Generating fraction of a decimal number
A video game graphics engine calculates a probability and returns it as $0{,}02\overline{45}$. To program it, you need an exact fraction, not a decimal that never ends. Review the three generating fractions and, above all, learn how to use them within longer calculations.
Quick review of the three generating fractions
Calculate the generating fraction of these terminating decimals. Do not forget to simplify the fraction to its simplest form. a) $0,8$ b) $1,25$ c) $0,064$ d) $12,5$
Calculate the generating fraction of these terminating decimals. Do not forget to simplify the fraction to its simplest form.
- a) $0,8$
- b) $1,25$
- c) $0,064$
- d) $12,5$
A smartwatch shows that you have completed $0,65$ of your daily step goal, as shown by the ring in the figure. What fraction of the total number of steps does this…
A smartwatch shows that you have completed $0,65$ of your daily step goal, as shown by the ring in the figure. What fraction of the total number of steps does this amount represent? Express the result as an irreducible fraction.
Using the generating fraction to calculate without approximating
When an operation combines recurring decimals, working directly with the digits "...3333" builds up error. The solution: first convert to a fraction, and then work with fractions.
Calculate the exact value of the following expression. To do this, you must first convert each decimal number into its respective irreducible generating fraction: $$1,25…
Calculate the exact value of the following expression. To do this, you must first convert each decimal number into its respective irreducible generating fraction:
$$1,25 - 0,\hat{3} \cdot \left( \frac{1}{2} + 0,1\hat{6} \right)$$Calculate the exact value of the following mixed expression. To avoid approximation errors, convert each decimal number into its respective generating fraction before…
Calculate the exact value of the following mixed expression. To avoid approximation errors, convert each decimal number into its respective generating fraction before calculating and simplify the result to an irreducible fraction:
$$L = \frac{1,2\widehat{6} \cdot \sqrt{0,25}}{(-2)^{-2} + 0,8\widehat{3}}$$Comparing values using the generating fraction
When two numbers seem very close (a decimal and a fraction, for example), the generating fraction lets you compare them using a common denominator, with no doubts about rounding.
A young programmer is designing a video game and needs to set the probability of a rare item appearing. The code requires the probability to be entered as an irreducible…
A young programmer is designing a video game and needs to set the probability of a rare item appearing. The code requires the probability to be entered as an irreducible fraction, but the graphics engine returns the value as a mixed recurring decimal: $P = 0,02\widehat{45}$.
Find the generating fraction that the programmer must enter and justify whether this probability is greater than or less than $\frac{1}{40}$.
In a popular strategy video game, a hero's attack speed is increased by a factor of $1,75$ and their defence is multiplied by $0,\hat{6}$. To make precise calculations…
In a popular strategy video game, a hero's attack speed is increased by a factor of $1,75$ and their defence is multiplied by $0,\hat{6}$. To make precise calculations in the game engine, the programmers need to work with fractions. Find the irreducible generating fractions of both numbers to help them.
Back to the beginning: To program the exact probability in the video game engine, you must enter the irreducible fraction $\frac{27}{1100}$, obtained from its generating fraction.