significant figures practice worksheet
how many significant figures do each of the following measured numbers have, and to what precision have they been measured?
example: 90 grams has one significant figure and is precise to the nearest ten grams.
1) 1234 liters
2) 3010 grams
3) 890 degrees
4) 9010.0 grams
5) 9010. grams
6) 9010 grams
7) 3.4 × 10³ meters
8) 3.40 × 10³ meters
9) 0.0023 grams
10) 1.0023 grams
11) 72.30 milliliters
12) 0.001 kilometers
13) 7.991 × 10⁻¹⁰ meters
14) 0.43 × 10⁻³ meters
15) i have 10 fingers

Question

Accepted Answer

### 1) 1234 liters
# Explanation:
## Step1: Identify significant figures
All non - zero digits are significant, and there are no leading or trailing zeros that are ambiguous here. So 1, 2, 3, 4 are significant.
## Step2: Determine precision
The number is 1234, so it is precise to the nearest liter (the ones place).
# Answer: 4 significant figures, precise to the nearest liter.

### 2) 3010 grams
# Explanation:
## Step1: Identify significant figures
Non - zero digits (3, 1) and the zero between non - zero digits are significant. The trailing zero may be ambiguous, but in 3010, the significant figures are 3, 0, 1 (the trailing zero is not significant as there's no decimal). So 3 significant figures.
## Step2: Determine precision
The number is 3010, so it is precise to the nearest ten grams (the tens place).
# Answer: 3 significant figures, precise to the nearest ten grams.

### 3) 890 degrees
# Explanation:
## Step1: Identify significant figures
Non - zero digits (8, 9) are significant, the trailing zero is not (no decimal). So 2 significant figures.
## Step2: Determine precision
The number is 890, so it is precise to the nearest ten degrees (the tens place).
# Answer: 2 significant figures, precise to the nearest ten degrees.

### 4) 9010.0 grams
# Explanation:
## Step1: Identify significant figures
All non - zero digits (9, 1), the zero between non - zero digits, and the trailing zeros after the decimal are significant. So 9, 0, 1, 0, 0 are significant. 5 significant figures.
## Step2: Determine precision
The number has a decimal at the end, so it is precise to the nearest tenth of a gram (the tenths place).
# Answer: 5 significant figures, precise to the nearest tenth of a gram.

### 5) 9010. grams
# Explanation:
## Step1: Identify significant figures
Non - zero digits (9, 1), the zero between non - zero digits, and the trailing zero is significant because of the decimal. So 9, 0, 1, 0 are significant. 4 significant figures.
## Step2: Determine precision
The number has a decimal, so it is precise to the nearest gram (the ones place).
# Answer: 4 significant figures, precise to the nearest gram.

### 6) 9010 grams
# Explanation:
## Step1: Identify significant figures
Non - zero digits (9, 1) and the zero between non - zero digits are significant. The trailing zero is not (no decimal). So 3 significant figures.
## Step2: Determine precision
The number is 9010, so it is precise to the nearest ten grams (the tens place).
# Answer: 3 significant figures, precise to the nearest ten grams.

### 7) $3.4\times10^{3}$ meters
# Explanation:
## Step1: Identify significant figures
In scientific notation, the digits before the power of 10 are significant. So 3 and 4 are significant. 2 significant figures.
## Step2: Determine precision
The number is $3.4\times 10^{3}=3400$, so it is precise to the nearest hundred meters (the hundreds place, since $3.4\times10^{3}$ implies the measurement is to the nearest 100 meters).
# Answer: 2 significant figures, precise to the nearest hundred meters.

### 8) $3.40\times10^{3}$ meters
# Explanation:
## Step1: Identify significant figures
In scientific notation, the digits before the power of 10 are significant. Here, 3, 4, 0 are significant (the trailing zero after 4 is significant because it's after the decimal in the coefficient). 3 significant figures.
## Step2: Determine precision
The number is $3.40\times 10^{3} = 3400$, and since the coefficient has a zero in the hundredths place (of the non - scientific notation number), it is precise to the nearest ten meters (the tens place).
# Answer: 3 significant figures, precise to the nearest ten meters.

