Question

What is (3. 1 times 10 Superscript 5 Baseline) (2. 2 times 10 Superscript 7 Baseline) in scientific notation? 5. 5 times 10 Superscript 12 6. 82 times 10 Superscript 12 5. 5 times 10 Superscript 35 6. 82 times 10 Superscript 35.

Answer 1

The sum of the numbers expressed in scientific notations is given by: Option B:  $6.82 \times 10^{12}$

How does scientific notations work?

The number is written in the form $a \times 10^b$  where we have $1 \leq a < 10$

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations have some of the profits as:

• Better readability due to compact representation
• Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

The given expression is:

$(3.1 \times 10^5) \times (2.2 \times 10^7)$

Evaluating the multiplication, we get:

$3.1 \times 2.2 \times 10^5 \times 10^7 = 6.82 \times 10^{5 +7} = 6.82 \times 10^{12}$

It is because of exponent rule that $a^b \times a^c = a^{b+c}$, and because of commutative property of addition.

Thus, the sum of the numbers expressed in scientific notations is given by: Option B:  $6.82 \times 10^{12}$

Learn more about scientific notation here:

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