Because I round all the numbers when I write them down,
sometimes intermediate (rounded) numbers in a calculation don't exactly
match the final answer or total;
the final answer (obtained without any
intermediate rounding) is more accurate.
These minor numerical disagreements
don't affect any of the arguments in this book.
DRAFT 2
Because I round all the numbers when I write them down,
there will be cases where intermediate (rounded) numbers in a calculation don't exactly
add up or multiply up to the final answer or total I've written down.
In such cases the final answer given (which I obtained without any
intermediate rounding) is more accurate.
These minor numerical disagreements don't affect any of the arguments in this book.
DRAFT 1
Because I round all the numbers when I write them down,
there will be cases where the sum of some numbers in the book does
not exactly agree with the total that I've written
down. These minor numerical disagreements are an unavoidable consequence
of the rounding habit; they don't affect any of the arguments in this book.