Question

Write bar (bar (7)) as a fraction in simplest form:

Answer 1

To write bar (bar (7)) as a fraction in simplest form, you should interpret it as the repeating decimal 0.7777... The fraction equivalent is then found to be 7/9.

Step-by-step explanation:

The term 'bar' in mathematics refers to the repetition of a number.Write bar (bar (7)) as a fraction in simplest form:

To interpret bar(bar(7)), we consider '7' repeating indefinitely. This forms a recurring decimal, 0.7777..., which can be converted into a fraction.

Here are the steps to convert a repeating decimal into a fraction:

1. Let x = 0.7777...
2. Multiply both sides by 10 to shift the decimal point one place to the right: 10x = 7.7777...
3. Subtract the original equation from this to eliminate the decimal on the right: 10x - x = 7.7777... - 0.7777...
4. This simplifies to 9x = 7
5. Lastly, divide both sides by 9 to solve for x: x = 7/9. So, bar(bar(7)) as a fraction in simplest form is 7/9.

Learn more about Repeating Decimal to Fraction