Is there a way to multiply any number with integers to get specific digits at specific place values?

Another way to look at the same question is whether any integer multiple of 71631 will have zeros in the thousands and ten-thousands place, and a one in the hundreds place.

This "brute force" method is tedious for hand calculations, but quite easy to write as a computer routine.

Here's a FORTRAN loop:
DO 10 J = 1 TO 9999
N = 71631*J
K = N/100
Comment: the K will simply be a truncation.
IF MOD(K,1000) .EQ. 1 THEN
WRITE (6,*) 'SUCCESS AT ', J, ' ', N
STOP
ENDIF
10 CONTINUE
WRITE(6,*) 'NO LUCK FOR J < 10000'
END

you are talking about rounding
and or truncating..

0.716 cannot be multiplied by a integer to get less than 0.716

but maybe you mean.. you want 3 digits after the decimal

that is easy

intermediate number = ((number to round) * 10 ^(digits after dec) )+ 0.5

this basically turns the floating point number into a larger number by the amount of the decimals you wish to save ..

you then convert this number into an INTEGER

Integer = intermediate number

then you convert this back to a decimal number

rounded number = ((double) integer) /(10^(digits))

that gives your number rounded

so if you have this number using 3 as digits the steps look like this

intermediate number = 0.71631 * 1000 + 0.5
intermediate number = 716.31 + 0.5 = 716.8

the integer of this is
Integer = 716

then we convert it back

rounded number = 716/1000 = 0.716

NOW this is not completely true because in computers the floating point number is base 2 so it wont be nice and neat all the time but it should be close