Calculate the Absolute Value: Finding |0.8|

Absolute Value with Positive Decimals

0.8= \left|0.8\right|=

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1

Understand the problem

0.8= \left|0.8\right|=

2

Step-by-step solution

To find the absolute value of 0.80.8, we will use the definition of absolute value, which states:

  • If a number xx is positive or zero, then its absolute value is the same number: x=x|x| = x.
  • If a number xx is negative, then its absolute value is the positive version of that number: x=x|x| = -x.

Let's apply this to our problem:

Since 0.80.8 is a positive number, its absolute value is simply itself:

0.8=0.8|0.8| = 0.8

Therefore, the absolute value of 0.80.8 is 0.80.8.

Looking at the given answer choices:

  • Choice 1: "There is no absolute value" is incorrect, as every real number has an absolute value.
  • Choice 2: 0.8-0.8 is incorrect, because absolute values are never negative.
  • Choice 3: 00 is incorrect, as the number is not zero.
  • Choice 4: 0.80.8 is correct, as it matches the calculated absolute value.

Thus, the correct choice is 0.80.8.

Therefore, the solution to the problem is 0.80.8.

3

Final Answer

0.8 0.8

Key Points to Remember

Essential concepts to master this topic
  • Rule: Absolute value of positive numbers equals the number itself
  • Technique: Since 0.8 > 0, then |0.8| = 0.8
  • Check: Distance from zero to 0.8 is 0.8 units ✓

Common Mistakes

Avoid these frequent errors
  • Thinking absolute value always changes the sign
    Don't automatically make 0.8 negative because you see absolute value bars = |-0.8|! Absolute value only removes negative signs, never adds them. Always remember: absolute value of positive numbers stays positive.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

\( \left|18\right|= \)

FAQ

Everything you need to know about this question

Why isn't the answer -0.8 if we're finding absolute value?

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Great question! Absolute value removes negative signs, it doesn't add them. Since 0.8 0.8 is already positive, 0.8=0.8 |0.8| = 0.8 . Only negative numbers change sign inside absolute value bars.

What does absolute value actually mean?

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Absolute value measures the distance from zero on a number line. Whether you go 0.8 units left or right from zero, the distance is always positive 0.8!

Can absolute value ever equal zero?

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Yes! 0=0 |0| = 0 because zero is exactly zero units away from itself. But absolute value is never negative - it's always zero or positive.

How do I remember when absolute value changes the number?

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Easy trick: If the number inside is positive or zero, absolute value doesn't change it. If it's negative, absolute value makes it positive by removing the minus sign.

What if I see |x| and don't know if x is positive or negative?

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  • If x0 x ≥ 0 , then x=x |x| = x
  • If x<0 x < 0 , then x=x |x| = -x

In our problem, we know 0.8 is positive, so we use the first rule!

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