2. express the answer to each of the following calculations with the correct number of significant figures.
a) 3.42 + 8.132 d) 3.882 - 2.1
b) 4.9 + 3.822 e) 4.894 - 2.03
c) 17.8 + 12.115 f) 15.6600 - 12.838

Question

2. express the answer to each of the following calculations with the correct number of significant figures.
    a) 3.42 + 8.132        d) 3.882 - 2.1
    b) 4.9 + 3.822         e) 4.894 - 2.03
    c) 17.8 + 12.115       f) 15.6600 - 12.838

Accepted Answer

### Part (a)
# Explanation:
## Step1: Add the numbers
$3.42 + 8.132 = 11.552$
## Step2: Determine significant figures (decimal places)
3.42 has 2 decimal places, 8.132 has 3. We round to 2 decimal places.
$11.552 \approx 11.55$ (Wait, no: when adding, we go by decimal places. 3.42 has two decimal places, so the result should have two decimal places. Wait, 3.42 + 8.132 = 11.552. Rounding to two decimal places: look at the third decimal, which is 2, so we keep the second decimal as is? Wait, no: 3.42 is to the hundredth place, 8.132 to the thousandth. The least number of decimal places is two (from 3.42). So we round 11.552 to two decimal places: 11.55? Wait, no, 11.552 rounded to two decimal places: the third decimal is 2, which is less than 5, so we don't round up the second decimal. Wait, but 3.42 + 8.132 = 11.552. So with two decimal places, it's 11.55? Wait, no, 3.42 is 3.42 (two decimal places), 8.132 is 8.132 (three). The sum should be rounded to the least number of decimal places, which is two. So 11.552 rounded to two decimal places: 11.55? Wait, 11.552: the first decimal is 5, second is 5, third is 2. So yes, 11.55. Wait, but maybe I made a mistake. Wait, 3.42 + 8.132: 3 + 8 = 11, 0.42 + 0.132 = 0.552, so total 11.552. Rounded to two decimal places: 11.55.

# Answer:
$11.55$

### Part (b)
# Explanation:
## Step1: Add the numbers
$4.9 + 3.822 = 8.722$
## Step2: Determine significant figures (decimal places)
4.9 has 1 decimal place, 3.822 has 3. We round to 1 decimal place.
$8.722 \approx 8.7$ (since the second decimal is 2, less than 5, so we keep the first decimal as 7)

# Answer:
$8.7$

### Part (c)
# Explanation:
## Step1: Add the numbers
$17.8 + 12.115 = 29.915$
## Step2: Determine significant figures (decimal places)
17.8 has 1 decimal place, 12.115 has 3. We round to 1 decimal place.
$29.915 \approx 29.9$ (the second decimal is 1, less than 5, so we keep the first decimal as 9)

# Answer:
$29.9$

### Part (d)
# Explanation:
## Step1: Subtract the numbers
$3.882 - 2.1 = 1.782$
## Step2: Determine significant figures (decimal places)
3.882 has 3 decimal places, 2.1 has 1. We round to 1 decimal place.
$1.782 \approx 1.8$ (the second decimal is 8, which is more than 5, so we round up the first decimal from 7 to 8)

# Answer:
$1.8$

### Part (e)
# Explanation:
## Step1: Subtract the numbers
$4.894 - 2.03 = 2.864$
## Step2: Determine significant figures (decimal places)
4.894 has 3 decimal places, 2.03 has 2. We round to 2 decimal places.
$2.864 \approx 2.86$ (the third decimal is 4, less than 5, so we keep the second decimal as 6)

# Answer:
$2.86$

### Part (f)
# Explanation:
## Step1: Subtract the numbers
$15.6600 - 12.838 = 2.822$
## Step2: Determine significant figures (decimal places)
15.6600 has 4 decimal places, 12.838 has 3. We round to 3 decimal places? Wait, no: 15.6600 is to the ten - thousandth place, 12.838 to the thousandth. The least number of decimal places is 3? Wait, 15.6600 has decimal places: the trailing zeros after the decimal are significant. 15.6600 has four decimal places, 12.838 has three. When subtracting, we go by the least number of decimal places, which is three? Wait, no: 15.6600 is 15.6600 (four decimal places), 12.838 is 12.838 (three). So the result should be rounded to three decimal places? Wait, 15.6600 - 12.838 = 2.822. Wait, 15.6600 - 12.838: 15.6600 - 12.838 = 2.8220? Wait, no, 15.6600 - 12.838 = 2.822. Wait, 15.6600 has four decimal places, 12.838 has three. So the number of decimal places in the result should match the least number, which is three. But 2.822 has three decimal places. Wait, 15.6600 is 15.6600 (the zeros at the end are significant), 12.838 is 12.838. So 15.6600 - 12.838 = 2.822. Since 12.838 has three decimal places, the result should have three decimal places. 2.822 is already to three decimal places. Wait, but let's check the subtraction again: 15.6600 - 12.838 = 2.822 (because 15.6600 - 12.838 = 2.8220, but we can write it as 2.822 since the fourth decimal is zero). Wait, maybe the correct way is: 15.6600 has four decimal places, 12.838 has three. The rule for addition/subtraction is that the result has the same number of decimal places as the least precise measurement. So 12.838 has three decimal places, so the result should have three decimal places. 15.6600 - 12.838 = 2.822, which has three decimal places. So the answer is 2.822? Wait, no, wait: 15.6600 is 15.6600 (the zeros are significant, so it's precise to the ten - thousandth place), 12.838 is precise to the thousandth place. So when subtracting, we look at the number of decimal places. 15.6600 has 4 decimal places, 12.838 has 3. So we round to 3 decimal places. 15.6600 - 12.838 = 2.8220. Rounding to 3 decimal places: the fourth decimal is 0, so we keep the third decimal as 2. So 2.822.

# Answer:
$2.822$

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Add the numbers

Step2: Determine significant figures (decimal places)

Step1: Add the numbers

Step2: Determine significant figures (decimal places)

Step1: Add the numbers

Step2: Determine significant figures (decimal places)

Answer:

Part (b)