Multiply the expression on the left and match them with their appropriate result.(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
(6.77 × 10−12) ⋅ (1.12 × 10−6)
(2 × 10−3) ⋅ (3 × 107)
(9.1 × 109) ⋅ (2.6 × 102)
(6.77 × 10−12) ⋅ (1.12 × 10−6) = 7.5864 × 10^(-18)
(2 × 10−3) ⋅ (3 × 10^7) = 6 × 10^4
(9.1 × 10^9) ⋅ (2.6 × 10^2) = 2.366 × 10^12
To solve these multiplication problems, we can use the rules of exponents.
(6.77 × 10−12) ⋅ (1.12 × 10−6)
To multiply two numbers in scientific notation, multiply the coefficients and add the exponents:
(6.77 × 1.12) × (10^(-12) × 10^(-6)) = 7.5664 × 10^(-18)
(2 × 10^(-3)) ⋅ (3 × 10^7)
Again, multiply the coefficients and add the exponents:
(2 × 3) × (10^(-3) × 10^7) = 6 × 10^4
(9.1 × 10^9) ⋅ (2.6 × 10^2)
Multiply the coefficients and add the exponents:
(9.1 × 2.6) × (10^9 × 10^2) = 23.66 × 10^(9+2) = 23.66 × 10^11
So, the results are:
(6.77 × 10^(-12)) ⋅ (1.12 × 10^(-6)) = 7.5664 × 10^(-18)
(2 × 10^(-3)) ⋅ (3 × 10^7) = 6 × 10^4
(9.1 × 10^9) ⋅ (2.6 × 10^2) = 23.66 × 10^11
To multiply two numbers written in scientific notation, you need to multiply the numerical parts and add the exponents of the powers of 10.
Let's calculate each expression one by one:
(6.77 × 10^(-12)) ⋅ (1.12 × 10^(-6))
- Multiply the numerical parts: 6.77 × 1.12 = 7.5704
- Add the exponents: -12 + (-6) = -18
- Write the answer in scientific notation: 7.5704 × 10^(-18)
(2 × 10^(-3)) ⋅ (3 × 10^7)
- Multiply the numerical parts: 2 × 3 = 6
- Add the exponents: -3 + 7 = 4
- Write the answer in scientific notation: 6 × 10^(4)
(9.1 × 10^9) ⋅ (2.6 × 10^2)
- Multiply the numerical parts: 9.1 × 2.6 = 23.66
- Add the exponents: 9 + 2 = 11
- Write the answer in scientific notation: 23.66 × 10^(11)
So, the expressions and their results are:
(6.77 × 10^(-12)) ⋅ (1.12 × 10^(-6)) = 7.5704 × 10^(-18)
(2 × 10^(-3)) ⋅ (3 × 10^7) = 6 × 10^(4)
(9.1 × 10^9) ⋅ (2.6 × 10^2) = 23.66 × 10^(11)