Practice worksheet for identifying significant figures in various numbers.
Worksheet titled "Significant Figures" with 16 numbered problems asking how many significant digits are in each number, from 0.29060 to 1000.
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Show Answer Key & Explanations
Step-by-step solution for: Significant Figures Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Significant Figures Worksheets
To find the number of significant digits (or significant figures) in a number, we follow these rules:
1. Non-zero digits are always significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros at the beginning of a decimal number, like 0.05) are not significant; they just show where the decimal point is.
4. Trailing zeros (zeros at the end) are significant only if there is a decimal point in the number. If there is no decimal point, trailing zeros are usually not considered significant (they are just placeholders).
Let's go through each problem step by step:
1) 0.29060
- The leading '0' is not significant.
- The digits '2', '9', '0', '6' are significant. The '0' is between non-zeros.
- The final '0' is significant because there is a decimal point.
- Count: 2, 9, 0, 6, 0 → 5 significant digits.
2) 10203005
- All non-zero digits are significant.
- All zeros are sandwiched between non-zero digits, so they are significant.
- Count: 1, 0, 2, 0, 3, 0, 0, 5 → 8 significant digits.
3) 1785
- All digits are non-zero.
- Count: 1, 7, 8, 5 → 4 significant digits.
4) 50
- The '5' is significant.
- The '0' is at the end, but there is no decimal point. So, it is just a placeholder.
- Count: 5 → 1 significant digit.
5) 0.02
- The leading zeros are not significant.
- Only the '2' is significant.
- Count: 2 → 1 significant digit.
6) 47.2950
- All non-zero digits are significant.
- The zero is at the end, and there is a decimal point. So, it is significant.
- Count: 4, 7, 2, 9, 5, 0 → 6 significant digits.
7) 23.0
- '2' and '3' are significant.
- The '0' is at the end, and there is a decimal point. So, it is significant.
- Count: 2, 3, 0 → 3 significant digits.
8) 0847020
- The leading '0' is not significant.
- The rest of the digits follow the rule: zeros between non-zeros are significant. The final '0' is tricky. In a whole number without a decimal point, trailing zeros are typically not significant. However, looking at standard worksheet conventions for this level, usually, if it's written as an integer like this, the trailing zero is a placeholder unless specified otherwise (like with a bar over it or a decimal point). Let's look closer. Actually, often in these specific types of problems, if a number starts with 0 (like a phone number format or ID), that leading zero is ignored. The number is effectively 847020. The zero between 7 and 2 is significant. The zero at the end? Without a decimal point, it is generally considered not significant.
- Let's re-evaluate standard rules for "0847020". Leading zero: ignore. Digits: 8, 4, 7, 0, 2, 0. The 0 between 7 and 2 is significant. The last 0 is trailing in a whole number. It is not significant.
- Count: 8, 4, 7, 0, 2 → 5 significant digits.
9) 0.91
- Leading zero is not significant.
- '9' and '1' are significant.
- Count: 9, 1 → 2 significant digits.
10) 1.234
- All digits are non-zero.
- Count: 1, 2, 3, 4 → 4 significant digits.
11) 007850
- Leading zeros are not significant.
- We are left with 7850.
- '7', '8', '5' are significant.
- The trailing '0' has no decimal point, so it is not significant.
- Count: 7, 8, 5 → 3 significant digits.
12) 0660
- Leading zero is not significant.
- We are left with 660.
- '6', '6' are significant.
- Trailing '0' has no decimal point, so it is not significant.
- Count: 6, 6 → 2 significant digits.
13) 23.0561
- All digits are non-zero except the middle zero.
- The zero is between non-zero digits, so it is significant.
- Count: 2, 3, 0, 5, 6, 1 → 6 significant digits.
14) 8.0
- '8' is significant.
- The '0' is at the end, and there is a decimal point. So, it is significant.
- Count: 8, 0 → 2 significant digits.
15) 1.020000
- '1' is significant.
- The first '0' is between non-zeros (1 and 2), so it is significant.
- '2' is significant.
- The trailing zeros are after a decimal point, so they are all significant.
- Count: 1, 0, 2, 0, 0, 0, 0 → 7 significant digits.
16) 1000
- '1' is significant.
- The three zeros are trailing and there is no decimal point. They are placeholders.
- Count: 1 → 1 significant digit.
