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TWO TRUTHS AND A LIE

Circle which one of the three statements below is a lie?
Explain how you made your choice.
• -8.53247 is irrational
• 8 ½ is rational
• -1.4 is rational

1 answer

To determine which statement is the lie, let's evaluate each one:

  1. -8.53247 is irrational: A number is considered irrational if it cannot be expressed as a fraction of two integers. However, -8.53247 is a decimal that can be represented as a fraction (specifically, -853247/100000). Therefore, this statement is false, meaning -8.53247 is actually a rational number.

  2. 8 ½ is rational: The number 8 ½ (which can be expressed as 8.5 or as a fraction 17/2) can also be represented as a fraction of two integers. Thus, this statement is true.

  3. -1.4 is rational: The number -1.4 can also be expressed as a fraction (-14/10) or in simpler form (-7/5). Consequently, this statement is true.

Based on the analysis:

  • The lie is -8.53247 is irrational, because it is actually a rational number despite being presented as an irrational one.