Question

What fractions are equivalent to 4.05 with a bar notation over the 0 and 5

Answer 1

Part 1) The fractions in the list are not equal to the decimal number indicated

Part 2) The fractions 401/99 and 802/198 are equal to the decimal number indicated.

Part 1)

we have the decimal number

4.05 -----> is a terminating decimal ( t's a decimal with a finite number of digits)

Convert to fraction number

Multiply and divide by 100

Simplify

Divide by 5 both numerator and denominator

therefore

The fractions in the list are not equal to the decimal number indicated.

Part 2) we have

4.050505... ------> is a repeating decimal (is a decimal that has a digit, or a block of digits, that repeat without ever ending)

Let

x=4.050505...

we have that

Multiply by 2 both numerator and denominator

therefore

The fractions 401/99 and 802/198 are equal to the decimal number indicated.

Explanation: