Which mathematical symbol can be placed between 5 and 9 to form a single number that is greater than 5 but smaller than 9?

Introduction / Context:
This classic puzzle checks your understanding of numbers, symbols and place value rather than simple arithmetic. You are asked to place a mathematical symbol between 5 and 9 such that the result is a number greater than 5 but less than 9. At first glance, it might appear that any operation combining 5 and 9 will either make the value much bigger than 9 or smaller than 5, but the trick lies in thinking beyond basic operations like addition and subtraction.

Given Data / Assumptions:

• We start with the digits 5 and 9 written side by side.
• We are allowed to insert a mathematical symbol between them.
• The final result must be a single number whose value is greater than 5 and smaller than 9.
• The options suggest several possible symbols, such as a decimal point, plus sign, division sign and comparison sign.

Concept / Approach:
The key idea is to remember that mathematical symbols are not limited to arithmetic operations like plus or minus. A decimal point is also a mathematical symbol, and when placed between two digits, it forms a decimal number. By placing a decimal point between 5 and 9, we get 5.9, which clearly lies between 5 and 9 on the number line. In contrast, placing arithmetic or comparison operators between the digits usually produces an expression, not a single number in the required interval.

Step-by-Step Solution:
Step 1: Consider placing a plus sign: 5+9 gives 14, which is greater than 9 and therefore does not satisfy the condition. Step 2: Consider placing a division sign: 5÷9 gives a decimal less than 1, which is smaller than 5 and so this option fails. Step 3: Consider placing a greater-than sign: 5>9 is not a single number at all, it is just a false statement, and therefore does not match the puzzle requirement. Step 4: Now consider placing a decimal point between the digits to form 5.9. This is a single decimal number lying strictly between 5 and 9. Step 5: Check the condition: 5.9 is greater than 5 and smaller than 9, so this choice satisfies the puzzle exactly.

Verification / Alternative check:
To verify, imagine a number line from 0 to 10. The number 5 is to the left and 9 is to the right. The decimal 5.9 is between 5 and 6, so it clearly lies between 5 and 9. None of the other options produce a single number in this interval. In exam situations, checking quickly on a mental number line is a reliable way to confirm that your answer fits the inequality conditions.

Why Other Options Are Wrong:
The plus sign produces 14, which is far greater than 9. The division sign produces a result less than 1, so it does not lie between 5 and 9. The greater-than symbol produces a comparison statement, not a numeric value, and is also logically incorrect as 5 is not greater than 9. Therefore, only the decimal point meets the specific requirement of forming one valid number in the correct range.

Common Pitfalls:
Many learners initially focus only on arithmetic operators and try combinations such as 9−5, 9÷5 or 5+9, forgetting that the puzzle explicitly talks about placing a symbol between 5 and 9, not necessarily performing an operation in the usual way. Another pitfall is to interpret the question as requiring an equation instead of a single number. The best way to avoid these mistakes is to think flexibly about what counts as a mathematical symbol and to test the resulting value against the inequality condition.

Final Answer:
The correct symbol is a decimal point, forming the number 5.9, which is greater than 5 and smaller than 9.