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What is0.7(with a line over the 7) as a simplified fraction

User Pathikrit
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Final answer:

The recurring decimal 0.7 with a line over the 7 can be represented as the simplified fraction ⅔. This is done by setting the decimal equal to x, multiplying by 10 to create 10x, and then subtracting x to solve for x and find the fraction.

Step-by-step explanation:

When you see a number like 0.7 with a line over the 7, it indicates that the 7 is repeating indefinitely, making it a recurring decimal. To convert this recurring decimal to a simplified fraction, you can use a simple algebraic method. Let's denote the recurring decimal as x:

x = 0.777...

Multiplying both sides of the equation by 10 shifts the decimal point one position to the right:

10x = 7.777...

Now, subtract the original x from 10x to eliminate the repeating digits:

10x - x = 7.777... - 0.777...

9x = 7

Dividing both sides by 9 gives us the fraction:

x = ⅔

Therefore, 0.7 with a line over the 7 is equal to ⅔ as a simplified fraction.

User BlueTune
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