Math Problem Statement

A number p, when rounded to the nearest 10, is equal to 940. Find the upper and lower bound of p.

Solution

The problem states that a number pp, when rounded to the nearest 10, is equal to 940. The task is to find the upper and lower bounds of pp.

Explanation:

  1. Rounding Rule: When rounding to the nearest 10, numbers are rounded up if they are halfway or more to the next multiple of 10, and rounded down otherwise.
    • For p=940p = 940, the range of numbers that round to 940 is between 935 and 944 inclusive:
      • Lower Bound: 935935 (the smallest number that rounds to 940).
      • Upper Bound: 944944 (the largest number that rounds to 940).

Final Answer:

  • Lower Bound: 935935
  • Upper Bound: 944944

Would you like a detailed breakdown of why these bounds are determined this way?

Here are some related questions to expand on this topic:

  1. How do rounding rules differ for decimal places versus whole numbers?
  2. What would the bounds be if pp were rounded to the nearest 100 instead of 10?
  3. Why is the upper bound inclusive of 944 and not 945?
  4. How does rounding to different levels of precision (e.g., nearest 5, nearest 0.1) affect bounds?
  5. Can you determine the bounds for pp if it were rounded to the nearest 1?

Tip: Always check the midpoint when working with rounding problems—it helps clarify whether a value rounds up or down.

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Math Problem Analysis

Mathematical Concepts

Rounding to the nearest ten
Upper and lower bounds

Formulas

Lower bound: number - 5
Upper bound: number + 4

Theorems

Rounding rules for whole numbers

Suitable Grade Level

Grades 6-8