Rounding 5-Digit Numbers
4A · Chapter 1 · Lesson 5 · MATH-4A-C01-L05
Learning goal. Round five-digit values to stated places using bounding benchmarks and midpoints.
Before you begin
Recall: Grade 3: four-digit place value, regrouping, comparison and rounding; Comparing and Ordering Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Insert <, >, or =: 269,595 ___ 268,615.
Show answer & reasoning
Compare the leftmost place where the digits differ: 269,595 is greater than 268,615.
Insert <, >, or =: 123,267 ___ 110,943.
Show answer & reasoning
Compare the leftmost place where the digits differ: 123,267 is greater than 110,943.
Order these numbers from least to greatest: 814,467, 815,697, 393,697.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Key vocabulary
- place value
- value determined by a digit position
- expanded form
- sum of each nonzero place value
- benchmark
- nearby convenient multiple
- midpoint
- number exactly halfway between two bounds
Understand the concept
Rounding asks which benchmark multiple is closer to the original number. To round 46,270 to the nearest thousand, compare 46,000 and 47,000; their midpoint is 46,500. Since 46,270 is below the midpoint, it rounds to 46,000. Always start from the original value, never an intermediate rounded answer.
Model it: benchmarks and a midpoint on a scaled number line. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Round 92,751 to the nearest 100.
The bounding multiples are 92,700 and 92,800. The midpoint is 92,750, so the nearer benchmark is 92,800.
Check your understanding 1
Round 83,544 to the nearest 100.
Show answer & reasoning
The bounding multiples are 83,500 and 83,600. The midpoint is 83,550, so the nearer benchmark is 83,500.
Worked example 2
Round 60,176 to the nearest 100.
The bounding multiples are 60,100 and 60,200. The midpoint is 60,150, so the nearer benchmark is 60,200.
Check your understanding 2
Round 80,857 to the nearest 100.
Show answer & reasoning
The bounding multiples are 80,800 and 80,900. The midpoint is 80,850, so the nearer benchmark is 80,900.
Worked example 3
Round 86,084 to the nearest 100.
The bounding multiples are 86,000 and 86,100. The midpoint is 86,050, so the nearer benchmark is 86,100.
Check your understanding 3
Round 86,038 to the nearest 100.
Show answer & reasoning
The bounding multiples are 86,000 and 86,100. The midpoint is 86,050, so the nearer benchmark is 86,000.
Guided practice
Round 63,135 to the nearest 100.
Show answer & reasoning
The bounding multiples are 63,100 and 63,200. The midpoint is 63,150, so the nearer benchmark is 63,100.
Round 67,515 to the nearest 100.
Show answer & reasoning
The bounding multiples are 67,500 and 67,600. The midpoint is 67,550, so the nearer benchmark is 67,500.
Round 40,831 to the nearest 100.
Show answer & reasoning
The bounding multiples are 40,800 and 40,900. The midpoint is 40,850, so the nearer benchmark is 40,800.
Round 23,653 to the nearest 100.
Show answer & reasoning
The bounding multiples are 23,600 and 23,700. The midpoint is 23,650, so the nearer benchmark is 23,700.
What is the midpoint between 55,100 and 55,200?
Show answer & reasoning
Half of the interval of 100 is 50. Add it to the lower benchmark.
Independent practice
Round 89,424 to the nearest 100.
Show answer & reasoning
The bounding multiples are 89,400 and 89,500. The midpoint is 89,450, so the nearer benchmark is 89,400.
Round 63,037 to the nearest 100.
Show answer & reasoning
The bounding multiples are 63,000 and 63,100. The midpoint is 63,050, so the nearer benchmark is 63,000.
Round 11,904 to the nearest 100.
Show answer & reasoning
The bounding multiples are 11,900 and 12,000. The midpoint is 11,950, so the nearer benchmark is 11,900.
What is the midpoint between 56,700 and 56,800?
Show answer & reasoning
Half of the interval of 100 is 50. Add it to the lower benchmark.
Explain why rounding 64,607 to the nearest 100 gives 64,600.
Show answer & reasoning
64,607 is between 64,600 and 64,700; the midpoint is 64,650.
Round 46,076 to the nearest 100.
Show answer & reasoning
The bounding multiples are 46,000 and 46,100. The midpoint is 46,050, so the nearer benchmark is 46,100.
Round 39,892 to the nearest 100.
Show answer & reasoning
The bounding multiples are 39,800 and 39,900. The midpoint is 39,850, so the nearer benchmark is 39,900.
Round 90,713 to the nearest 100.
Show answer & reasoning
The bounding multiples are 90,700 and 90,800. The midpoint is 90,750, so the nearer benchmark is 90,700.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student rounds 48,450 to the nearest hundred as 48,400. Explain why this is wrong.
Show answer & reasoning
48,450 is halfway between 48,400 and 48,500; our rounding convention sends halfway values up.
Round 50,070 to the nearest 100.
Show answer & reasoning
The bounding multiples are 50,000 and 50,100. The midpoint is 50,050, so the nearer benchmark is 50,100.
Exit check
Round 17,835 to the nearest 100.
Show answer & reasoning
The bounding multiples are 17,800 and 17,900. The midpoint is 17,850, so the nearer benchmark is 17,800.
What is the midpoint between 21,400 and 21,500?
Show answer & reasoning
Half of the interval of 100 is 50. Add it to the lower benchmark.
Explain why rounding 89,997 to the nearest 100 gives 90,000.
Show answer & reasoning
89,997 is between 89,900 and 90,000; the midpoint is 89,950.