A game on your phone says you have completed $0.75$ of a level. What exact fraction is that? Every terminating decimal can be written as a fraction. This fraction is called its generating fraction.
Generating fraction of a terminating decimal
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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:
On offer in a music shop, a digital album costs $9.90$ €. Express the price of the album as a fraction of natural numbers and simplify it until it cannot be reduced any…
On offer in a music shop, a digital album costs $9.90$ €. Express the price of the album as a fraction of natural numbers and simplify it until it cannot be reduced any further.
Going further: generating fraction of a recurring decimal
Recurring decimals with a non-recurring part
When there are digits before the recurring block (the non-recurring part), the rule extends a little.
Back to the start: $0.75 = \frac{75}{100} = \frac{3}{4}$, so you have completed exactly three quarters of the level. (Extension: if the game had said $0.\dot{6}$, one repeating digit gives $\frac{6}{9} = \frac{2}{3}$, two thirds of the level.)