Question

test your knowledge 3
determine the number of significant figures in each number.
50.0
50.
5.0
500
005
0.005
5.00 x 10^{-1}

Explanation:

Step1: Rules for significant figures

• Non - zero digits are always significant.
• Zeros between non - zero digits are significant.
• Trailing zeros in a number with a decimal point are significant.
• Leading zeros (zeros before non - zero digits) are not significant.
• For numbers in scientific notation \(a\times10^{n}\), the number of significant figures is the number of digits in \(a\).

Step2: Analyze each number

• For \(50.0\):
• The non - zero digit \(5\) is significant.
• The zeros after the decimal and after the non - zero digit \(5\) are trailing zeros in a number with a decimal, so they are significant.
• Number of significant figures \(= 3\).
• For \(50.\):
• The non - zero digit \(5\) is significant.
• The zero after the non - zero digit \(5\) and before the decimal (in the context of a number like \(50.\) which is equivalent to \(50.0\) in terms of significance rules for trailing zeros when a decimal is present) is significant.
• Number of significant figures \(= 2\).
• For \(5.0\):
• The non - zero digit \(5\) is significant.
• The zero after the non - zero digit \(5\) and after the decimal is a trailing zero in a number with a decimal, so it is significant.
• Number of significant figures \(= 2\).
• For \(500\):
• The non - zero digit \(5\) is significant.
• The zeros after the non - zero digit \(5\) without a decimal are ambiguous. But if we assume no decimal, we consider only the non - zero digit as a significant figure (if we want to show more significant figures, we would write it in scientific notation).
• Number of significant figures \(= 1\).
• For \(005\):
• The leading zeros are not significant.
• Only the non - zero digit \(5\) is significant.
• Number of significant figures \(= 1\).
• For \(0.005\):
• The leading zeros (before the non - zero digit \(5\)) are not significant.
• Only the non - zero digit \(5\) is significant.
• Number of significant figures \(= 1\).
• For \(5.00\times 10^{-1}\):
• In scientific notation \(a\times 10^{n}\), the number \(a = 5.00\).
• The non - zero digit \(5\) is significant.
• The zeros after the non - zero digit \(5\) and after the decimal are trailing zeros in a number with a decimal, so they are significant.
• Number of significant figures \(= 3\).

Answer:

• \(50.0\): \(3\)
• \(50.\): \(2\)
• \(5.0\): \(2\)
• \(500\): \(1\)
• \(005\): \(1\)
• \(0.005\): \(1\)
• \(5.00\times 10^{-1}\): \(3\)