Question

multiply.
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$$\begin{array}{r} 95.8 \\\\ \\times\\ 2.06 \\\\ \\hline \\end{array}$$

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Explanation:

Step1: Multiply 95.8 by 6 (the hundredths place of 2.06)

$95.8\times6 = 574.8$ (we'll consider the decimal places later, but for now, note the position: since it's the hundredths place, we'll shift appropriately at the end)

Step2: Multiply 95.8 by 0 (the tenths place of 2.06)

$95.8\times0 = 0$ (but since it's the tenths place, we add a zero as a placeholder: 00.0, but actually, when we do the multiplication step - by - step, we shift one position to the left for the tenths place, so it's 0.0)

Step3: Multiply 95.8 by 2 (the ones place of 2.06)

$95.8\times2 = 191.6$ (since it's the ones place, we shift two positions to the left compared to the hundredths place multiplication, so it's 19160.0 when considering the place values for addition)

Step4: Add the results together

First, adjust the decimal positions properly. When multiplying decimals, we count the total number of decimal places in the factors. 95.8 has 1 decimal place, 2.06 has 2 decimal places, so total decimal places = 1 + 2 = 3.

But let's do the addition as if we were doing long multiplication:

    95.8
  ×2.06
  ------
    574.8  (95.8×6)
     00.0   (95.8×0, shifted one place)
  1916.0    (95.8×2, shifted two places)
  ------
  Now add them: 574.8+0.0 + 1916.0 = 2490.8? Wait, no, wait, the correct way is to align the numbers by place value.

Wait, actually, long multiplication for decimals:

Treat them as whole numbers first: 958×206, then divide by 10^(1 + 2)=1000.

Calculate 958×206:

First, 958×6 = 5748

Then, 958×0 = 0, but since it's the tens place (0 in 206 is in the tens place), we write 000 (shift one place: 958×0×10 = 0)

Then, 958×2 = 1916, and since it's the hundreds place (2 in 206 is in the hundreds place), we shift two places: 1916×100 = 191600

Now add 5748+0 + 191600 = 197348

Now, divide by 1000 (because we had 1 + 2 = 3 decimal places)

197348÷1000 = 197.348

Wait, let's check that again. 95.8 is 958×10^(- 1), 2.06 is 206×10^(- 2). So (958×10^(- 1))×(206×10^(- 2)) = 958×206×10^(- 3)

958×206:

206 = 200 + 6

958×200 = 191600

958×6 = 5748

191600+5748 = 197348

Then 197348×10^(- 3)=197.348

So the correct calculation is:

Step1: Calculate the product as whole numbers

Multiply 958 (95.8 without decimal) and 206 (2.06 without decimal):
First, $958\times6 = 5748$
Second, $958\times0 = 0$ (but in 206, the 0 is in the tens place, so we consider it as $958\times0\times10 = 0$)
Third, $958\times2 = 1916$ (and since 2 is in the hundreds place, we consider it as $958\times2\times100 = 191600$)
Add these results: $5748+0 + 191600=197348$

Step2: Adjust for decimal places

The number 95.8 has 1 decimal place, and 2.06 has 2 decimal places. So the total number of decimal places in the product is $1 + 2=3$.
To get the final result, divide the product of the whole numbers by $10^{3}$ (or 1000):
$\frac{197348}{1000}=197.348$

Answer:

197.348