Final Answer:
1) 5
2) 8
3) 4
4) 1
5) 1
6) 6
7) 3
8) 5
9) 2
10) 4
11) 3
12) 2
13) 6
14) 2
15) 7
16) 1
1. Non-zero digits are always significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros at the beginning of a decimal number, like 0.05) are not significant; they just show where the decimal point is.
4. Trailing zeros (zeros at the end) are significant only if there is a decimal point in the number. If there is no decimal point, trailing zeros are usually not considered significant (they are just placeholders).
Let's go through each problem step by step:
1) 0.29060
- The leading '0' is not significant.
- The digits '2', '9', '0', '6' are significant. The '0' is between non-zeros.
- The final '0' is significant because there is a decimal point.
- Count: 2, 9, 0, 6, 0 → 5 significant digits.
2) 10203005
- All non-zero digits are significant.
- All zeros are sandwiched between non-zero digits, so they are significant.
- Count: 1, 0, 2, 0, 3, 0, 0, 5 → 8 significant digits.
3) 1785
- All digits are non-zero.
- Count: 1, 7, 8, 5 → 4 significant digits.
4) 50
- The '5' is significant.
- The '0' is at the end, but there is no decimal point. So, it is just a placeholder.
- Count: 5 → 1 significant digit.
5) 0.02
- The leading zeros are not significant.
- Only the '2' is significant.
- Count: 2 → 1 significant digit.
6) 47.2950
- All non-zero digits are significant.
- The zero is at the end, and there is a decimal point. So, it is significant.
- Count: 4, 7, 2, 9, 5, 0 → 6 significant digits.
7) 23.0
- '2' and '3' are significant.
- The '0' is at the end, and there is a decimal point. So, it is significant.
- Count: 2, 3, 0 → 3 significant digits.
8) 0847020
- The leading '0' is not significant.
- The rest of the digits follow the rule: zeros between non-zeros are significant. The final '0' is tricky. In a whole number without a decimal point, trailing zeros are typically not significant. However, looking at standard worksheet conventions for this level, usually, if it's written as an integer like this, the trailing zero is a placeholder unless specified otherwise (like with a bar over it or a decimal point). Let's look closer. Actually, often in these specific types of problems, if a number starts with 0 (like a phone number format or ID), that leading zero is ignored. The number is effectively 847020. The zero between 7 and 2 is significant. The zero at the end? Without a decimal point, it is generally considered not significant.
- Let's re-evaluate standard rules for "0847020". Leading zero: ignore. Digits: 8, 4, 7, 0, 2, 0. The 0 between 7 and 2 is significant. The last 0 is trailing in a whole number. It is not significant.
- Count: 8, 4, 7, 0, 2 → 5 significant digits.
9) 0.91
- Leading zero is not significant.
- '9' and '1' are significant.
- Count: 9, 1 → 2 significant digits.
10) 1.234
- All digits are non-zero.
- Count: 1, 2, 3, 4 → 4 significant digits.
11) 007850
- Leading zeros are not significant.
- We are left with 7850.
- '7', '8', '5' are significant.
- The trailing '0' has no decimal point, so it is not significant.
- Count: 7, 8, 5 → 3 significant digits.
12) 0660
- Leading zero is not significant.
- We are left with 660.
- '6', '6' are significant.
- Trailing '0' has no decimal point, so it is not significant.
- Count: 6, 6 → 2 significant digits.
13) 23.0561
- All digits are non-zero except the middle zero.
- The zero is between non-zero digits, so it is significant.
- Count: 2, 3, 0, 5, 6, 1 → 6 significant digits.
14) 8.0
- '8' is significant.
- The '0' is at the end, and there is a decimal point. So, it is significant.
- Count: 8, 0 → 2 significant digits.
15) 1.020000
- '1' is significant.
- The first '0' is between non-zeros (1 and 2), so it is significant.
- '2' is significant.
- The trailing zeros are after a decimal point, so they are all significant.
- Count: 1, 0, 2, 0, 0, 0, 0 → 7 significant digits.
16) 1000
- '1' is significant.
- The three zeros are trailing and there is no decimal point. They are placeholders.
- Count: 1 → 1 significant digit.
Final Answer:
1) 5
2) 8
3) 4
4) 1
5) 1
6) 6
7) 3
8) 5
9) 2
10) 4
11) 3
12) 2
13) 6
14) 2
15) 7
16) 1
Parent Tip: Review the logic above to help your child master the concept of significant figures worksheet.
