To convert the decimal 5.4 to a mixed number and an improper fraction, we start by expressing it in both forms.
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As a mixed number:
- The whole number part is 5.
- The decimal part, 0.4, can be converted to a fraction.
- Since 0.4 is equivalent to \( \frac{4}{10} \), we can simplify this fraction: \[ \frac{4}{10} = \frac{2}{5} \]
- Therefore, we can write 5.4 as a mixed number: \[ 5.4 = 5 \frac{2}{5} \]
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As an improper fraction:
- To convert the mixed number \( 5 \frac{2}{5} \) to an improper fraction, we use the formula: \[ \text{Improper fraction} = \text{Whole number} \times \text{Denominator} + \text{Numerator} \]
- Here, the whole number is 5, the numerator is 2, and the denominator is 5: \[ 5 \times 5 + 2 = 25 + 2 = 27 \]
- So, we can express this as: \[ 5.4 = \frac{27}{5} \]
In summary:
- As a mixed number: \( 5 \frac{2}{5} \)
- As an improper fraction: \( \frac{27}{5} \)
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