Historical text explaining the Louisiana Purchase of 1803, highlighting its significance and the key figures involved.

Let’s go through this step by step.

The question is:
“How much did the United States pay per square mile for the Louisiana Purchase?”

We’re told in the text:
- The U.S. paid $15 million total.
- The land was about 827,000 square miles.

So we need to divide the total cost by the total area to find the price per square mile.

Step 1: Write down the numbers.
Total cost = $15,000,000
Total area = 827,000 square miles

Step 2: Divide cost by area.
$15,000,000 ÷ 827,000 = ?

Let’s do the math carefully.

First, simplify by removing three zeros from both numbers (since dividing by 1,000 doesn’t change the ratio):

→ $15,000 ÷ 827 ≈ ?

Now calculate:

827 × 18 = 14,886
15,000 - 14,886 = 114 → so 18 + (114/827) ≈ 18.138

But wait — that’s if we removed 3 zeros. Actually, we removed 3 zeros from each side, so the real answer is still around $18.14 per square mile? Let me double-check with exact division.

Actually, let’s do it properly without simplifying too early.

$15,000,000 ÷ 827,000

Divide numerator and denominator by 1,000:

= $15,000 ÷ 827

Now use calculator-style long division or approximate:

827 × 18 = 14,886
Subtract: 15,000 - 14,886 = 114
So 18 + 114/827 ≈ 18 + 0.1378 ≈ 18.14

Wait — but hold on! That can’t be right historically. I think I made a mistake here.

Actually, let me check known facts: Historically, the Louisiana Purchase was about 4 cents per acre, and there are 640 acres in a square mile.

So 4 cents × 640 = $25.60 per square mile? But that contradicts our calculation.

Wait — no, let’s re-read the problem.

The text says: “the United States agreed to pay $15 million to buy New Orleans and Florida...” — actually, that’s not quite accurate. The full Louisiana Purchase included way more than just New Orleans and Florida — it was 827,000 sq mi for $15 million.

And yes, standard history says it was about 4 cents per acre.

Let’s verify using that.

There are 640 acres in 1 square mile.

So if it’s 4 cents per acre, then per square mile:
4 cents × 640 = 2,560 cents = $25.60 per square mile

But according to our earlier math: $15,000,000 ÷ 827,000 ≈ $18.14

That’s a discrepancy. Which one is correct?

Wait — maybe the 827,000 square miles is wrong? Or the $15 million?

Actually, historical record: The Louisiana Purchase was approximately 530 million acres for $15 million.

Let’s try that.

530,000,000 acres ÷ $15,000,000 = ? acres per dollar → better to do dollars per acre.

$15,000,000 ÷ 530,000,000 acres = $0.0283 per acre → about 2.83 cents per acre

Then per square mile: 2.83 cents × 640 = ~$18.11 per square mile — which matches our first calculation!

Ah — so the 4 cents per acre is a rounded figure sometimes used, but actual was closer to 2.8–3 cents.

In the text, it says “about 827,000 square miles” — let’s confirm how many acres that is.

827,000 sq mi × 640 acres/sq mi = 529,280,000 acres — yes, about 530 million.

So $15 million ÷ 529,280,000 acres = $0.02834 per acre → times 640 = $18.14 per square mile.

Perfect — so our original math was correct.

Therefore, the United States paid approximately $18.14 per square mile.

But since the question likely expects a simple answer based on the given numbers (without going into acres), we’ll stick with:

$15,000,000 ÷ 827,000 = ?

Let me compute exactly:

15,000,000 ÷ 827,000 = 15,000 ÷ 827 (divided top and bottom by 1,000)

Now 827 × 18 = 14,886
Remainder 114 → so 18 + 114/827

114 ÷ 827 ≈ 0.1378

So 18.1378...

Rounded to nearest cent: $18.14

Final Answer:
$18.14