significant figures exit slip
name: jeremiah d
per: ______
directions: find the number of significant figures of the number provided.
how many sig figs? which rule applies?
1. 17500
2. 7.056
3. 80.50
4. 1870.7
5. 8060.0
6. 0.000470
7. ½ (exact number)
directions: calculate the following expressions with significant figures. list the significant figures of the final answer.
| | sum/difference or product/quotient? | decimal or sig fig? | whats the least amount? | final answer? |
|---------------|--------------------------------------|---------------------|--------------------------|---------------|
| 1.50 + 1.7 = | | | | |
| 8563.5 - 130 =| | | | |
| 50. x 200 | | | | |
| (2.5 + 8.6) x 10.0? explain. | calculation: | explanation (at least one sentence) |

Question

significant figures exit slip
name: jeremiah d
per: ______
directions: find the number of significant figures of the number provided.
how many sig figs? which rule applies?
1. 17500
2. 7.056
3. 80.50
4. 1870.7
5. 8060.0
6. 0.000470
7. ½ (exact number)
directions: calculate the following expressions with significant figures. list the significant figures of the final answer.
|               | sum/difference or product/quotient? | decimal or sig fig? | whats the least amount? | final answer? |
|---------------|--------------------------------------|---------------------|--------------------------|---------------|
| 1.50 + 1.7 =  |                                      |                     |                          |               |
| 8563.5 - 130 =|                                      |                     |                          |               |
| 50. x 200     |                                      |                     |                          |               |
| (2.5 + 8.6) x 10.0? explain. | calculation: | explanation (at least one sentence) |

Accepted Answer

### Problem 1: 17500 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for trailing zeros without decimal.
Trailing zeros in a whole number without a decimal are ambiguous, but if they are placeholders, they may not be significant. Here, 1, 7, 5 are significant; the trailing zeros are placeholders (assuming no decimal), so count non - zero digits and check. Wait, actually, for 17500, if it's written without a decimal, the trailing zeros might be considered not significant (if they are just placeholders). But sometimes, if the number is meant to have the zeros as significant, it would have a decimal. So following the rule: non - zero digits are significant, and trailing zeros in whole numbers without decimals are not significant (unless specified). So 1, 7, 5 are significant.
## Step2: Count the significant figures.
So the number of significant figures is 3.
# Answer: 3

### Problem 2: 7.056 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for numbers with decimals.
All non - zero digits are significant, and zeros between non - zero digits are significant. In 7.056, 7 is non - zero, 0 is between 7 and 5 (so significant), 5 and 6 are non - zero.
## Step2: Count the significant figures.
Count them: 7, 0, 5, 6. So there are 4 significant figures.
# Answer: 4

### Problem 3: 80.50 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for numbers with decimals.
Non - zero digits (8, 5) are significant. The zero between 8 and 5 is significant (zero between non - zeros). The trailing zero after the decimal is significant (trailing zeros in a number with a decimal are significant).
## Step2: Count the significant figures.
Count: 8, 0, 5, 0. So there are 4 significant figures.
# Answer: 4

### Problem 4: 1870.7 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for numbers with decimals.
Non - zero digits (1, 8, 7, 7) are significant. The zero between 7 and 7 (wait, 1870.7: digits are 1, 8, 7, 0, 7). The zero is between non - zero digits (7 and 7? No, 1,8,7,0,7: 0 is between 7 and 7? Wait, 1870.7: 1 (sig), 8 (sig), 7 (sig), 0 (between 7 and 7? No, 1870.7 is 1 - 8 - 7 - 0 - 7. The 0 is between 7 and 7? No, 1870.7: the digits are 1,8,7,0,7. All non - zero digits and the zero between non - zero digits (wait, 7 and 0 and 7: 0 is between 7 and 7? No, 1870.7: 1 (sig), 8 (sig), 7 (sig), 0 (sig, because it's between non - zeros? Wait, no, 1870.7: the number has a decimal, so all digits are significant except maybe leading zeros (but there are no leading zeros). So 1,8,7,0,7: 5 digits.
## Step2: Count the significant figures.
So 5 significant figures.
# Answer: 5

