Convert 299 fractions, 1/2, 1/3, 1/4, ……, 1/300 to decimals. How many finite fractions in those fractions?

9514 1404 393

  20

Step-by-step explanation:

An equivalent decimal fraction is non-repeating if and only if the fraction denominator has a prime factorization consisting only of powers of 2 and 5.

Powers of 2 less than 300 are ...

  2, 4, 8, 16, 32, 64, 128, 256

Powers of 5 less than 300 are ...

  5, 25, 125

A fraction will have a finite decimal representation if its denominator is one of these numbers, or some product of these numbers.

Products would include ...

  10, 50, 250, 20, 100, 40, 200, 80, 160

The count of all of the listed numbers is ...

  8 powers of 2 + 3 powers of 5 + 9 powers of 2 and 5 = 20 listed numbers

There are 20 finite decimal fractions among the fractions 1/2 ... 1/300.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950