Question

etermine the number of significant figures in each number.

1. 0.02 ______
2. 0.020 ______
3. 501 ______
4. 501.0 ______
5. 5,000. ______
6. 6,051.00 ______
7. 0.0005 ______
8. 0.1020 ______
9. 10.001 5

Explanation:

To determine the number of significant figures, we use the rules:

• Leading zeros (zeros before the first non - zero digit) are not significant.
• Non - zero digits are always significant.
• Zeros between non - zero digits are significant.
• Trailing zeros in a number with a decimal point are significant; trailing zeros in a whole number without a decimal point may or may not be significant (but if there is a decimal point shown, like in \(5000.\) or \(501.0\), the trailing zeros are significant).

1. For \(0.02\)

Step 1: Identify non - zero and zero types

The leading zeros (the two zeros before \(2\)) are not significant. The non - zero digit is \(2\).
So the number of significant figures is \(1\).

2. For \(0.020\)

Step 1: Analyze zeros and non - zero digits

Leading zeros (the two zeros before \(2\)) are not significant. The non - zero digit \(2\) is significant, and the trailing zero after \(2\) (because there is a decimal point) is also significant.
So the number of significant figures is \(2\).

3. For \(501\)

Step 1: Check each digit

The non - zero digits \(5\) and \(1\) are significant, and the zero between them (\(5\) and \(1\)) is also significant.
So the number of significant figures is \(3\).

4. For \(501.0\)

Step 1: Evaluate each digit

The non - zero digits \(5\), \(0\) (between \(5\) and \(1\)), \(1\) are significant, and the trailing zero after the decimal point is also significant.
So the number of significant figures is \(4\).

6. For \(5000.\)

Step 1: Consider the decimal point

The non - zero digit \(5\) is significant, and the three trailing zeros are significant because of the decimal point.
So the number of significant figures is \(4\).

7. For \(6051.00\)

Step 1: Analyze all digits

The non - zero digits \(6\), \(5\), \(1\) are significant. The zero between \(6\) and \(5\) is significant. The two trailing zeros after the decimal point are significant.
So the number of significant figures is \(6\) (Wait, there is a mistake in the original answer. Let's recalculate: \(6\), \(0\) (between \(6\) and \(5\)), \(5\), \(1\), \(0\) (after \(1\)), \(0\) (last zero) are all significant. So it should be \(6\) significant figures).

8. For \(0.0005\)

Step 1: Look at zeros and non - zero

Leading zeros (the four zeros before \(5\)) are not significant. The non - zero digit \(5\) is significant.
So the number of significant figures is \(1\).

9. For \(0.1020\)

Step 1: Check each part

Leading zero (before \(1\)) is not significant. The non - zero digit \(1\) is significant, the zero between \(1\) and \(2\) is significant, the non - zero digit \(2\) is significant, and the trailing zero after \(2\) (because of the decimal point) is significant.
So the number of significant figures is \(4\).

If we assume that the original answer for question 7 is a typo and we go with the correct calculation:

1. \(0.02\): \(\boldsymbol{1}\)
2. \(0.020\): \(\boldsymbol{2}\)
3. \(501\): \(\boldsymbol{3}\)
4. \(501.0\): \(\boldsymbol{4}\)
5. \(5000.\): \(\boldsymbol{4}\)
6. \(6051.00\): \(\boldsymbol{6}\)
7. \(0.0005\): \(\boldsymbol{1}\)
8. \(0.1020\): \(\boldsymbol{4}\)

Answer:

To determine the number of significant figures, we use the rules:

• Leading zeros (zeros before the first non - zero digit) are not significant.
• Non - zero digits are always significant.
• Zeros between non - zero digits are significant.
• Trailing zeros in a number with a decimal point are significant; trailing zeros in a whole number without a decimal point may or may not be significant (but if there is a decimal point shown, like in \(5000.\) or \(501.0\), the trailing zeros are significant).

1. For \(0.02\)

Step 1: Identify non - zero and zero types

The leading zeros (the two zeros before \(2\)) are not significant. The non - zero digit is \(2\).
So the number of significant figures is \(1\).

2. For \(0.020\)

Step 1: Analyze zeros and non - zero digits

Leading zeros (the two zeros before \(2\)) are not significant. The non - zero digit \(2\) is significant, and the trailing zero after \(2\) (because there is a decimal point) is also significant.
So the number of significant figures is \(2\).

3. For \(501\)

Step 1: Check each digit

The non - zero digits \(5\) and \(1\) are significant, and the zero between them (\(5\) and \(1\)) is also significant.
So the number of significant figures is \(3\).

4. For \(501.0\)

Step 1: Evaluate each digit

The non - zero digits \(5\), \(0\) (between \(5\) and \(1\)), \(1\) are significant, and the trailing zero after the decimal point is also significant.
So the number of significant figures is \(4\).

6. For \(5000.\)

Step 1: Consider the decimal point

The non - zero digit \(5\) is significant, and the three trailing zeros are significant because of the decimal point.
So the number of significant figures is \(4\).

7. For \(6051.00\)

Step 1: Analyze all digits

The non - zero digits \(6\), \(5\), \(1\) are significant. The zero between \(6\) and \(5\) is significant. The two trailing zeros after the decimal point are significant.
So the number of significant figures is \(6\) (Wait, there is a mistake in the original answer. Let's recalculate: \(6\), \(0\) (between \(6\) and \(5\)), \(5\), \(1\), \(0\) (after \(1\)), \(0\) (last zero) are all significant. So it should be \(6\) significant figures).

8. For \(0.0005\)

Step 1: Look at zeros and non - zero

Leading zeros (the four zeros before \(5\)) are not significant. The non - zero digit \(5\) is significant.
So the number of significant figures is \(1\).

9. For \(0.1020\)

Step 1: Check each part

Leading zero (before \(1\)) is not significant. The non - zero digit \(1\) is significant, the zero between \(1\) and \(2\) is significant, the non - zero digit \(2\) is significant, and the trailing zero after \(2\) (because of the decimal point) is significant.
So the number of significant figures is \(4\).

If we assume that the original answer for question 7 is a typo and we go with the correct calculation:

1. \(0.02\): \(\boldsymbol{1}\)
2. \(0.020\): \(\boldsymbol{2}\)
3. \(501\): \(\boldsymbol{3}\)
4. \(501.0\): \(\boldsymbol{4}\)
5. \(5000.\): \(\boldsymbol{4}\)
6. \(6051.00\): \(\boldsymbol{6}\)
7. \(0.0005\): \(\boldsymbol{1}\)
8. \(0.1020\): \(\boldsymbol{4}\)