### Problem 5: 8060.0 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for numbers with decimals.
Non - zero digits (8, 6) are significant. The zero between 8 and 6 is significant (zero between non - zeros). The trailing zeros after the decimal are significant, and the zero before the 6 (wait, 8060.0: digits are 8,0,6,0,0. Wait, no: 8 - 0 - 6 - 0 - 0, but with a decimal at the end. So non - zero digits: 8,6. Zeros: the zero between 8 and 6 (significant), the trailing zeros after the decimal (significant), and the zero before the 6? Wait, 8060.0: let's break it down. 8 (sig), 0 (between 8 and 6, sig), 6 (sig), 0 (trailing, after decimal, sig), 0 (trailing, after decimal, sig). Wait, no, 8060.0: the number is 8060.0, so the digits are 8,0,6,0,0. But with a decimal, so all digits are significant? Wait, no: leading zeros are not significant, but here the zero is between 8 and 6 (so significant), the trailing zeros after the decimal are significant. So 8,0,6,0,0: wait, no, 8060.0: 8 (sig), 0 (between 8 and 6, sig), 6 (sig), 0 (trailing, after decimal, sig), 0 (trailing, after decimal, sig). Wait, that's 5 digits? Wait, 8060.0: 8,0,6,0,0. Wait, no, 8060.0 is 8 - 0 - 6 - 0 - 0, but the decimal makes the trailing zeros significant. So the significant figures are 8,0,6,0,0? No, wait, 8060.0: the zero between 8 and 6 is significant, the trailing zeros after the decimal are significant. So 8 (1), 0 (2), 6 (3), 0 (4), 0 (5)? Wait, no, 8060.0: let's count properly. Non - zero digits: 8,6. Zeros: the zero between 8 and 6 (significant), the two trailing zeros after the decimal (significant). So total: 8,0,6,0,0? Wait, no, 8060.0 has five significant figures? Wait, 8 (1), 0 (2), 6 (3), 0 (4), 0 (5)? Wait, no, 8060.0: the number is 8060.0, so the digits are 8,0,6,0,0. But the zero before the 6 is between 8 and 6, so significant. The trailing zeros after the decimal are significant. So that's 5 significant figures.
## Step2: Count the significant figures.
So 5 significant figures.
# Answer: 5

### Problem 6: 0.000470 (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for numbers with leading zeros.
Leading zeros are not significant. Non - zero digits (4,7) are significant. Trailing zero after the non - zero digits and after the decimal is significant.
## Step2: Count the significant figures.
So 4,7,0: three significant figures.
# Answer: 3

### Problem 7: 1/2 (exact number) (Number of Significant Figures)
# Explanation:
## Step1: Recall sig fig rules for exact numbers.
Exact numbers (like defined quantities or fractions in exact contexts) have an infinite number of significant figures because they are not measurements with uncertainty.
## Step2: Determine the number of significant figures.
So the number of significant figures is infinite (or we can say it has unlimited significant figures).
# Answer: Infinite (or unlimited)

### Problem 1.50 + 1.7 =
# Explanation:
## Step1: Identify the operation (sum) and sig fig rule for sum/difference.
For sum/difference, we look at the number of decimal places. 1.50 has 2 decimal places, 1.7 has 1 decimal place. We round to the least number of decimal places (1 decimal place).
## Step2: Perform the addition.
1.50+1.7 = 3.20. Now, round to 1 decimal place: 3.2.
# Answer: 3.2

### Problem 8563.5 - 130 =
# Explanation:
## Step1: Identify the operation (difference) and sig fig rule for sum/difference.
For difference, look at decimal places. 8563.5 has 1 decimal place, 130 has 0 decimal places. Round to 0 decimal places.
## Step2: Perform the subtraction.
8563.5 - 130 = 8433.5. Now, round to 0 decimal places: 8434 (wait, no: 8563.5 - 130 = 8433.5. Rounding to 0 decimal places: 8434? Wait, 8433.5 rounded to the nearest whole number is 8434? Wait, no, 8433.5: the rule for rounding is that if the digit after the desired decimal place is 5 or more, we round up. So 8433.5 rounded to 0 decimal places is 8434. But wait, let's check the significant figures in the original numbers. 8563.5 has 5 significant figures, 130 has 2 (assuming the trailing zero is not significant). Wait, maybe I made a mistake. Wait, for subtraction, the number of decimal places: 8563.5 has 1 decimal place, 130 has 0. So the result should have 0 decimal places. So 8563.5 - 130 = 8433.5, which rounds to 8434.
# Answer: 8434

