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Answer :
To determine which division represents a non-terminating decimal, we will consider each division and look for those that produce decimals that go on infinitely without repeating a clear pattern.
Here's a step-by-step explanation:
1. Understanding Non-Terminating Decimals:
- A non-terminating decimal is one that goes on forever without forming a repeating pattern or sequence.
2. Analyze Each Division:
- [tex]$100 \div 50$[/tex]:
- This is the same as 2.
- This results in a terminating decimal, as it is an exact whole number.
- [tex]$100 \div 27$[/tex]:
- This division results in approximately 3.7037037037...
- Notice the repeating sequence "703" in the decimal part, making it non-terminating as it continues indefinitely with a pattern.
- [tex]$100 \div 8$[/tex]:
- This is equivalent to 12.5.
- This results in a terminating decimal since it stops after one decimal place.
- [tex]$100 \div 25$[/tex]:
- This equals 4.
- This results in a terminating decimal because it is an exact whole number.
3. Conclusion:
- Out of all the divisions, [tex]$100 \div 27$[/tex] results in a non-terminating decimal. The decimal part has a repeating sequence which continues indefinitely, fulfilling the criteria of a non-terminating decimal.
Therefore, the division [tex]$100 \div 27$[/tex] represents a non-terminating division.
Here's a step-by-step explanation:
1. Understanding Non-Terminating Decimals:
- A non-terminating decimal is one that goes on forever without forming a repeating pattern or sequence.
2. Analyze Each Division:
- [tex]$100 \div 50$[/tex]:
- This is the same as 2.
- This results in a terminating decimal, as it is an exact whole number.
- [tex]$100 \div 27$[/tex]:
- This division results in approximately 3.7037037037...
- Notice the repeating sequence "703" in the decimal part, making it non-terminating as it continues indefinitely with a pattern.
- [tex]$100 \div 8$[/tex]:
- This is equivalent to 12.5.
- This results in a terminating decimal since it stops after one decimal place.
- [tex]$100 \div 25$[/tex]:
- This equals 4.
- This results in a terminating decimal because it is an exact whole number.
3. Conclusion:
- Out of all the divisions, [tex]$100 \div 27$[/tex] results in a non-terminating decimal. The decimal part has a repeating sequence which continues indefinitely, fulfilling the criteria of a non-terminating decimal.
Therefore, the division [tex]$100 \div 27$[/tex] represents a non-terminating division.
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