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Question

a) To add 3.2 x 10^4 and 1.95 x 10^6, we need to make sure that the exponents are the same. In this case, we can rewrite 3.2 x 10^4 as 0.32 x 10^5:
3.2 x 10^4 + 1.95 x 10^6 = 0.32 x 10^5 + 1.95 x 10^6

Now, let's add the two numbers together:

0.32 x 10^5 + 1.95 x 10^6 = 2.27 x 10^6

So the sum is 2.27 x 10^6.

b) To subtract 1.95 x 10^6 from 3.2 x 10^4, we can rewrite 3.2 x 10^4 as 0.032 x 10^6:

3.2 x 10^4 - 1.95 x 10^6 = 0.032 x 10^6 - 1.95 x 10^6

Now, let's subtract the two numbers:

0.032 x 10^6 - 1.95 x 10^6 = -1.918 x 10^6

So the difference is -1.918 x 10^6.

c) To multiply 3.2 x 10^4 and 1.95 x 10^6, we can multiply the numbers and add the exponents:

(3.2 x 10^4) * (1.95 x 10^6) = (3.2 * 1.95) x (10^4 * 10^6) = 6.24 x 10^10

So the product is 6.24 x 10^10.

d) To divide 1.95 x 10^6 by 3.2 x 10^4, we can divide the numbers and subtract the exponents:

(1.95 x 10^6) / (3.2 x 10^4) = (1.95 / 3.2) x (10^6 / 10^4) = 0.609375 x 10^2

Now, let's simplify the decimal:

0.609375 x 10^2 = 6.09375 x 10^1

So the quotient is 6.09375 x 10^1.

Answer 1

a) To add 3.2 x 10^4 and 1.95 x 10^6, rewrite 3.2 x 10^4 as 0.32 x 10^5:
3.2 x 10^4 + 1.95 x 10^6 = 0.32 x 10^5 + 1.95 x 10^6
The sum is 2.27 x 10^6.

b) To subtract 1.95 x 10^6 from 3.2 x 10^4, rewrite 3.2 x 10^4 as 0.032 x 10^6:
3.2 x 10^4 - 1.95 x 10^6 = 0.032 x 10^6 - 1.95 x 10^6
The difference is -1.918 x 10^6.

c) To multiply 3.2 x 10^4 and 1.95 x 10^6, multiply the numbers and add the exponents:
(3.2 x 10^4) * (1.95 x 10^6) = 6.24 x 10^10
The product is 6.24 x 10^10.

d) To divide 1.95 x 10^6 by 3.2 x 10^4, divide the numbers and subtract the exponents:
(1.95 x 10^6) / (3.2 x 10^4) = 0.609375 x 10^2
The quotient is 6.09375 x 10^1.