13. Multiply the expression on the left and match them with their appropriate result. (2 x 10^-3) x (3 x 10^7), (9.1 x 10^9) x (2.6 x 10^2), (6.77 x 10^-12) x *1.12 x 10^-6). Options are (6 x 10^4), (2.366 x 10^-12), and (7.5824 x 10^-18).
(2 x 10^-3) x (3 x 10^7) = 6 x 10^4
(9.1 x 10^9) x (2.6 x 10^2) = 2.366 x 10^12
(6.77 x 10^-12) x (1.12 x 10^-6) = 7.5824 x 10^-18
So, the matches are:
1. (2 x 10^-3) x (3 x 10^7) = (6 x 10^4)
2. (9.1 x 10^9) x (2.6 x 10^2) = (2.366 x 10^-12)
3. (6.77 x 10^-12) x (1.12 x 10^-6) = (7.5824 x 10^-18)
Let's multiply the expressions step by step:
1. (2 x 10^-3) x (3 x 10^7):
To multiply the numbers with the same base, we multiply the coefficients and add the exponents.
(2 x 3) x (10^-3 x 10^7) = 6 x 10^4
2. (9.1 x 10^9) x (2.6 x 10^2):
(9.1 x 2.6) x (10^9 x 10^2) = 23.66 x 10^11 = 2.366 x 10^12
3. (6.77 x 10^-12) x (1.12 x 10^-6):
(6.77 x 1.12) x (10^-12 x 10^-6) = 7.5824 x 10^-18
Therefore, the correct matches are:
(2 x 10^-3) x (3 x 10^7) = (6 x 10^4)
(9.1 x 10^9) x (2.6 x 10^2) = (2.366 x 10^-12)
(6.77 x 10^-12) x (1.12 x 10^-6) = (7.5824 x 10^-18)
To solve these multiplications involving scientific notation, you need to multiply the numerical coefficients together and then add the exponents of 10. Let's go step by step for each expression:
(2 x 10^-3) x (3 x 10^7):
1. For the numerical coefficients, multiply 2 and 3: 2 x 3 = 6.
2. For the exponents of 10, add -3 and 7: -3 + 7 = 4.
3. The result is 6 x 10^4.
So, the first expression (2 x 10^-3) x (3 x 10^7) matches with (6 x 10^4).
(9.1 x 10^9) x (2.6 x 10^2):
1. For the numerical coefficients, multiply 9.1 and 2.6: 9.1 x 2.6 = 23.66.
2. For the exponents of 10, add 9 and 2: 9 + 2 = 11.
3. The result is 2.366 x 10^11.
Therefore, the second expression (9.1 x 10^9) x (2.6 x 10^2) matches with (2.366 x 10^11).
(6.77 x 10^-12) x (1.12 x 10^-6):
1. For the numerical coefficients, multiply 6.77 and 1.12: 6.77 x 1.12 ≈ 7.5824.
(Note: The exact value is too long, so we will use an approximation.)
2. For the exponents of 10, add -12 and -6: -12 + (-6) = -18.
3. The result is approximately 7.5824 x 10^-18.
Thus, the third expression (6.77 x 10^-12) x (1.12 x 10^-6) matches with (7.5824 x 10^-18).
So, the appropriate match for the expressions are:
- (2 x 10^-3) x (3 x 10^7) → (6 x 10^4)
- (9.1 x 10^9) x (2.6 x 10^2) → (2.366 x 10^11)
- (6.77 x 10^-12) x (1.12 x 10^-6) → (7.5824 x 10^-18)