Final answer:
Regrouping is renaming the number and writing it in a different form without changing its value, often used in operations to simplify calculations, such as carrying and borrowing in arithmetic or adjusting the format in scientific notation.
Step-by-step explanation:
When you are regrouping in mathematics, you are not changing the value of the number but are instead renaming the number and writing it in a different form. This is often done to make calculations easier, such as when carrying over digits in addition or borrowing in subtraction. It is also common in the multiplication and division of numbers in scientific notation, where you can move the decimal point to create a new number with the same value, adjusting the exponent part accordingly.
In scientific notation, for example, regrouping involves changing the format of a number to a product of a number (N) and a power of ten (10^n), which makes it easier to comprehend and work with, especially for very large or very small numbers. Multiplication and division rules in scientific notation include multiplying the values of N and adding exponents for multiplication, or dividing values of N and subtracting exponents for division.