### 9) 0.0023 grams
# Explanation:
## Step1: Identify significant figures
Leading zeros are not significant. The non - zero digits (2, 3) are significant. So 2 significant figures.
## Step2: Determine precision
The number is 0.0023, which is $2.3\times10^{- 3}$, so it is precise to the nearest ten - thousandth of a gram (the $10^{-4}$ place) or $0.0001$ grams.
# Answer: 2 significant figures, precise to the nearest $0.0001$ grams.

### 10) 1.0023 grams
# Explanation:
## Step1: Identify significant figures
All non - zero digits (1, 2, 3) and the zeros between non - zero digits are significant. So 1, 0, 0, 2, 3 are significant. 5 significant figures.
## Step2: Determine precision
The number is 1.0023, so it is precise to the nearest ten - thousandth of a gram (the $10^{-4}$ place) or $0.0001$ grams.
# Answer: 5 significant figures, precise to the nearest $0.0001$ grams.

### 11) 72.30 milliliters
# Explanation:
## Step1: Identify significant figures
Non - zero digits (7, 2, 3) and the trailing zero after the decimal are significant. So 4 significant figures.
## Step2: Determine precision
The number is 72.30, so it is precise to the nearest hundredth of a milliliter (the $10^{-2}$ place).
# Answer: 4 significant figures, precise to the nearest $0.01$ milliliters.

### 12) 0.001 kilometers
# Explanation:
## Step1: Identify significant figures
Leading zeros are not significant. The non - zero digit (1) is significant. So 1 significant figure.
## Step2: Determine precision
The number is 0.001, which is $1\times10^{-3}$ kilometers or 1 meter. So it is precise to the nearest meter (or the nearest $10^{-3}$ kilometers).
# Answer: 1 significant figure, precise to the nearest meter.

### 13) $7.991\times10^{-10}$ meters
# Explanation:
## Step1: Identify significant figures
In scientific notation, the digits in the coefficient (7, 9, 9, 1) are significant. So 4 significant figures.
## Step2: Determine precision
The coefficient is 7.991, so the number is precise to the nearest $10^{-13}$ meters (since the last digit is in the $10^{-13}$ place when considering the scientific notation $a\times10^{n}$, the precision is based on the least significant digit of $a$).
# Answer: 4 significant figures, precise to the nearest $10^{-13}$ meters.

### 14) $0.43\times10^{-3}$ meters
# Explanation:
## Step1: Identify significant figures
In scientific notation (we can rewrite it as $4.3\times10^{-4}$), the digits in the coefficient (4, 3) are significant. So 2 significant figures.
## Step2: Determine precision
The coefficient is 4.3 (in $4.3\times10^{-4}$), so it is precise to the nearest $10^{-5}$ meters (the least significant digit of the coefficient is in the $10^{-5}$ place of the original number).
# Answer: 2 significant figures, precise to the nearest $10^{-5}$ meters.

### 15) I have 10 fingers
# Explanation:
## Step1: Identify significant figures
In this case, 10 is an exact number (counted), so all digits are significant in the context of an exact count. So 2 significant figures (but for exact counts, the concept of significant figures is a bit different as it's not a measured quantity, but if we consider it as a number, 1 and 0 are significant as it's a count).
## Step2: Determine precision
Since it's a count of fingers, it is precise to the nearest finger (the ones place, but since it's an exact count, precision is not really applicable in the same way as a measured quantity, but if we consider the number, it's precise to the nearest finger).
# Answer: 2 significant figures (exact count, so precision is to the nearest finger).

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QUESTION IMAGE

Question

Explanation:

1) 1234 liters

Step1: Identify significant figures

Step2: Determine precision

Step1: Identify significant figures

Step2: Determine precision

Step1: Identify significant figures

Step2: Determine precision

Answer:

2) 3010 grams