therefore,

Number of days either sunny or cloudy = 14 + 29 = 43

So,

Number of more days sunny or cloudy than rainy are

= 43 - 18 = 25

Hence,

Option C 25 is the correct answer.

HELP HELP HELP HELP HELP ITS URGENT :((((​

Answers

Answer: well if you listened on school you wouldn't need help sooo

Step-by-step explanation: LISTEN IN SCHOOL

complete the table of values for

y=3-x^3

Answers

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

x              |            y

---------------------------

-2            |            11  

-1             |             4

0             |             3

1              |             2

2             |            -5

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Brainliest?

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Please help !!!!!!!!!!!!!!

Answers

C is the correct answer :)

How many pieces of wire 3.6cm long can be cut from a coil of 1m long?What is the length of the piece left over?​

Answers

Answer:

We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over

Step-by-step explanation:

Find the "unit length" by dividing 1 m by 3.6 cm:

  1 m

-----------

3.6 cm

Recall that 1 m = 100 cm.  Multiply the following by the conversion factor 100 cm / 1 m:

  1 m            100 cm

----------- * ----------------- = 27,7777777...

3.6 cm            1 m

We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over (verify this by dividing 7 by 9 on a calculator).

Answer:

Solution :-

Pieces can be cut = 1/3.6

Pieces can be cut = 0.27 m

100 cm = 1 m

0.27 m = 27 cm

Therefore,

The length remaining of wire is 27 cm (approximately)

How to solve for shaded area

Answers

Answer:

(a)  12.96 ft²

(b)  21.5 in²

Step-by-step explanation:

(a) For the first diagram

Area of the shaded region (A) = Area of Tripezium- area of circle

A = [1/2(a+b)h]-[πr²]............... Equation 1

Where a and b are the parallel side of the tripezium respectively, h = height of the tripezium, r = radius of the circle.

From the diagram,

Given: a = 15 ft, b = 6 ft, h = 12 ft, r = h/2 = 12/2 = 6 ft.

Constant: π = 3.14

Substitute these values into equation 1

A = [12(15+6)/2]-(3.14×6²)

A = 126-113.04

A = 12.96 ft²

(b) For the second diagram,

Area of the shaded region (A') = Area of square- area of circle

A' = (L²)-(πr²)............. Equation 2

Where L = lenght of one side of the square, r = radius of the circle

From the diagram,

Given: L = 2r = (2×5) = 10 in, r = 5 in

Substitute these values into equation 2

A' = (10²)-(3.14×5²)

A' = 100-78.5

A = 21.5 in²

Center (-9,0) radius 1

Answers

Answer:

Step-by-step explanation:

im guessing you need the equation of the circle?

plugging it into the standard circle equaition you would get (x+9)^2+y^2=1 and then you would just need to rearaange it into standard form

what is the Surface area​

Answers

Answer:

104

Step-by-step explanation:

What is the probability of flipping a coin 3times and getting 3tailsin a row?

Answers

Answer:

1/8

Step-by-step explanation:

The probability of getting tails on a single flip is 1/2.

Each of the flips is an independent event so you must multiply the probability of getting tails on each flip together.

So, your answer will look like this

[tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex] ; which equals;

1/8

Answer:

1/8

Step-by-step explanation:

To calculate the probability you have to name all possible results first. If you mark a result of a single coin flip as  H  for heads or  T  for tails all results of  3  flips can be written as:

Ω = { ( H , H , H ) , ( H , H , T ) , ( H , T , H) , ( H , T , T ) , ( T , H , H ) , ( T , H , T ) , ( T ,T , H ) , ( T , T , T ) }

Each triplet contains results on  1st,  2 nd and  3 rd coin. So you can see that in total there are  8  elementary events in  Ω.

| Ω |  =  8

Now we have to define event  A  of getting tails three times.

The only elementary event which satisfies this condition is  ( T , T , T )  so we can write that:

A  =  { ( T, T , T ) }

| A |  =  1

Now according to the (classic) definition of probability we can write, that:

P ( A )  =  | A|/  | Ω |  =  1 /8

So finally we can write the answer:

The Probability of getting 3 tails in 3 coin flips is  1 /8 .

Dima called her friend to tell her that she saved 30% on her new skirt at a discount store. Her friend told her that she could have gotten a better deal at a different store that was advertising a sale of One-third off all clothing. If the original price of Dima’s skirt was $54, how much more could she have saved at the store her friend suggested?

Answers

Answer: I think it's 1.80

Answer:

B

Step-by-step explanation:

3. -20 + -15 + 11 + -6 =​

Answers

Answer:

-30

Step-by-step explanation:

How to solve (p^2)^5

Answers

Explanation: The power rule tells us that when we have a power taken to another power, we keep the base the same and we multiply the exponents.

So we have p¹⁰ which is our final answer.

Nadia has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change, I will buy more pencils.” How many pencils and how many rulers does she buy?

Answers

Answer:

Total pencils: 17

Total rulers: 15

Step-by-step explanation:

"I will buy 15 pencils."

15 * 8p = £1.20

15 pencils

"Then I will buy as many rulers as possible."

£5 - £1.20 = £3.80

£3.80/30p = 12 remainder 20p

12 rulers

"With my change, I will buy more pencils.”

20p/8p = 2 remainder 4 p

2 pencils

Total pencils: 17

Total rulers: 15

Measure the screwdriver's length to the nearest tenth of a centimeter. Express the answer as a decimal.

Answers

Answer:

17.1 cm

Step-by-step explanation:

A screw driver is a mechanical tool or device which is mainly used for screwing the screws and unscrewing them. It is also used for removing the nuts and bolts and also serves a variety of uses.

It is typically made of steel and has a handle and a shaft which ends as a tip.

In the context, the length of the screw driver from the given figure expressed to the nearest tenth of a centimeter is 17.1 cm.

It is also equivalent to [tex]$6\frac{3}{4}$[/tex] inch.

Write the number 6,800 in scientific notation.

Answers

Answer:

6.8*10^3

Step-by-step explanation:

Answer:

The answer is 6.8 × 103.

Step-by-step explanation:

I hope this helps! Have a great rest of your day!

Ceci can drive 225 miles in 3 hours (Rate - 75)
How many hours does it take her to drive 1,125 miles?

Answers

Answer:

it'll take 15h for her to drive 1125 miles

Step-by-step explanation:

take 225 ÷ 3 then you get how many miles she drives in an hour which is 75

75 × 15 = 1,125

7. A car drives 50 miles in the first hour on the road, 70 miles during the 2nd hour and 10 miles for 1/2 hour (traffic jam), then 60 miles in the final half hour of the trip. What was the average speed for the entire trip?

Answers

Answer:

Step-by-step explanation:

Average Speed = Total Distance / Total Time

Total Distance = 50+ 70 + 10 + 60 = 190 Miles

Total Time = 1 + 1 + 1/2 + 1/2 =  3 hours

Average speed = 190 / 3 = 63.3 mph

what is the value of x

Answers

answer: since they are linear pair therefore

x+34+ 2x+2=180

3x+36=180

3x=144

x=48°

Step-by-step explanation:

second opinion: ex are useless forget them

Answer:

B) x=48

Step-by-step explanation:

Hope it helps

Which is larger, a pound or a kilogram? Explain your reasoning.

Answers

Answer:

kg

Step-by-step explanation:

1pound is 0.45kg

Answer:

Both pound and kilogram are units of measurement of weight or mass. A pound is an imperial unit of mass or weight. ... A kilogram (kg) is stated to be 2.2 times heavier than a pound (represented as lbs). Thus, one kilo of mass is equal to 2.26lbs. Step-by-step explanation:

You deposit $4000 in an account earning 4% interest compounded monthly. How much will you
have in the account in 15 years?

Answers

You deposit $4000 in an account earning 4% interest compounded monthly. After 15 years, you will have approximately $7224.44 in the account.

To calculate the future value of an account with compound interest, we can use the formula:

Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Time)

In this case, the principal (initial deposit) is $4000, the interest rate is 4% (or 0.04 as a decimal), and the compounding is done monthly, so there are 12 compounding periods in a year.

Substituting these values into the formula, we have:

Future Value = $4000 * (1 + (0.04 / 12))^(12 * 15)

Calculating this expression gives us:

Future Value ≈ $4000 * (1.003333)^180

Future Value ≈ $4000 * 1.806111

Future Value ≈ $7224.44

After 15 years, you will have approximately $7224.44 in the account, considering the given interest rate and compounding frequency.

For more such questions on deposit

https://brainly.com/question/29053212

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Over 5 days, Kimberly sheared 300 sheep. How many would she be able to shear in 26 days?
What was her rate per day?

Answers

Answer:

Kim shears 1560 sheep in 26 days.

Her rate per day is 60.

Step-by-step explanation:

For 26 days:

[tex]\frac{5}{300} =\frac{26}{x} \\\\5x=7800\\x=1560[/tex]

For per day:

[tex]\frac{5}{300} =\frac{1}{x} \\\\5x=300\\x=60[/tex]

HELP FAST

find the value of x.

Answers

Answer:

81=6x+3(vertically opposite angle are equal)

81-3=6x

78=6x

x=13°

hope it helps.

equivalent fractions for 2 1/5 and 1 5/6

Answers

2 1/5: 11/5, 22/10, 33/15, 44/20 etc.
1 5/6: 11/6, 22/12, 33/18, 44/24, etc.

Jesse is making fruit salad. She purchased 5 & 1/3 ounces of 6 different fruits. How many ounces of fruit did she purchase?

Answers

Answer:

32 ounces of fruits

Step-by-step explanation:

Given that :

Number of distinct fruits purcahed = 6

Number of ounces of each fruit = 5 1/3

The total ounces of fruits purchased :

(Number of distinct fruits purchased * Number of ounces of each fruit)

6 * 5 1/3 = 6 * 16/3

6 * 16/3 = (16 * 6) / 3 = 96 /3 = 32 ounces of fruits.

How was y'all day :)?

Answers

Except it’s 1 am it was pretty cool

Please help it's for my sister

Answers

A and d is the one I would pick
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