How do you write $\frac{7}{9}$ as a decimal?
A. $0.8 \overline{3}$
B. $0 . \overline{72}$
C. $0 . \overline{7}$
D. $0 . \overline{1}$
Answer (1)
Recognize that 9 1 = 0. 1 .
Multiply 0. 1 by 7 to find 9 7 .
Calculate 7 × 0. 1 = 0. 7 .
The decimal representation of 9 7 is 0. 7 .
Explanation
Understanding the Problem We are asked to convert the fraction 9 7 into a decimal. We can perform long division or recognize a pattern with fractions that have a denominator of 9.
Using the Pattern We know that 9 1 = 0. 1 . Therefore, 9 7 can be found by multiplying 0. 1 by 7.
Calculating the Decimal Multiplying 0. 1 by 7, we get 7 × 0. 1 = 0. 7 . This is because 7 × 0.1111... = 0.7777...
Long Division Method Alternatively, we can perform long division of 7 by 9. When we divide 7 by 9, we get 0 with a remainder of 7. We add a decimal point and a 0 to 7, making it 70. 9 goes into 70 seven times (9 x 7 = 63) with a remainder of 7. We add another 0, making it 70 again. This pattern continues, so we get 0.7777... = 0. 7 .
Final Answer Comparing our result with the given options, we see that the correct answer is 0. 7 .
Examples
Understanding how to convert fractions to decimals is useful in everyday situations, such as when splitting a bill with friends. If you need to divide a bill of 7 b e tw ee n 9 p eo pl e , yo u w o u l d c a l c u l a t e \frac{7}{9}$, which is approximately $0.78 per person. This helps ensure everyone pays their fair share.
