Problem
Locate and compare numbers on a number line
Of the three numbers 8,800, 10,500, and 10,100, decide which one is nearest to 10,000.
Base-ten numbers
Your answer
Watch out It's tempting to guess by how the numbers look instead of computing each number's distance from 10,000 — but only the smallest distance tells you which is closest.
How to solve
Strategy Draw a Diagram — Picture the numbers on a number line around 10,000 and measure how far each is from 10,000; the one with the smallest gap is closest.
1STEP 1
Distance of 8,800 from 10,000
8,800 is below 10,000 by 10,000 - 8,800 = 1,200.
10,000 - 8,800 = 1,200
On the number line 8,800 sits well to the left of 10,000.
4.NBT.A.2Draw A Diagram2STEP 2
Distance of 10,500 from 10,000
10,500 is above 10,000 by 10,500 - 10,000 = 500.
10,500 - 10,000 = 500
10,500 is just past 10,000.
4.NBT.A.2Draw A Diagram3STEP 3
Distance of 10,100 from 10,000
10,100 is above 10,000 by 10,100 - 10,000 = 100.
10,100 - 10,000 = 100
10,100 is barely past 10,000.
4.NBT.A.2Draw A Diagram4STEP 4
Compare the gaps
The distances are 1,200, 500, and 100. The smallest is 100, so 10,100 is closest to 10,000.
100 is less than 500, which is less than 1,200
The smallest gap wins; 100 is the smallest.
4.NBT.A.2Guess And CheckOf the three numbers, 10,100 is the one closest to 10,000.
Why?
Closest to 10,000 means the smallest distance from 10,000, and 10,100's distance of 100 is smaller than 10,500's 500 and 8,800's 1,200.
Why?
Each distance is found by subtracting the number and 10,000, because subtraction gives back the exact amount you would add to one number to reach the other.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The gap is only 100 because 10,100 matches 10,000 in every place except the hundreds, while 10,500 differs by more in the hundreds and 8,800 already differs up in the thousands.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
Answer
10,100
10,100 differs from 10,000 by only 100, far less than 500 (for 10,500) or 1,200 (for 8,800), so 10,100 being closest is correct.
Takeaway
This only needs Grade 4 comparing: measure each number's gap from 10,000 and pick the smallest gap!
- Distance of 8,800 from 10,000
- Distance of 10,500 from 10,000
- Distance of 10,100 from 10,000
- Compare the gaps
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