During the day plants feed themselves by using energy from the sun to convert carbon dioxide into sugars and starch, then through the night must depend on their store of starch to prevent starvation.
Plants make precise adjustments to their rate of starch consumption to ensure the starch store lasts until dawn even if the size of the starch store varies from night to night, the researchers found.
To adjust that consumption so precisely they must be performing a mathematical calculation -- arithmetic division, the researchers said.
"This is the first concrete example in a fundamental biological process of such a sophisticated arithmetic calculation," said mathematical modeler Martin Howard from the John Innes Center of the Norwich BioSciences Institutes said.
Information about time comes from a plant's internal clock, similar to our own body clock, and the size of the starch store is divided by the length of time until dawn to set the correct rate of starch consumption, so that, by dawn, around 95 percent of starch is used up, the researchers said.
"The calculations are precise so that plants prevent starvation but also make the most efficient use of their food," metabolic biologist Alison Smith said.
"If the starch store is used too fast, plants will starve and stop growing during the night. If the store is used too slowly, some of it will be wasted."
"The capacity to perform arithmetic calculation is vital for plant growth and productivity," she said.