The generating fraction of a decimal number
A video game says you have completed $0{,}\overline{6}$ of a mission. What exact fraction is that? Every terminating or recurring decimal, however strange it looks, comes from a fraction: it is its generating fraction.
Generating fraction of a terminating decimal
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…
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.
Calculate the generating fraction of the following terminating decimal numbers. Remember to simplify the result wherever possible: a) $0,5$ b) $1,2$ c) $0,25$ d) $0,08$
Calculate the generating fraction of the following terminating decimal numbers. Remember to simplify the result wherever possible:
- a) $0,5$
- b) $1,2$
- c) $0,25$
- d) $0,08$
Generating fraction of a purely recurring decimal
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…
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.
Find the generating fraction of the following pure recurring decimal numbers with a single digit in the recurring part. Simplify if you can: a) $0,\overline{3}$ b)…
Find the generating fraction of the following pure recurring decimal numbers with a single digit in the recurring part. Simplify if you can:
- a) $0,\overline{3}$
- b) $0,\overline{7}$
- c) $1,\overline{1}$
- d) $0,\overline{5}$
Going further: generating fraction of a mixed recurring decimal
When there are digits before the recurring block (the non-recurring part), the rule extends a little.
Classify the following decimal numbers into terminating, pure recurring or mixed recurring. Once classified, calculate the generating fraction of each of them and…
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:
- a) $3,15$
- b) $0,\widehat{12}$
- 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…
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.
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…
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):
- a) $5,888...$
- b) $0,1232323...$
- c) $14,5262626...$
Back to the start: Since $0{,}\overline{6}$ is a purely recurring decimal with a single recurring digit, its generating fraction is $\frac{6}{9}$, which simplifies by dividing by $3$ to $\frac{2}{3}$; you have completed exactly two thirds of the mission.