David W. answered • 08/24/15
Tutor
4.7
(90)
Experienced Prof
Well, is the problem:
999.abc = def.123
Or
999*abc = def*123 ?
Now, in either case we are dealing with decimal, which is a positional number system. Thus, each digit – a,b,c,d,e,f – is multiplied by a power of 10 in order to give it a positional value. Thus, for a value like
123=abc
The value of a must be 1, and b=2, and c=3. There are no other digits that can make this equal. This is true for decimal fractions also. And, it also fits multiplication and division, because:
abc / def = 123 / 999 [divide both sides by def*999]
999.abc = def.123
Or
999*abc = def*123 ?
Now, in either case we are dealing with decimal, which is a positional number system. Thus, each digit – a,b,c,d,e,f – is multiplied by a power of 10 in order to give it a positional value. Thus, for a value like
123=abc
The value of a must be 1, and b=2, and c=3. There are no other digits that can make this equal. This is true for decimal fractions also. And, it also fits multiplication and division, because:
abc / def = 123 / 999 [divide both sides by def*999]
(which can only be reduced to 041/333, so abc=041 and def=333 could also be an answer if a is allowed to equal 0 and multiple variables can equal the same digit.)
