Question

What is the product of 4.3 x 10^2 and 2.4 x 10^5 expressed in scientific notation?

Answer 1

Answer:   $1.032 \times 10^8$

You'll have 1.032 in the first box and 8 in the second box.

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Work Shown:

$A = 4.3 \times 10^2\\\\B = 2.4 \times 10^5\\\\A * B = (4.3 \times 10^2) * (2.4 \times 10^5)\\\\A * B = (4.3*2.4) \times (10^2*10^5)\\\\A * B = 10.32 \times 10^{2+5}\\\\A * B = (1.032 \times 10^1) \times 10^7\\\\A * B = 1.032 \times (10^1*10^7)\\\\A * B = 1.032 \times 10^{1+7}\\\\A * B = \boldsymbol{1.032 \times 10^8}$

When expanded out, the number $1.032 \times 10^8$ turns into $103,200,000$ which is just a bit over 103 million.

As the steps above show, we multiply the numbers out front to get 4.3*2.4 = 10.32 which then converts to $1.032\times10^1$. The exponential terms, when multiplied, will have the exponents add. The rule is $a^b*a^c = a^{b+c}$

The first number 1.032 of the answer above is between 1 and 10, excluding 10. So it's a sign that the value is in scientific notation. That's why I converted the 10.32 to $1.032\times10^1$