To round the fraction [tex]\( \frac{7}{9} \)[/tex] to 4 decimal places, follow these steps:
1. Determine the value of the fraction:
Divide the numerator by the denominator:
[tex]\[
\frac{7}{9} = 0.7777\ldots
\][/tex]
2. Identify the needed decimal places:
We need to round the quotient to 4 decimal places. This means we will keep 4 digits after the decimal point.
3. Look at the 5th decimal place:
To round correctly, examine the digit in the 5th decimal place. The 5th decimal place in [tex]\( 0.7777\ldots \)[/tex] is 7.
4. Apply rounding rules:
If the digit in the 5th decimal place is 5 or higher, round the 4th decimal place up by 1. If it is less than 5, the 4th decimal place remains the same. In this case, since the 5th decimal place is 7 (which is higher than 5), we round up the 4th decimal place.
5. Perform the rounding:
The 4th decimal place is 7, and we add 1 to it because the next digit (the 5th one) is 7:
[tex]\[
0.7777 \rightarrow 0.7778
\][/tex]
Hence, the fraction [tex]\( \frac{7}{9} \)[/tex] rounded to 4 decimal places is [tex]\( 0.7778 \)[/tex].