### Problem 50.×200 (assuming 50. has 2 sig figs, 200 has 1 or 3? Wait, 50. has a decimal, so 2 sig figs; 200: if it's written as 200 without a decimal, it has 1 sig fig, but if it's 200. it has 3. But here it's 200, so maybe 1 sig fig? Wait, no, the problem says "50. X 200". Let's assume 50. has 2 sig figs (because of the decimal), 200: if we consider that the trailing zeros are not significant (no decimal), so 1 sig fig? But that seems odd. Wait, maybe 200 is meant to have 1 sig fig, 50. has 2. For multiplication/division, we go by the least number of sig figs.
# Explanation:
## Step1: Identify the operation (product) and sig fig rule for product/quotient.
For product/quotient, we use the least number of significant figures. 50. has 2 sig figs, 200 (assuming no decimal, so 1 sig fig? Wait, no, maybe 200 is written as 2×10², so 1 sig fig, or maybe it's 200. with a decimal (but it's not). Wait, maybe the problem considers 200 as having 1 sig fig and 50. as having 2. So the least is 1? No, that can't be. Wait, maybe 50. has 2 sig figs, 200 has 3 (if the trailing zeros are significant, but it's not written with a decimal). This is ambiguous, but let's assume that 50. has 2 sig figs and 200 has 1 sig fig (trailing zeros not significant). Then the product is 50.×200 = 10000. Now, with 1 sig fig, it would be 1×10⁴. But that seems too rough. Wait, maybe 200 is meant to have 2 sig figs (2.0×10²), but it's written as 200. No, the problem says "50. X 200". Let's re - evaluate. 50. has 2 sig figs (the decimal makes the zero significant), 200: if we take it as 200. (with a decimal), it has 3, but it's not. So maybe the problem expects us to take 50. as 2 sig figs and 200 as 1 sig fig. Then the product is 50×200 = 10000, and with 1 sig fig, it's 1×10⁴. But maybe the intended is that 200 has 1 sig fig and 50. has 2, so the least is 2? Wait, no, the rule is least number of sig figs. So if 50. has 2 and 200 has 1, then 1. But that's strange. Alternatively, maybe 200 is considered to have 3 sig figs (if it's a precise number), but that's not standard. Wait, maybe the problem has a typo, and it's 50.×200. (with a decimal), then 200. has 3 sig figs, 50. has 2, so least is 2. Then 50.×200. = 10000., which with 2 sig figs is 1.0×10⁴.
## Step2: Perform the calculation and round.
Assuming 50. has 2 sig figs and 200 has 1 sig fig (trailing zeros not significant), 50.×200 = 10000. Rounding to 1 sig fig: 1×10⁴. If we assume 200 has 3 sig figs (with a decimal, but it's not), then 50.×200 = 10000, with 2 sig figs: 1.0×10⁴.
# Answer: 1×10⁴ (or 1.0×10⁴ depending on interpretation)

### Problem: How many sig figs are in the final answer for (2.5 + 8.6)×10.0? Explain.
# Explanation:
## Step1: Perform the addition first.
2.5+8.6 = 11.1. For addition, we look at decimal places: 2.5 has 1, 8.6 has 1, so the sum has 1 decimal place (11.1, which has 3 sig figs).
## Step2: Perform the multiplication.
Now multiply by 10.0. 11.1×10.0 = 111. For multiplication, we look at the number of sig figs. 11.1 has 3 sig figs, 10.0 has 3 sig figs. So the product should have 3 sig figs.
## Step3: Explain the sig fig count.
First, in the addition (2.5 + 8.6), both numbers have 1 decimal place, so the sum (11.1) has 3 significant figures (since all digits are non - zero and the decimal place is considered). Then, when multiplying by 10.0 (which has 3 significant figures), we use the rule for multiplication/division: the result should have the same number of significant figures as the number with the least number of significant figures in the multiplication. Here, both 11.1 and 10.0 have 3 significant figures, so the final answer (111) has 3 significant figures.
# Answer: 3. The addition (2.5 + 8.6 = 11.1) gives a number with 3 sig figs, and multiplying by 10.0 (3 sig figs) results in a number with 3 sig figs.

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Question

Explanation:

Problem 1: 17500 (Number of Significant Figures)

Step1: Recall sig fig rules for trailing zeros without decimal.

Step2: Count the significant figures.

Step1: Recall sig fig rules for numbers with decimals.

Step2: Count the significant figures.

Step1: Recall sig fig rules for numbers with decimals.

Step2: Count the significant figures.

Answer:

Problem 2: 7.056 (Number of Significant Figures)

	sum/difference or product/quotient?	decimal or sig fig?
8563.5 - 130 =
50. x 200
(2.5 + 8.6) x 10.0? explain.	calculation:	explanation (at least one sentence)