3 + 2/9 as a improper fraction and as a decimal
The correct answer and explanation is:
Correct Answers:
- Improper fraction: 299\frac{29}{9}
- Decimal: 3.2222‾3.222\overline{2} or approximately 3.222
300-Word Explanation:
To convert the mixed number 3 + 2/9 into an improper fraction and a decimal, we follow a few clear steps.
Step 1: Convert to an Improper Fraction
A mixed number is a number that has a whole part and a fractional part. In this case:
- Whole number = 3
- Fractional part = 29\frac{2}{9}
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and then add the numerator: Improper fraction=(3×9)+29=27+29=299\text{Improper fraction} = \frac{(3 \times 9) + 2}{9} = \frac{27 + 2}{9} = \frac{29}{9}
So, the improper fraction form of 3+293 + \frac{2}{9} is 299\frac{29}{9}.
Step 2: Convert to a Decimal
To convert a fraction like 299\frac{29}{9} to a decimal, divide the numerator by the denominator: 299=3.222…\frac{29}{9} = 3.222\ldots
The decimal repeats, because 9 is a factor that often produces repeating decimals. Specifically:
- 9 goes into 29 3 times (3 × 9 = 27)
- Remainder is 2
- Bring down 0 → 20 ÷ 9 = 2 remainder 2 (again)
- This cycle repeats
So the decimal is: 3.2‾3.\overline{2}
Which means 3.222… with the digit 2 repeating forever. You can write this as 3.222… or more precisely, 3.2̅.
Conclusion:
- Improper Fraction: 299\frac{29}{9}
- Decimal: 3.22‾3.2\overline{2}
These conversions are useful in algebra, measurements, and real-world applications where consistent forms of numbers are needed for calculations.