🏰 Number Kingdom · Bounds

Minimum after rounding

Find the smallest value that could round to a stated integer or multiple. In this lesson, focus on a rounded value represents an interval of possible originals.

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Understand Minimum after rounding

Find the smallest value that could round to a stated integer or multiple. In this lesson, focus on a rounded value represents an interval of possible originals.

A rounded value represents an interval of possible originals. Subtract half the rounding unit for the included lower bound and add half the unit for the excluded upper bound. For minimum after rounding, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Minimum after rounding: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the minimum after rounding representation visible until the final line.

Picture the idea

Drag interval gates around the rounded value and test values just inside and just outside the interval. Use the model to explain one change you notice while working on minimum after rounding.

Check as you go

Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Write that check beside the final minimum after rounding answer.

Key vocabulary

lower boundupper bounderror intervalinclusivestrict upper limitminimumrounding

Rules and key facts

Lower bound = rounded value − half unit; upper bound = rounded value + half unit.

  • Identify the rounding unit.
  • Halve the unit.
  • Subtract half for the included lower endpoint.
  • Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for minimum after rounding.

Step-by-step method

  1. Identify the rounding unit.
  2. Halve the unit.
  3. Subtract half for the included lower endpoint.
  4. Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for minimum after rounding.

What you need first

  • Recognise the vocabulary: lower bound, upper bound, error interval.
  • Be able to explain the purpose of minimum after rounding before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Manufacturing tolerances
  • Measured dimensions

Visual / interactive

See the idea, then move it around

Skip to Practice

Drag interval gates around the rounded value and test values just inside and just outside the interval. Use the model to explain one change you notice while working on minimum after rounding.

Bounds slider + error interval simulator Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Minimum after rounding — A value rounds to 13 to the nearest 1. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Find the lower bound.5. Final answer: 12.5. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify the rounding unit.
  2. Halve the unit.
  3. Subtract half for the included lower endpoint.
Secure example

Use the normal method

Given information: Minimum after rounding — A value rounds to 1300 to the nearest 100. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 1300 to the nearest 100. Find the lower bound. Final answer: 1250. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Add half for the upper bound and use a strict upper limit.

Challenge example

Stretch the idea

Given information: Minimum after rounding — A value rounds to 130 to the nearest 10. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 130 to the nearest 10. Find the lower bound. Final answer: 125. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Minimum after rounding — A value rounds to 13 to the nearest 1. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Find the lower bound.5. Final answer: 12.5. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: The upper bound is usually written with <, because the endpoint rounds to the next value.

Common mistakes

  • Including the upper endpoint. This is a key trap when answering minimum after rounding questions.
  • Adding or subtracting a full rounding unit instead of half.

How to check your answer

Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Write that check beside the final minimum after rounding answer.

Extension challenge

Create a minimum after rounding problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Minimum after rounding challenge

Use interval sort controls to solve three checked minimum after rounding rounds. Solve at least two of three marked rounds and use feedback to correct any error.

Press Start Game to enter a topic-specific maths arena.

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Challenge The Lower Gatekeeper

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Study cards

Core idea

Minimum after rounding: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the minimum after rounding representation visible until the final line.

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Key vocabulary

lower bound · upper bound · error interval · inclusive · strict upper limit · minimum · rounding

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Rules

Identify the rounding unit. Halve the unit. Subtract half for the included lower endpoint. Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for minimum after rounding.

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Formula / fact

Lower bound = rounded value − half unit; upper bound = rounded value + half unit.

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Foundation example

Given information: Minimum after rounding — A value rounds to 13 to the nearest 1. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Find the lower bound.5. Final answer: 12.5. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Minimum after rounding — A value rounds to 1300 to the nearest 100. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 1300 to the nearest 100. Find the lower bound. Final answer: 1250. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Minimum after rounding — A value rounds to 130 to the nearest 10. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 130 to the nearest 10. Find the lower bound. Final answer: 125. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Minimum after rounding — A value rounds to 13 to the nearest 1. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Find the lower bound.5. Final answer: 12.5. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Including the upper endpoint. This is a key trap when answering minimum after rounding questions.

Tap to mark reviewed
Exam tip

For minimum after rounding, show the key representation before the final calculation. Use this final check: Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them.

Tap to mark reviewed
Real-world use

Manufacturing tolerances, Measured dimensions

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Checklist

I can explain minimum after rounding, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Minimum after rounding

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Simple explanation

Minimum after rounding: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the minimum after rounding representation visible until the final line.

Think of minimum after rounding as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify the rounding unit.
  2. Halve the unit.
  3. Subtract half for the included lower endpoint.
  4. Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for minimum after rounding.

Hint 1

Start by naming the given information and the exact result required for minimum after rounding.

Hint 2

Identify the rounding unit.

Full worked solution

Given information: Minimum after rounding — A value rounds to 13 to the nearest 1. Find the lower bound. Method choice: use the minimum after rounding method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Find the lower bound.5. Final answer: 12.5. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify the rounding unit. → Halve the unit. → Subtract half for the included lower endpoint. → Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for minimum after rounding.

Common mistake warning

Including the upper endpoint. This is a key trap when answering minimum after rounding questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain minimum after rounding in my own words.
  • I can use these words accurately: lower bound, upper bound, error interval.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Including the upper endpoint.
  • I can apply this check: Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them.
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