Exercises: Generating fraction of a decimal number

To start working with generating fractions, it is essential to know what type of number we are dealing with. Classify the following decimal numbers into terminating decimal, pure recurring or mixed recurring:

1. a) $3.15$
2. b) $0.666...$
3. c) $12.4777...$
4. d) $5.232323...$
5. e) $8.02333...$

In the Natural Sciences laboratory, you have weighed a sample of sand and the scale reads $0.75$ grams. Write this number as a decimal fraction (with a power of 10 in the denominator) and then simplify it to obtain its irreducible generating fraction.

Identify the elements of the following repeating decimal numbers. For each one, state its integer part, its non-repeating part (if it has one) and its repeating part (period):

1. a) $5.888...$

1. b) $0.1232323...$

1. c) $14.5262626...$

Calculate the generating fraction of the following terminating decimal numbers. Remember to simplify the result wherever possible:

1. a) $0.5$
2. b) $1.2$
3. c) $0.25$
4. d) $0.08$

A video game indicates that you have completed $0,\overline{6}$ of a mission. To find out the exact part of the map you have covered, convert that pure recurring decimal number into its generating fraction.

Match each decimal number with its corresponding fraction. Long calculations are not required, use the logic of terminating decimals:

Find the generating fraction of the following pure recurring decimal numbers with a single digit in the recurring part. Simplify if you can:

1. a) $0,\overline{3}$
2. b) $0,\overline{7}$
3. c) $1,\overline{1}$
4. d) $0,\overline{5}$

On offer in a music shop, a digital album costs $9.90$ pesos. Express the price of the album as a fraction of natural numbers and simplify it until it cannot be reduced any further.

Classify the following decimal numbers into terminating, pure recurring or mixed recurring. Once classified, calculate the generating fraction of each of them and simplify the result to obtain the irreducible fraction:

1. a) $3.15$
2. b) $0,\widehat{12}$
3. c) $2.1\widehat{6}$

In a strategy video game, a loading bar indicates that $0.85$ of a special mission has been completed. What irreducible fraction of the mission has already been completed? Calculate the generating fraction of that decimal number and simplify it.