Final answer:
To solve every long division with ease, one should divide the digit term of the numerator by the digit term of the denominator and subtract the exponents when dividing exponentials. Remember to multiply or divide every term on both sides of an equation and simplify by canceling units or terms, checking that the final answer is reasonable.
Step-by-step explanation:
To solve every long division with ease, you should follow these steps:
- Divide the digit term of the numerator by the digit term of the denominator.
- Multiply accordingly when dealing with exponential terms or fractions.
- Subtract the exponents when dividing exponential terms.
- Bring down the next digit in a long division problem if necessary.
- Identify the remainder if the division does not result in a whole number.
When dividing exponentials, the process involves dividing the numerical coefficients and subtracting the powers of the same base.
In the case of multiplication or division by the same number on both sides of an equation, remember to apply the operation to every term on either side of the equality. Always look to simplify by canceling out units or terms wherever possible and checking that your final answer is reasonable.
For example, if we have 4.5 × 109 ÷ 106, we would divide 4.5 by 1 (since 106 is essentially '1' with six zeros) and subtract the exponents of ten to get 4.5 × 10(9-6) which simplifies to 4.5 × 103.
Using these strategies, you can approach long division problems methodically and accurately whether they involve simple numbers, fractions, or powers of ten.