Answer:
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.
Step-by-step 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
[tex]4.05(\frac{100}{100})=\frac{405}{100}[/tex]
Simplify
Divide by 5 both numerator and denominator
[tex]\frac{405}{100}=\frac{81}{20}[/tex]
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
[tex]100x=405.0505...\\100x-x=405.0505...-4.0505...\\99x=401\\x=401/99[/tex]
Multiply by 2 both numerator and denominator
[tex]401/99=802/198[/tex]
therefore
The fractions 401/99 and 802/198 are equal to the decimal number indicated.
