š° Number Kingdom Ā· Bounds
Find all decimal values that could round to a given decimal result. In this lesson, focus on whole-number rounding chooses the closest multiple of the requested power of ten.
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Find all decimal values that could round to a given decimal result. In this lesson, focus on whole-number rounding chooses the closest multiple of the requested power of ten.
Whole-number rounding chooses the closest multiple of the requested power of ten. The midpoint separates the numbers that round down from those that round up. For possible values after decimal rounding, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Possible values after decimal rounding: Whole-number rounding chooses the closest multiple of the requested power of ten. Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval. Keep the possible values after decimal rounding representation visible until the final line.
Place the number between neighbouring multiples on a draggable number line and reveal the midpoint decision gate. Use the model to explain one change you notice while working on possible values after decimal rounding.
Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval. Write that check beside the final possible values after decimal rounding answer.
Lower bound = rounded value ā half unit; upper bound = rounded value + half unit.
Visual / interactive
Place the number between neighbouring multiples on a draggable number line and reveal the midpoint decision gate. Use the model to explain one change you notice while working on possible values after decimal rounding.
Worked examples
Understand the idea with small numbers, one representation and one clear step.
Use the standard Year 8 method with mixed examples and normal wording.
Handle multi-step or less familiar questions and explain choices.
Solve a worded question, show reasoning, check accuracy and write a final sentence.
Given information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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.
Given information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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.
Given information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval. Write that check beside the final possible values after decimal rounding answer.
Create a possible values after decimal 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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Use round drag controls to solve three checked possible values after decimal rounding rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Possible values after decimal rounding: Whole-number rounding chooses the closest multiple of the requested power of ten. Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval. Keep the possible values after decimal rounding representation visible until the final line.
Tap to mark reviewedplace value Ā· nearest multiple Ā· midpoint Ā· round up Ā· round down Ā· possible Ā· values
Tap to mark reviewedIdentify the requested power of ten. Write the neighbouring multiples. Find their midpoint. Choose the nearer multiple; at halfway, round upward. Record the check explicitly for possible values after decimal rounding.
Tap to mark reviewedLower bound = rounded value ā half unit; upper bound = rounded value + half unit.
Tap to mark reviewedGiven information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedRounding to the wrong column. This is a key trap when answering possible values after decimal rounding questions.
Tap to mark reviewedFor possible values after decimal rounding, show the key representation before the final calculation. Use this final check: Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval.
Tap to mark reviewedCrowd estimates, Mental calculation checks
Tap to mark reviewedI can explain possible values after decimal rounding, use the method, check for mistakes, and answer an exam-style question.
Tap to mark reviewedIām Stuck
Use this whenever a question feels confusing. Nothing here is locked.
Possible values after decimal rounding: Whole-number rounding chooses the closest multiple of the requested power of ten. Check that the answer is a multiple of the requested unit and that the original lies in its rounding interval. Keep the possible values after decimal rounding representation visible until the final line.
Think of possible values after decimal 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.
Start by naming the given information and the exact result required for possible values after decimal rounding.
Identify the requested power of ten.
Given information: Possible values after decimal rounding ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the possible values after decimal rounding method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Method: Identify the requested power of ten. ā Write the neighbouring multiples. ā Find their midpoint. ā Choose the nearer multiple; at halfway, round upward. Record the check explicitly for possible values after decimal rounding.
Rounding to the wrong column. This is a key trap when answering possible values after decimal rounding questions.
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