1.66667 as a fraction

1.66667 as a fraction

The Correct Answer and Explanation is :

To convert the decimal (1.66667) into a fraction, we can follow a systematic process.

Step 1: Express as a Fraction

First, we note that (1.66667) can be rewritten as:

[
1.66667 = 1 + 0.66667
]

Next, we focus on converting (0.66667) into a fraction.

Step 2: Understanding the Decimal

The decimal (0.66667) is approximately equal to (\frac{2}{3}). This is because (0.66667) is close to (0.666…), which is the repeating decimal representation of (\frac{2}{3}).

Step 3: Combining the Whole Number and Fraction

Now we can express the whole number and the fractional part together:

[
1.66667 \approx 1 + \frac{2}{3}
]

To combine these, we need to express (1) as a fraction with a common denominator of (3):

[
1 = \frac{3}{3}
]

Now, adding the two fractions:

[
1.66667 \approx \frac{3}{3} + \frac{2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
]

Step 4: Finalizing the Fraction

Thus, (1.66667) can be approximated as the fraction (\frac{5}{3}).

Conclusion

To summarize, (1.66667) is approximately (\frac{5}{3}) when converted to a fraction. The process involved separating the whole number from the decimal, approximating the decimal as a fraction, and then combining them into a single fraction. This approach not only helps in converting decimals into fractions but also reinforces an understanding of rational numbers.

Additional Note

If precision is necessary, keep in mind that (1.66667) can be represented as (\frac{5}{3}) for most practical applications, but the exact decimal (0.66667) would require more careful handling if an exact representation is needed.