When estimating a quotient, explain what to do if rounding...

When estimating a quotient, explain what to do if rounding the numbers to one nonzero digit produces a division that is difficult to perform mentally.Then find the actual quotient.
$\frac{24,400}{610}$

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Key Concepts

Mental Math Strategies

Mental math strategies often include adjusting the degree of rounding or using alternative rounding techniques to simplify arithmetic operations. When a division remains challenging even after initial rounding, fine-tuning the approximation by rounding to two or more significant digits can yield numbers that are easier to divide in your head.

Exact Calculation

Exact calculation is the process of performing the operation without approximations to find the precise answer. In this problem, simplifying the fraction by canceling common factors leads to an exact quotient of 40, which confirms the result obtained through estimation.

Estimation

Estimation involves approximating numbers to simplify calculations and quickly understand the magnitude of an answer. It is useful when an exact answer isn't necessary or when checking the reasonableness of a computed result.

Rounding to Significant Figures

Rounding numbers to a specific number of significant figures, such as one nonzero digit, is a common estimation strategy. However, if this level of rounding results in numbers that are still cumbersome to work with mentally, using more significant figures can make the division easier without greatly sacrificing accuracy.

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