What is the value of 83 percent of 2350?

Introduction / Context:
This is a direct percentage calculation involving a non-round percentage, 83 percent, applied to a given number 2350. The question checks whether the student can handle multiplication of a decimal by a multi digit number and interpret the result correctly as a decimal.

Given Data / Assumptions:

• We have the number 2350.
• We are asked to find 83 percent of this number.
• All calculations are in ordinary decimal arithmetic.

Concept / Approach:
To find 83 percent of a quantity, we convert 83 percent to decimal form as 0.83 and then multiply. Alternatively, we can treat 83 percent as 83 / 100 and compute (83 * 2350) / 100. Choosing the easier way of multiplication helps reduce mistakes. Since 2350 ends with two zeros, multiplying by 83 and then dividing by 100 is particularly simple.

Step-by-Step Solution:
Step 1: Express 83 percent as a fraction: 83 percent = 83 / 100.Step 2: Compute 83 / 100 of 2350 as (83 * 2350) / 100.Step 3: Multiply 2350 by 83. We can do this as 2350 * 80 + 2350 * 3.Step 4: Compute 2350 * 80 = 188000 and 2350 * 3 = 7050.Step 5: Add these results: 188000 + 7050 = 195050.Step 6: Divide by 100: 195050 / 100 = 1950.50.

Verification / Alternative check:
We can use the decimal form 0.83 directly. Multiply 2350 by 0.83. Note that 0.83 = 83 / 100, so 2350 * 0.83 = 1950.5. Writing this with two decimal places gives 1950.50. This matches the result obtained using the fraction method. You can also approximate by noting that 80 percent of 2350 is 1880, and 3 percent of 2350 is 70.5, which sum to 1950.5, confirming the result.

Why Other Options Are Wrong:
The value 1889.95 is close to 80 percent of 2350 but not exactly 83 percent. The value 1912.35 is also not equal to 1950.5 and corresponds to a slightly lower percentage. The value 1875.25 is significantly lower and not associated with 83 percent. The value 1925.00 would correspond to about 81.9 percent. Only 1950.50 is exactly 83 percent of 2350.

Common Pitfalls:
Errors can arise from misplacing the decimal point during multiplication or from incorrectly converting 83 percent to a decimal such as 8.3 or 0.083. Another issue is rounding too early in intermediate steps instead of keeping the exact arithmetic until the final answer. Using the fraction method with division by 100 is a safe way to keep track of decimal places here.

Final Answer:
The value of 83 percent of 2350 is 1950.50, so the correct option is 1950.50.