carry out each calculation and give the answers using the proper number of significant figures.
part 1 of 2
10.00 × 2.0 =
part 2 of 2
$\frac{0.808}{23339}$ =

Question

Accepted Answer

### Part 1 of 2
# Explanation:
## Step 1: Multiply the numbers
To find the product of $ 10.00 $ and $ 2.0 $, we use the multiplication operation. When multiplying, we consider the significant figures. $ 10.00 $ has 4 significant figures and $ 2.0 $ has 2 significant figures. The result should be reported with 2 significant figures (the least number of significant figures in the factors).

First, calculate the product: $ 10.00\times2.0 = 20.0 $

Then, round to 2 significant figures: $ 20. $ (or $ 2.0\times10^{1} $, but in decimal form, it's $ 20. $ to show two significant figures)

Wait, actually, let's do the multiplication properly. $ 10.00\times2.0 $:

$ 10.00\times2.0 = 20.00 $

Now, considering significant figures: $ 2.0 $ has 2 significant figures, so the result should have 2 significant figures. So $ 20.00 $ rounded to 2 significant figures is $ 20. $ (or $ 2.0\times10^{1} $, but as a decimal, $ 20. $ indicates two significant figures? Wait, no. Wait, $ 10.00 $ is 4 sig figs, $ 2.0 $ is 2 sig figs. When multiplying, the result should have the same number of sig figs as the least precise measurement, which is 2. So $ 10.00\times2.0 = 20.00 $, which we round to 20. (with a decimal to show that the zero is significant? Wait, no. Wait, $ 2.0 $ has two sig figs, so the answer should have two sig figs. So $ 20.00 $ rounded to two sig figs is $ 20. $? Wait, no, $ 20. $ has two sig figs? Wait, no, $ 20 $ without a decimal has one sig fig, $ 20. $ has two. So yes, $ 20. $

But maybe I made a mistake. Let's check again. $ 10.00 $ is 4 sig figs, $ 2.0 $ is 2 sig figs. The rule for multiplication/division is that the result has the same number of sig figs as the input with the least number of sig figs. So $ 2.0 $ has 2, so the result should have 2. So $ 10.00\times2.0 = 20.00 $, which we round to $ 20. $ (two sig figs).

Alternatively, maybe the problem expects us to just do the multiplication without worrying about sig figs first, then apply. Wait, the problem says "give the answers using the proper number of significant figures". So let's do the multiplication:

$ 10.00\times2.0 = 20.00 $

Now, $ 2.0 $ has 2 significant figures, so the answer should have 2. So $ 20.00 $ rounded to 2 significant figures is $ 20. $ (or $ 2.0\times10^{1} $, but as a decimal, $ 20. $ is correct for two significant figures? Wait, no, $ 20. $ has two significant figures (the 2 and the 0 after the decimal? No, wait, $ 20. $ is two significant figures: the 2 and the 0 is significant because of the decimal. Wait, no, $ 20. $ is two significant figures? Wait, no, $ 20. $ is two significant figures? Wait, no, $ 20 $ (without decimal) is one, $ 20. $ (with decimal) is two. Yes. So $ 20. $ is two significant figures.

But maybe the problem is simpler, and we just multiply $ 10.00\times2.0 = 20.00 $, and since $ 2.0 $ has two decimal places? No, significant figures, not decimal places.

Wait, maybe the problem is not strict on significant figures and just wants the product. Let's check: $ 10.00\times2.0 = 20.00 $, but if we consider that $ 10.00 $ is 10, and $ 2.0 $ is 2, then $ 10\times2 = 20 $, but with decimals, $ 10.00\times2.0 = 20.00 $.

Wait, maybe the problem is in a context where significant figures are considered, but maybe the answer is $ 20. $ or $ 2.0\times10^{1} $, but let's proceed.

## Step 2: Finalize the answer
After multiplying and considering significant figures, the result is $ 20. $ (or $ 2.0\times10^{1} $, but as a decimal, $ 20. $)

Wait, maybe I overcomplicated. Let's just do the multiplication: $ 10.00\times2.0 = 20.00 $, and if we take the proper number of significant figures, since $ 2.0 $ has 2, the answer is $ 20. $ (two significant figures).

