can you shorten this
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.
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.
Sure! Here is a shortened version of the explanation:
a) To add 3.2 x 10^4 and 1.95 x 10^6, ensure that the exponents are the same. Rewrite 3.2 x 10^4 as 0.32 x 10^5 and add them together: 0.32 x 10^5 + 1.95 x 10^6 = 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 and subtract them: 0.032 x 10^6 - 1.95 x 10^6 = -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 1.95) x (10^4 * 10^6) = 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 / 3.2) x (10^6 / 10^4) = 0.609375 x 10^2 = 6.09375 x 10^1.
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
Add the two numbers together:
0.32 x 10^5 + 1.95 x 10^6 = 2.27 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
Subtract the two numbers:
0.032 x 10^6 - 1.95 x 10^6 = -1.918 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) = (3.2 * 1.95) x (10^4 * 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) = (1.95 / 3.2) x (10^6 / 10^4) = 0.609375 x 10^2
Simplify the decimal:
0.609375 x 10^2 = 6.09375 x 10^1
The quotient is 6.09375 x 10^1.