Multiply (4.12 × 10−9)(8.3 × 1015). Write the final answer in scientific notation.
a) 34.196 × 10−134
b) 3.4196 × 107
d) 3.4196 × 10−135
d) 34.196 × 106
To multiply two numbers written in scientific notation, you need to multiply the numerical parts together and add the exponents.
(4.12 × 10^(-9))(8.3 × 10^15) = (4.12 * 8.3) × (10^(-9) * 10^15)
= 34.196 × 10^(-9 + 15)
= 34.196 × 10^(6)
The final answer in scientific notation is: 3.4196 × 10^7
Therefore, the correct answer is option b) 3.4196 × 10^7
To multiply numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of 10.
(4.12 × 10−9)(8.3 × 1015) = (4.12 × 8.3) × (10−9 × 1015)
= 34.196 × 10(−9 + 15)
= 34.196 × 10^6
The final answer in scientific notation is 3.4196 × 10^7, which corresponds to option b) 3.4196 × 10^7.
To multiply numbers in scientific notation, you need to multiply the coefficients (numbers at the front) and add the exponents (the powers of 10).
Let's multiply the coefficients first: 4.12 × 8.3 = 34.196
Now, let's add the exponents: -9 + 15 = 6
So, the final answer is 34.196 × 10^6.
Looking at the options given:
a) 34.196 × 10^(-134) - The exponent is too large; this is not the correct answer.
b) 3.4196 × 10^7 - The coefficient is incorrect; this is not the correct answer.
c) 3.4196 × 10^(-135) - The exponent is too small; this is not the correct answer.
d) 34.196 × 10^6 - The coefficient and exponent match our calculations, making this the correct answer.
Therefore, the final answer in scientific notation is d) 34.196 × 10^6.