A child writes five hundred three as 5003. It shows that

The correct answer is: "the child does not know the concept of place value"

Step-by-Step Explanation:

1. Analyze the Child's Writing:
The child is asked to write the number "five hundred three".
Instead of writing it correctly as 503, the child writes it as 5003.

2. Deconstruct the Error:
The child knows how to write "five hundred" as 500.
The child also knows how to write "three" as 3.
When writing them together, the child juxtaposes or concatenates the two numbers: 500 and 3, resulting in 5003. This is a common phonetic or additive approach to writing numbers (writing exactly what is heard: "five hundred" → 500, then "three" → 3).

3. Connect to Mathematical Concepts:
In our decimal positional numeral system, the position of a digit determines its value (place value).
For the number five hundred three:
- The "five" represents 5 hundreds ($5\times 100=500$).
- There are no tens, so we place a 0 in the tens place.
- The "three" represents 3 ones ($3\times 1=3$).
Putting them together according to place value gives: 5 hundreds, 0 tens, and 3 ones, which is written as 503.

4. Evaluate the Options:
- "the child does not know how to write numbers in words": Incorrect, as the task was to write the number in figures from words, and the child understood the verbal cues for "five hundred" and "three".
- "the child needs to learn recognition of digits": Incorrect, the child correctly recognized and wrote the digits 5, 0, and 3.
- "the child needs to learn counting": Incorrect, this error is not about counting items but about notation.
- "the child does not know the concept of place value": Correct. The child does not understand that the digits must be placed in specific columns (hundreds, tens, ones) and that the number 5003 actually represents five thousand three, not five hundred three.