Question

Yes or no to tell wether the fact the fraction is equivalent to this decimal

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(4.05)

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Is the following fractions equal to the one decimal listed?
405/99
401/99
81/33
802/198

Answer 1

401/99 and 802/198

Explanation:

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Answer 2

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.

Explanation:

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

`4.05((100)/(100))=(405)/(100)`

Simplify

Divide by 5 both numerator and denominator

`(405)/(100)=(81)/(20)`

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

`100x=405.0505...\\100x-x=405.0505...-4.0505...\\99x=401\\x=401/99`

Multiply by 2 both numerator and denominator

`401/99=802/198`

therefore

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