grade 11 physics quiz – significant digits
total: 17 marks
part a: multiple choice (1 mark each – total: 5 marks)
1. how many significant digits are in the number 0.0040?
a) 2
b) 3
c) 4
d) 5
2. which of the following is not a rule for determining significant digits?
a) all non-zero digits are significant
b) zeros between two significant digits are significant
c) leading zeros are significant
d) trailing zeros in a number with a decimal are significant
3. which of the following measurements has 4 significant digits?
a) 1.099
b) 1.09
c) 3.450
d) 3450
4. how many significant digits are in the number 40.00?
a) 1
b) 2
c) 3
d) 4
5. which number is correctly rounded to 2 significant digits?
a) 98.765 – 98.7
b) 0.004567 – 0.0046
c) 10.01 – 10.0
d) 305.55 – 305

Question

Accepted Answer

### Question 1: How many significant digits are in the number 0.0040?
# Explanation:
## Step 1: Recall significant digit rules
Leading zeros (zeros before the first non - zero digit) are not significant. Non - zero digits are significant. Trailing zeros in a decimal number (after the non - zero digits) are significant. In the number 0.0040, the leading zeros (the three zeros before 4) are not significant. The digit 4 is significant, and the trailing zero after 4 is also significant because it is in a decimal number.
## Step 2: Count the significant digits
So, the significant digits are 4 and 0. So there are 2 significant digits.
# Answer: B

### Question 2: Which of the following is not a rule for determining significant digits?
# Brief Explanations:
- Option A: All non - zero digits are significant. This is a valid rule for significant digits. For example, in 234, all three digits are significant.
- Option B: Zeros between two significant digits are significant. For example, in 203, the zero between 2 and 3 is significant.
- Option C: Leading zeros are significant. This is incorrect. Leading zeros (zeros before the first non - zero digit) like in 0.023 are not significant.
- Option D: Trailing zeros in a number with a decimal are significant. For example, in 2.30, the zero is significant.
# Answer: C

### Question 3: Which of the following measurements has 4 significant digits?
# Explanation:
## Step 1: Analyze each option
- Option A: 1.099. The digits are 1, 0, 9, 9. All non - zero digits are significant, and the zero between 1 and 9 is also significant. So it has 4 significant digits.
- Option B: 340. If there is no decimal, the trailing zero may be ambiguous. But usually, without a decimal, the trailing zero in 340 is not considered significant. So 340 has 2 significant digits (3 and 4).
- Option C: 1.00. The digits are 1, 0, 0. Here, we have 3 significant digits (the 1 and the two trailing zeros in the decimal number).
- Option D: 3450. Without a decimal, the trailing zero is not significant. So it has 3 significant digits (3, 4, 5).
# Answer: A

### Question 4: How many significant digits are in the number 40.00?
# Explanation:
## Step 1: Recall significant digit rules for decimals
In a decimal number, all the digits including the trailing zeros are significant. The number 40.00 has the digits 4, 0, 0, 0. The 4 is significant, and the three zeros after the decimal (and the zero between 4 and the decimal) are also significant because it is a decimal number.
## Step 2: Count the significant digits
So, we count 4 (the non - zero digit) and the three zeros. So there are 4 significant digits.
# Answer: D

### Question 5: Which number is correctly rounded to 2 significant digits?
# Explanation:
## Step 1: Analyze each option
- Option A: 98.765−98.7. To round 98.765 to 2 significant digits, we look at the first two significant digits (9 and 8) and the next digit (7). Since 7≥5, we round up the 8 to 9. So 98.765 rounded to 2 significant digits is 99, not 98.7.
- Option B: 0.004567−0.0046. To round 0.004567 to 2 significant digits, we consider the first two non - zero significant digits (4 and 5). The next digit is 6≥5, so we round up the 5 to 6. But 0.0046 has 2 significant digits? Wait, no. Wait, 0.004567: the first significant digit is 4 (the first non - zero), the second is 5. Rounding to 2 significant digits: 0.0046? Wait, no, 0.004567 rounded to 2 significant digits is 0.0046? Wait, no, 4.567×10⁻³, rounded to 2 significant digits is 4.6×10⁻³ or 0.0046. But let's check other options.
- Option C: 10.01 - 10.0. To round 10.01 to 2 significant digits, the first two significant digits are 1 and 0 (wait, no: 10.01, the significant digits are 1, 0, 0, 1. To round to 2 significant digits, we look at the first two: 1 and 0, and the next digit is 0. So 10.01 rounded to 2 significant digits is 10 (but in scientific notation, 1.0×10¹). But 10.0 has 3 significant digits.
- Option D: 305.55 - 305. Wait, no. 305.55: to round to 2 significant digits, the first two significant digits are 3 and 0? No, wait, 305.55: the first significant digit is 3, the second is 0? No, that's not right. Wait, 305.55: if we consider significant digits, 3, 0, 5, 5, 5. To round to 2 significant digits, we look at the first two: 3 and 0, but the next digit is 5. Wait, no, maybe I made a mistake. Wait, let's re - evaluate Option B. Wait, 0.004567: the first significant digit is 4 (position: 10⁻³ place), the second is 5 (10⁻⁴ place). The next digit is 6 (10⁻⁵ place) which is ≥5, so we round the 5 up to 6. So 0.004567 rounded to 2 significant digits is 0.0046 (which is 4.6×10⁻³), and 0.0046 has 2 significant digits (4 and 6). Wait, but let's check Option A again. 98.765: first two significant digits are 9 and 8. The next digit is 7, which is ≥5, so we round 8 up to 9, so 98.765 rounded to 2 significant digits is 99 (which is 9.9×10¹), not 98.7. Option C: 10.01: first two significant digits are 1 and 0? No, 10.01: the significant digits are 1, 0, 0, 1. To round to 2 significant digits, we take 1 and 0, but the next digit is 0, so 10 (but 10 has 1 significant digit? No, wait, 10.01 rounded to 2 significant digits: 1.0×10¹ (which is 10. with a decimal, but 10 has 1 significant digit without a decimal). Wait, maybe the correct option is B? Wait, no, let's check the number of significant digits in each rounded number. Option B: 0.0046 has two significant digits (4 and 6). Option A: 98.7 has three significant digits. Option C: 10.0 has three significant digits. Option D: 305 has three significant digits. So the correct answer is B? Wait, no, wait the original number in Option B is 0.004567. Rounding to 2 significant digits: the first significant digit is 4 (the first non - zero), the second is 5. The next digit is 6, so we round 5 up to 6. So 0.004567 rounded to 2 significant digits is 0.0046, which has 2 significant digits. So Option B is correct.
# Answer: B

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QUESTION IMAGE

Question

Explanation:

Question 1: How many significant digits are in the number 0.0040?

Step 1: Recall significant digit rules

Step 2: Count the significant digits

Step 1: Analyze each option

Answer:

Question 2: Which of the following is not a rule for determining significant digits?