Question

sig figs and scientific notation - physical science created by jon holland 1 determine the number of significant figures in the measurement 0.004560 g. a 2 b 4 c 5 d 6

Explanation:

Step1: Recall sig fig rules

Leading zeros (before non - zero digits) are not significant. Non - zero digits are significant. Trailing zeros after a decimal are significant.
For the number \(0.004560\):

• The leading zeros (\(0.00\)) are not significant.
• The non - zero digits \(4\), \(5\), \(6\) are significant.
• The trailing zero (\(0\)) after the decimal is significant.

Step2: Count significant figures

Count the significant digits: \(4\), \(5\), \(6\), \(0\) (the trailing zero) and the non - zero digits before? Wait, no. Wait, the number is \(0.004560\). Let's break it down:

• Leading zeros: \(0.00\) (3 zeros) - not significant.
• Then we have \(4\) (significant), \(5\) (significant), \(6\) (significant), and the trailing \(0\) (significant because it's after the decimal and after non - zero digits). So the significant figures are \(4\), \(5\), \(6\), \(0\)? Wait, no, wait: \(0.004560\) has digits: the first non - zero digit is \(4\), then \(5\), \(6\), and then \(0\) at the end. So that's \(4\) (1), \(5\) (2), \(6\) (3), \(0\) (4)? Wait, no, I made a mistake. Wait, \(0.004560\): let's write it in scientific notation to see better. \(0.004560 = 4.560\times10^{- 3}\). In scientific notation, the significant figures are the digits in the coefficient. So \(4\), \(5\), \(6\), \(0\) - that's 4? Wait, no, wait \(4.560\) has four significant figures? Wait, no: \(4\) (1), \(5\) (2), \(6\) (3), \(0\) (4). Wait, but wait the original number is \(0.004560\). Let's count again:
• Leading zeros: 3 (not significant).
• Then \(4\) (significant, 1), \(5\) (significant, 2), \(6\) (significant, 3), \(0\) (significant, 4). Wait, but that's 4? But wait, maybe I messed up. Wait, no, the trailing zero after the decimal in a number is significant. So in \(0.004560\), the digits are: positions (from left, ignoring leading zeros):

1. \(4\) (significant)
2. \(5\) (significant)
3. \(6\) (significant)
4. \(0\) (significant)

Wait, but that's 4? But the options have 4 as option B. Wait, but wait, maybe I made a mistake. Wait, let's check the rules again.
Rule 1: All non - zero digits are significant. So \(4\), \(5\), \(6\) are significant (3 digits).
Rule 2: Zeros between non - zero digits are significant (not applicable here).
Rule 3: Trailing zeros in a decimal number are significant. So the zero at the end (after \(6\)) is significant. So that's \(4\), \(5\), \(6\), \(0\) - 4 significant figures? Wait, no, \(4\), \(5\), \(6\) are three, plus the trailing zero is four. So total of 4 significant figures.

Answer:

B. 4