Octal Fractions

Interview

Time limit1sMemory limit128 MB

Summary

Read octal fractions from 0 to 1 and print each one's exact decimal value, with trailing zeros stripped.

Level: Medium4 of 10
Topics: Math, String, Implementation, Simulation
Solved: No attempts yet

Problem

A fraction written in octal (base 8) can always be written exactly in decimal (base 10). For example, the octal number 0.75 equals $7/8 + 5/64 = 0.953125$ in decimal. Every octal fraction with $n$ digits after the point can be written with at most $3n$ digits after the decimal point.

Write a program that converts octal fractions strictly between 0 and 1 into the equivalent decimal fractions.

Input

The input is a list of octal numbers to convert, one per line. Each number has the form $0.d_1 d_2 d_3 \dots d_k$ , where every $d_i$ is an octal digit ( $0$ through $7$ ). There is no limit on the number of digits $k$ . Input continues until end of file.

Output

For each input line, print one line of the form

X [8] = 0.Y [10]

where $X$ is the input octal number copied verbatim and $0.Y$ is its decimal value. On the decimal side, strip every trailing zero so the last digit is never $0$ .

Examples3

Example 1

Input

0.75
0.0001
0.01234567

Expected output

0.75 [8] = 0.953125 [10]
0.0001 [8] = 0.000244140625 [10]
0.01234567 [8] = 0.020408093929290771484375 [10]

Example 2

Input

0.1
0.7
0.4

Expected output

0.1 [8] = 0.125 [10]
0.7 [8] = 0.875 [10]
0.4 [8] = 0.5 [10]

Example 3

Input

0.2
0.5
0.6
0.3

Expected output

0.2 [8] = 0.25 [10]
0.5 [8] = 0.625 [10]
0.6 [8] = 0.75 [10]
0.3 [8] = 0.375 [10]