Question

WRITE .7¯ IN SIMPLEST FORM (repeating decimal)

a) 7/10
b) 7/100
c) 7/7
d) 70/100

Answer 1

7/10, representing the repeating decimal 0.7¯ in its simplest form, where the digit 7 repeats indefinitely. This fraction accurately captures the essence of the given repeating decimal.

a) 7/10

Step-by-step explanation:

The decimal 0.7¯ is a repeating decimal, where the digit 7 repeats indefinitely. To express this decimal in simplest form, we can set it as a variable x and subtract it from 10x to eliminate the repeating decimal part:

`\[ 10x - x = 9x = 0.777... - 0.7... = 0.077... \]`

Now, we can simplify the resulting equation by dividing both sides by 9:

`\[ (9x)/(9) = (0.077...)/(9) \]`

Simplifying further:

`\[ x = (0.077...)/(9) \]`

To express the decimal as a fraction, we can multiply both the numerator and denominator by 100 to move the decimal point two places to the right:

`\[ x = (0.077... * 100)/(9 * 100) \]`

This simplifies to:

`\[ x = (7.7...)/(900) \]`

Since the digit 7 repeats in the numerator, we can express it as:

`\[ x = (7)/(9) \]`

Therefore, the decimal 0.7¯ in simplest form is equivalent to the fraction 7/10 (Option a). This result confirms that answer 7/10, representing the repeating decimal 0.7¯ in its simplest form.