I need help with scientific/exponential notation arithmetic (please show all of your work)?

Scientific notation is when you have 10 to the power of a number to show how many places a decimal place would move to the right or left of a number (right if the exponent is positive and negative if the exponent is negative)

For example, if I say 5.4 x 10^6 that would be equal to 5,400,000

When multiplying two numbers in scientific notation all you need to do is add the exponents of the 10s and multiply the base numbers you are multiplying.

I'll use your first and second problems with different numbers as an example so you may do the rest (as a tutor I can't do your homework for you)

(2 x 10^4) x (6 x 10^2) =

2 x 6 = 12 so we can now say 10 x (10^4) x (10^2)

When multiplying numbers that have exponents but the same bases we add the exponents, thus we can now say:

4 + 2 = 6

Making the answer 12 x 10^6

In standard notation that would be 12,000,000 (but scientific notation makes it much shorter)

(4 x 10^-3) x (8 x 10^6)

4 x 8 = 32

-3 + 6 = 3 (negative plus a positive is the same as subtracting the smaller number from the larger and keeping the sign of the larger number)

Our answer is 32 x 10^3 which is 32,000 in standard notation.

Hope this helps. :-)

Scientific notation form

X=a*10^n

where n is an integer number

and 1=< a <10

EX : 42000 =4.2*10^4

0.00013 =1.3*10^(-4)

First you multiply the powers

10^m * 10^n= 10^(m+n)

10^n /10^m = 10^(n-m)

Then you multiply the numbers those multiply the powers. You get the answers.

1. (1×10³) × (3×10¹)= (1 x 3) x 10³⁺¹ = 3 x 10⁴

2. (5×10⁻⁵) × (11×10⁴)= (5 x 11) x 10⁻⁵⁺⁴ = 55 x 10⁻¹ = 5.5 x 10¹ x 10⁻¹ = 5.5 x 10¹⁻¹ = 5.5 x 10⁰

3. (4×10³) ÷ (8×10⁵)= (4 ÷ 8) x (10³÷10⁵) = 0.5 x 10³⁻⁵ = 0.5 x 10⁻² = 5 x 10⁻¹x 10⁻² = 5 x 10⁻³

4. (4×10³) + (3×10²)= (4x10¹x10²) + (3×10²) = (40+3)x10² = 43 x 10² = 4.3 x 10³

5. (8x10⁶) + (3.2×10⁷)= (8x10⁶) + (3.2×10¹ x 10⁶) = (8 + 32) x 10⁶ = 40 x 10⁶ = 4.0 x 10⁷