Question

Congratulations! Because of your new skills with rewriting fractions and decimals, you have been put in charge of the Designer Decimals Department of the Fraction Factory. People write to your department and order their favorite fractions rewritten as beautiful decimals.

Recently, your department has received some strange orders. Review each order below and decide if you can complete it. If possible, find the new fraction or decimal. If it is not possible to complete the order, write to the customer and explain why the order cannot be completed.


Order 1: “I’d like a terminating decimal to represent 44/99.”

Order 2: “Could you send me 0.208 as two different fractions, one with 3000 in the denominator and one with 125 in the denominator.”

Order 3: “Please send me 0.43 written as a fraction.”

Answer 1

1. cannot be completed. 9 is not a multiple of 2 and/or 5
2. 0.208 = 624/3000 = 26/125
3. 43/100

Explanation:

In order for a fraction to be a terminating decimal fraction, the denominator can only consist of powers of 2 and 5 (factors of 10).

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Order 1:

The denominator factors as 99 = 3²·11. The denominator contains factors other than 2 and 5, so 44/99 cannot be written as a terminating decimal.

The decimal equivalent is ...

`(44)/(99)=(4)/(9)=0.\overline{4}`

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Order 2:

The numerator of each fraction can be found by multiplying the fraction by the desired denominator.

3000(0.208) = 624 ⇒ 0.208 = 624/3000

125(0.208) = 26 ⇒ 0.208 = 26/125

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Order 3:

0.43 = forty-three hundredths = 43/100