(Scientific rules and explanation)
A student revises the procedure for multiplying numbers written in scientific notation.
(i) State the general rule for writing the product of two numbers each expressed in the form a×10n, where 1≤a<10.
(ii) Using the laws of indices, explain why the exponents are added when the coefficients are multiplied. Illustrate your explanation by expanding the expression (4.0×105)(3.0×102) without using a calculator.
(iii) After obtaining the numerical product in part (ii), show the steps required to rewrite the answer in proper scientific notation and indicate the number of significant figures that must appear in the final result.
a. State the general rule for writing the product of two numbers each expressed in scientific notation.
b. Using the laws of indices, explain why the exponents are added when the coefficients are multiplied. Illustrate with (4.0×105)(3.0×102).
c. Normalize the result obtained in part (ii) and state the correct number of significant figures for the final answer.