Final answer:
The product of 22 and 2.1×10³² is calculated by first expressing 22 as 2.2×10¹, then multiplying the coefficients and adding the exponents, resulting in 4.62×10³³. This is adjusted to 0.462×10³4 to fit the proper scientific notation format. Therefore, the product of 22 and 2.1×10³² expressed in scientific notation is 0.462×10³³4.
Step-by-step explanation:
The question involves multiplying two numbers expressed in scientific notation and finding the product in scientific notation. To find the product of 22 and 2.1×10³², we first express 22 as 2.2×10¹ to fit the proper format of scientific notation, where the number (the coefficient) is between 1 and 10. Then, we multiply the coefficients (2.2 and 2.1) and add the exponents (1 and 32) as per the rules for multiplying in scientific notation.
The calculation is as follows:
(2.2×10¹) × (2.1×10³²) = (2.2×2.1) × 10¹³³ = 4.62 × 10¹³³
Now, since 4.62 is more than 10, we need to adjust it to preserve the scientific notation form. Dividing it by 10, we get 0.462×10, a new decimal that does follow the scientific notation format, and we increase the exponent by 1 to compensate for the division by 10:
4.62 × 10³³ = (0.462×10) × 10³³ = 0.462×10³³4
Therefore, the product of 22 and 2.1×10³² expressed in scientific notation is 0.462×10³³4.