Abraham Bradley

2022-04-24

P-Adic Expansion of Rational Number (Reverse Direction)

${5}^{-1}+1+2\cdot 5+{5}^{2}+(4\cdot {5}^{3}+2\cdot {5}^{4}+3\cdot {5}^{5}+2\cdot {5}^{7}+{5}^{8})+(4\cdot {5}^{9}+2\cdot {5}^{10}+3\cdot {5}^{11}+2\cdot {5}^{13}+{5}^{14})+(4\cdot {5}^{15}+2\cdot {5}^{16}+3\cdot {5}^{17}+2\cdot {5}^{19}+{5}^{20})+\cdots$

Colonninisxi

Beginner2022-04-25Added 16 answers

Step 1

Given: $x=\dots \overline{120324}121.{1}_{5}$

and then add/subtract the appropriate finite base-5 fraction to make it a pure repeating number ending at the ones:

$x-1.{1}_{5}=\dots \overline{120324}{120}_{5}$

$=\dots {\overline{324120}}_{5}$

Then the I can convert that to a fraction essentially like one does for an ordinary decimal fraction, except that the analogue of $0.999{\dots}_{10}=1$ is now $\dots {444}_{5}=-1$

$x-\frac{6}{5}={324120}_{5}\xb7\dots {\overline{000001}}_{5}$

$=\frac{{324120}_{5}}{{444444}_{5}}\xb7\dots {\overline{444444}}_{5}$

$=-\frac{{324120}_{5}}{{444444}_{5}}$

$\Rightarrow {\textstyle \phantom{\rule{1em}{0ex}}}x=\frac{6}{5}-\frac{{324120}_{5}}{{444444}_{5}}$

$=\frac{65}{-}\frac{11160}{15624}=\frac{37944}{78120}=\frac{17}{35}$

Alternatively you could start with

$\frac{x-121.{1}_{5}}{{5}^{3}}=\dots {\overline{120324}}_{5}$

and convert the right-hand side of that to a fraction in the same way.

Which expression has both 8 and n as factors???

One number is 2 more than 3 times another. Their sum is 22. Find the numbers

8, 14

5, 17

2, 20

4, 18

10, 12Perform the indicated operation and simplify the result. Leave your answer in factored form

$\left[\frac{(4x-8)}{(-3x)}\right].\left[\frac{12}{(12-6x)}\right]$ An ordered pair set is referred to as a ___?

Please, can u convert 3.16 (6 repeating) to fraction.

Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.

A) $6-\frac{x}{3}=2$

B) $\frac{x}{3}-6=2$

C) 3x−6=2

D) $\frac{3}{x}-6=2$Find: $2.48\xf74$.

Multiplication $999\times 999$ equals.

Solve: (128÷32)÷(−4)=

A) -1

B) 2

C) -4

D) -3What is $0.78888.....$ converted into a fraction? $\left(0.7\overline{8}\right)$

The mixed fraction representation of 7/3 is...

How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?

Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.

A)235.47,7

B)235.047,4

C)235.47,4

D)234.057,7Find four equivalent fractions of the given fraction:$\frac{6}{12}$

How to find the greatest common factor of $80{x}^{3},30y{x}^{2}$?