### Part 2 of 2
# Explanation:
## Step 1: Divide the numbers
To find $ \frac{0.808}{23339} $, we perform the division.

$ 0.808\div23339 \approx 0.00003462 $

Now, consider significant figures. $ 0.808 $ has 3 significant figures, $ 23339 $ is a whole number (assuming it's exact, or has 5 significant figures). So the result should have 3 significant figures.

Calculating $ 0.808\div23339 $:

$ 0.808\div23339 \approx 3.462\times10^{-5} $

Rounding to 3 significant figures: $ 3.46\times10^{-5} $ or $ 0.0000346 $

Let's do the division:

$ 0.808\div23339 \approx 0.00003462 $

Now, $ 0.808 $ has 3 sig figs, so the result should have 3. So $ 0.0000346 $ (which is $ 3.46\times10^{-5} $)

# Answers:

### Part 1 of 2
# Explanation:
## Step 1: Multiply $ 10.00 $ and $ 2.0 $
$ 10.00\times2.0 = 20.00 $
## Step 2: Apply significant figures
$ 2.0 $ has 2 significant figures, so round $ 20.00 $ to 2 significant figures: $ 20. $ (or $ 2.0\times10^{1} $)

# Answer:
$ 20. $ (or $ 2.0\times10^{1} $, but as a decimal, $ 20. $)

### Part 2 of 2
# Explanation:
## Step 1: Divide $ 0.808 $ by $ 23339 $
$ \frac{0.808}{23339} \approx 0.00003462 $
## Step 2: Apply significant figures
$ 0.808 $ has 3 significant figures, so round to 3: $ 0.0000346 $ (or $ 3.46\times10^{-5} $)

# Answer:
$ 3.46\times10^{-5} $ (or $ 0.0000346 $)

Wait, but maybe the problem doesn't care about significant figures and just wants the numerical answer. Let's check:

Part 1: $ 10.00\times2.0 = 20.00 $, so the answer is $ 20.00 $ or $ 20. $ (if sig figs, but maybe the problem just wants $ 20 $)

Part 2: $ 0.808\div23339 \approx 0.0000346 $

Let me recalculate Part 2:

$ 0.808\div23339 $:

$ 23339\times0.00003 = 0.69997 $

$ 0.808 - 0.69997 = 0.10803 $

$ 23339\times0.000004 = 0.093356 $

$ 0.10803 - 0.093356 = 0.014674 $

$ 23339\times0.0000006 = 0.0140034 $

So total is $ 0.00003 + 0.000004 + 0.0000006 = 0.0000346 $, and the remainder is $ 0.014674 - 0.0140034 = 0.0006706 $, so approximately $ 0.0000346 $

So Part 2 answer is approximately $ 0.0000346 $ or $ 3.46\times10^{-5} $

Part 1: $ 10.00\times2.0 = 20.00 $, so the answer is $ 20.00 $ (or $ 20. $ if sig figs, but maybe just $ 20 $)

Let me adjust the step-by-step for Part 1:

## Step 1: Multiply the numbers
$ 10.00 \times 2.0 = 20.00 $

# Answer (Part 1): $ 20.00 $ (or $ 20 $ if no sig figs, but the problem says "proper number of significant figures", so $ 20. $ (2 sig figs) or $ 20.00 $ (4 sig figs, but $ 2.0 $ has 2, so 2 sig figs)

Part 1: The least number of significant figures in the factors is 2 (from $ 2.0 $), so the answer should have 2. So $ 20. $ (two significant figures)

Part 2: $ 0.808 $ has 3 significant figures, so the answer should have 3. So $ 0.0000346 $ (three significant figures)

So final answers:

Part 1: $ 20. $

Part 2: $ 3.46\times10^{-5} $ (or $ 0.0000346 $)

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QUESTION IMAGE

Question

Explanation:

Part 1 of 2

Step 1: Multiply the numbers

Step 2: Finalize the answer

Step 1: Divide the numbers

Step 1: Multiply \( 10.00 \) and \( 2.0 \)

Step 2: Apply significant figures

Answer:

Part 1 of 2