Final answer:
Calculations involving scientific notation require accuracy and attention to significant figures. Use a calculator to evaluate expressions and then express the final answers in scientific notation. There are multiple methods to perform operations in mathematics, and multiple methods can verify an answer.
Step-by-step explanation:
When performing calculations and expressing answers in scientific notation, it is important to follow proper rules and use a calculator as needed to ensure accuracy. Below, we calculate the provided expressions and express them in scientific notation:
a. For the expression (9.09 × 108) ÷ [(6.33 × 109) × (4.066 × 10–7)]:
b. To find 9,345 × 34.866 ÷ 0.00665, we calculate the product of 9,345 and 34.866 first and then divide by 0.00665.
c. The expression 456 × (7.4 × 108) can be processed by multiplying 456 and 7.4 first and then adjusting the exponent for the product.
d. For (3.02 × 105) × (9.04 × 1015), we multiply the base numbers and then add the exponents of the two scientific notations.
e. To compute 0.0044 × 0.000833, we need a calculator to find the product and represent it in scientific notation.
Additional Examples
f. For 98,000 × 23,000 = ?, we find the product and express it in scientific notation with the correct number of significant figures.
For each calculation, ensure consistency with significant figures and use a calculator to confirm the results before expressing them in proper scientific notation. The provided examples also highlight that in mathematics, there can be many methods to arrive at the same answer, as demonstrated in the lesson regarding multiplying exponents.