Verified Answer :

  • Convert the fraction \(\frac{2}{5}\) to decimal: \(\frac{2}{5} = \frac{4}{10} = 0.4\).
  • Note that adding trailing zeros does not change the value, so \(0.4 = 0.40\).
  • Compare the list: \(0.4\) and \(0.40\) match the value.
  • Final answer: \(\boxed{0.4, 0.40}\).

Explanation

  1. Convert Fraction to Decimal

To determine which of the given decimal numbers is equal to the fraction \(\frac{2}{5}\), we first perform the division of 2 by 5. We can express the fraction with a denominator of 10 to simplify the conversion:
\[\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}\]
The decimal representation of \(\frac{4}{10}\) is 0.4. Therefore, any decimal number equivalent to 0.4 is equal to \(\frac{2}{5}\).

  1. Evaluate Options and Conclude

We must now determine which of the given options are equal to 0.4. A fundamental property of decimal numbers is that adding or removing trailing zeros after the decimal point does not change the numerical value of the number. Thus, \(0.4 = 0.40 = 0.400 = \dots\).
Comparing our options:

  • \(0.4\): This is equal to 0.4.
  • \(0.40\): Since adding a trailing zero does not change the value, \(0.40 = 0.4\).
  • \(4.0\): This is equal to 4, which is not 0.4.
  • \(0.25\): This is equal to one-fourth, not two-fifths.
  • \(2.5\): This is equal to two and a half, not 0.4.
  • \(0.250\): This is equal to 0.25, which is not 0.4.

Examples

In real-life scenarios, such as measuring ingredients in a recipe, you might find that a measurement given in fractions, like \(\frac{2}{5}\) of a cup, needs to be converted to a decimal to match the markings on a measuring cup. For example, knowing that \(\frac{2}{5} = 0.4\) helps you measure precisely if your cup only shows decimals like 0.1, 0.2, 0.4, etc. Recognizing that 0.4 is the same as 0.40 ensures you use the correct amount regardless of how the measurement is written on your tool.

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