Rounding 6-Digit Numbers
4A · Chapter 1 · Lesson 6 · MATH-4A-C01-L06
Learning goal. Justify rounding six-digit values to thousands and higher places with midpoint arguments.
Before you begin
Recall: Grade 3: four-digit place value, regrouping, comparison and rounding; Rounding 5-Digit Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Round 39,340 to the nearest 100.
Show answer & reasoning
The bounding multiples are 39,300 and 39,400. The midpoint is 39,350, so the nearer benchmark is 39,300.
Round 33,426 to the nearest 100.
Show answer & reasoning
The bounding multiples are 33,400 and 33,500. The midpoint is 33,450, so the nearer benchmark is 33,400.
What is the midpoint between 75,700 and 75,800?
Show answer & reasoning
Half of the interval of 100 is 50. Add it to the lower benchmark.
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
Six-digit rounding works the same way as smaller-number rounding. For 995,000 to the nearest ten-thousand, the two nearby benchmarks are 990,000 and 1,000,000. Exactly halfway rounds upward under our classroom convention. A rounded number can cross into the next place, so check all placeholder zeros.
Model it: six-digit benchmark 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 310,685 to the nearest 1,000.
The bounding multiples are 310,000 and 311,000. The midpoint is 310,500, so the nearer benchmark is 311,000.
Check your understanding 1
Round 925,704 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 925,000 and 926,000. The midpoint is 925,500, so the nearer benchmark is 926,000.
Worked example 2
Round 472,643 to the nearest 1,000.
The bounding multiples are 472,000 and 473,000. The midpoint is 472,500, so the nearer benchmark is 473,000.
Check your understanding 2
Round 938,720 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 938,000 and 939,000. The midpoint is 938,500, so the nearer benchmark is 939,000.
Worked example 3
Round 337,295 to the nearest 1,000.
The bounding multiples are 337,000 and 338,000. The midpoint is 337,500, so the nearer benchmark is 337,000.
Check your understanding 3
Round 168,346 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 168,000 and 169,000. The midpoint is 168,500, so the nearer benchmark is 168,000.
Guided practice
Round 965,671 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 965,000 and 966,000. The midpoint is 965,500, so the nearer benchmark is 966,000.
Round 248,843 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 248,000 and 249,000. The midpoint is 248,500, so the nearer benchmark is 249,000.
Round 798,649 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 798,000 and 799,000. The midpoint is 798,500, so the nearer benchmark is 799,000.
Round 311,305 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 311,000 and 312,000. The midpoint is 311,500, so the nearer benchmark is 311,000.
What is the midpoint between 716,000 and 717,000?
Show answer & reasoning
Half of the interval of 1,000 is 500. Add it to the lower benchmark.
Independent practice
Round 223,106 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 223,000 and 224,000. The midpoint is 223,500, so the nearer benchmark is 223,000.
Round 102,517 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 102,000 and 103,000. The midpoint is 102,500, so the nearer benchmark is 103,000.
Round 488,378 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 488,000 and 489,000. The midpoint is 488,500, so the nearer benchmark is 488,000.
What is the midpoint between 862,000 and 863,000?
Show answer & reasoning
Half of the interval of 1,000 is 500. Add it to the lower benchmark.
Explain why rounding 227,844 to the nearest 1,000 gives 228,000.
Show answer & reasoning
227,844 is between 227,000 and 228,000; the midpoint is 227,500.
Round 290,224 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 290,000 and 291,000. The midpoint is 290,500, so the nearer benchmark is 290,000.
Round 228,186 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 228,000 and 229,000. The midpoint is 228,500, so the nearer benchmark is 228,000.
Round 695,895 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 695,000 and 696,000. The midpoint is 695,500, so the nearer benchmark is 696,000.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student rounds 264,500 down to 264,000 to the nearest thousand. Explain and correct it.
Show answer & reasoning
The midpoint between 264,000 and 265,000 is 264,500; halfway rounds upward.
What is the midpoint between 646,000 and 647,000?
Show answer & reasoning
Half of the interval of 1,000 is 500. Add it to the lower benchmark.
Exit check
Round 933,702 to the nearest 1,000.
Show answer & reasoning
The bounding multiples are 933,000 and 934,000. The midpoint is 933,500, so the nearer benchmark is 934,000.
What is the midpoint between 821,000 and 822,000?
Show answer & reasoning
Half of the interval of 1,000 is 500. Add it to the lower benchmark.
Explain why rounding 882,686 to the nearest 1,000 gives 883,000.
Show answer & reasoning
882,686 is between 882,000 and 883,000; the midpoint is 882,500.