Convert 4/9 into its decimal form and round to the nearest thousandth
The Correct Answer and Explanation is :
The correct answer is: 0.444
To convert the fraction ( \frac{4}{9} ) into its decimal form, we perform the division of 4 by 9. This process involves dividing the numerator (4) by the denominator (9).
Step-by-Step Conversion:
- Long Division:
- Start by dividing 4.000000 (adding zeros after the decimal point) by 9.
- 9 goes into 4 zero times, so we write 0 and then a decimal point.
- We bring down the first 0, making it 40.
- 9 goes into 40 four times (9 × 4 = 36), which gives us a remainder of 4.
- Bring down another 0 to make it 40 again.
- Repeat the process. You will find that 9 goes into 40 four times, leaving a remainder of 4 each time.
Continuing this way, we see that ( \frac{4}{9} ) results in a repeating decimal:
[
0.444444\ldots
]
This can be represented as ( 0.\overline{4} ), indicating that the digit 4 repeats indefinitely.
- Rounding to the Nearest Thousandth:
- The decimal ( 0.444444… ) needs to be rounded to the nearest thousandth. The third decimal place is 4, and the fourth decimal place is also 4.
- According to rounding rules, if the digit following the last place you are rounding to is 5 or greater, you round up. If it is less than 5, you leave the last digit as it is.
- Since the digit in the fourth decimal place is 4, we leave the third decimal place unchanged.
Thus, rounding ( 0.444444… ) to the nearest thousandth gives us:
[
0.444
]
Final Answer:
Therefore, the decimal form of ( \frac{4}{9} ) rounded to the nearest thousandth is 0.444.
In conclusion, understanding how to convert fractions into decimal form and rounding them correctly is an essential mathematical skill. It allows for easier calculations and interpretations in various real-world applications, such as financial calculations, measurements, and data analysis.