Final answer:
In expressions with multiplication and division but no grouping symbols, perform these operations from left to right. When using scientific notation, multiply by combining coefficients and adding exponents; divide by combining coefficients and subtracting exponents. Adhere to significant figure rules to maintain precision.
Step-by-step explanation:
If an expression without grouping symbols includes multiplication and division, you should perform these operations from left to right, according to the order they appear in the expression. This rule comes from the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Multiplication or division by the same number on both sides of an equation does not change equality. If one side of an equation contains more than one term, enclose that side in small brackets before performing multiplication or division, to ensure the operation applies to each term within the brackets.
For example, when dealing with scientific notation or significant figures, the process remains the same. In scientific notation, if you multiply two numbers, you multiply their coefficients (the N values) and add the exponents (the n values). Conversely, division involves dividing the coefficients and subtracting the exponents.
It's important to note that in scientific notation and with significant figures, you multiply or divide the numbers and adjust the result according to the lowest count of significant figures among the factors or the numbers being divided to maintain precision.