Question #94c0e

1 Answer
Jul 27, 2016

Answer:

Usually, six. If one of the terminal zeroes is an additional significant digit, we should indicate that, for example by using scientific notation.

Explanation:

Terminal zeroes before a decimal point are generally not sugnificant. They just serve as placeholders to give the actual significant digits their proper place values. Thus #530,405,000# is likely to be accurate only to the nearest thousand, but we need the last three zeroes to distinguish the number from #530,405#.

Terminal zeroes after a decimal point are significant because they are not mere placeholders. Thus #5.0# must have two significant digits instead of one. If #530,405,000# is accurate to the nearest multiple of #100# (i.e. the number is accurate enough for the first terminal zero to be a seventh significant digit), we can indicate that by including an extra zero in scientific notation where all digits but one are after the decimal point. Thus, #5.30405color(blue)0xx10^8# has the last zero after the decimal point, so it is indicated as an extra significant digit.