Generating Fraction of a Decimal Number
In a video game, a mission progress bar shows $0.\overline{6}$ complete. What exact fraction of the map is that? Every terminating or repeating decimal comes from a fraction: it is called its generating fraction.
Types of decimals and their parts
Not all decimals are converted the same way, so first you need to recognize them.
In $14.5262626\ldots$ the whole-number part is $14$, the pre-period is $5$, and the period is $26$. The bar goes only over what repeats.
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…
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:
- a) $3.15$
- b) $0.666...$
- c) $12.4777...$
- d) $5.232323...$
- e) $8.02333...$
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) $14.5262626...$
Generating fraction of a terminating decimal
Match each decimal number with its corresponding fraction. Long calculations are not required, use the logic of terminating decimals: | Decimal | Fraction | | :--- |…
Match each decimal number with its corresponding fraction. Long calculations are not required, use the logic of terminating decimals:
| Decimal | Fraction |
|---|---|
| $0.2$ | $\frac{1}{4}$ |
| $0.5$ | $\frac{3}{4}$ |
| $0.75$ | $\frac{1}{2}$ |
| $0.25$ | $\frac{1}{5}$ |
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) $0.08$
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.
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…
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.
Generating fraction of a purely repeating 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) $0,\overline{5}$
Generating fraction of a mixed repeating decimal
When there are digits before the period (the pre-period), the rule expands a little.
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.
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) $2.1\widehat{6}$
Back to the beginning: $0.\overline{6}$ is purely repeating with a one-digit period, so its generating fraction is $\frac{6}{9} = \frac{2}{3}$: you have completed exactly two thirds of the mission.