The researchers set out to test a prediction that had circulated in behavioral economics for years but had rarely been put to a direct, quantitative test. The idea is simple enough. When you are confident about a quantity, there is little reason to blur it. But when your internal estimate is noisy and unreliable, rounding to a prominent number such as 50 or 100 feels like an acceptable way to communicate a vague answer. Uncertainty, in other words, should predict rounding. Earlier experimental work, including studies by Ruud, Schunk, and Winter, had shown that people round more when they are made to feel uncertain, but the field lacked evidence that naturally occurring differences in uncertainty, measured within the same individuals across many estimates, actually forecast which responses get rounded.

To close that gap, the team turned to secondary analyses of two independent datasets, one involving numerosity estimation and the other involving temporal estimation. This dual approach matters because of a influential idea in cognitive science known as the theory of magnitude, proposed by Vincent Walsh in 2003, which holds that the brain represents time, space, number, and other quantities with a common metric code. If the round-number bias emerges from a general property of magnitude representation, it should appear in both domains, and its strength should track uncertainty in both domains as well. Testing two different quantity types with the same analytical logic gave the researchers a way to check whether the effect is domain-specific or genuinely general.

The datasets themselves came from earlier work by the same research group on what psychologists call metric error monitoring, the ability to judge not just how long something lasted or how many items were present, but how good your own estimate was. In these tasks, participants first produced an estimate and then rated their confidence in it, allowing the researchers to link each individual judgment to a metacognitive signal. That design is what makes the new analysis powerful: instead of comparing confident and anxious people, the team could ask whether the same person rounds more on the trials where they feel less sure of their answer.

The results supported the uncertainty hypothesis. Estimates that received a confidence rating indicating lower certainty were significantly more likely to be rounded to a multiple of five. The relationship held in both numerosity and temporal estimation, suggesting that the bias is not a quirk of counting objects or judging durations but a general strategy for coping with noisy internal signals. The finding dovetails with an older theoretical account from Yaniv and Foster, who argued in 1995 that judgment under uncertainty involves a trade-off between accuracy and informativeness. A coarse, round answer may be less precise, but it is easier to process, easier to remember, and easier to communicate. When the underlying evidence is weak, the mind apparently decides that the loss of precision is worth the gain in simplicity.

The study also tested a second, subtler prediction that flows from one of the best-documented laws in psychology. Magnitude estimates obey what is known as the scalar property, the human version of Weber’s law: the variability of an estimate grows in proportion to the size of the quantity being estimated. Judging whether a tone lasted two seconds or three seconds is easy; judging whether it lasted twenty seconds or thirty seconds is much harder, because the internal noise scales with duration. If uncertainty drives rounding, then larger magnitudes should naturally attract more rounding, since they are inherently more uncertain to represent. That is exactly what the data showed. Round-number bias increased at larger magnitudes in both estimation domains, providing an elegant confirmation that the bias follows the statistics of the mind’s own measurement apparatus.

Together, these two findings sketch a coherent cognitive architecture for the round-number bias. The internal representation of any magnitude comes with an uncertainty signature, a kind of built-in error bar. When that error bar is wide, either because the person lacks confidence or because the quantity is large enough that scalar variability dominates, the response system gravitates toward prominent, accessible numbers. This connects the bias to a broader family of metacognitive phenomena. Research by Fleming and Lau on how to measure metacognition, and by Kononowicz, Roger, and van Wassenhove on the neural decoding of temporal confidence, suggests that the brain continuously monitors the reliability of its own signals. The new study implies that this monitoring does not just color our feelings of confidence; it actively shapes the numbers we produce.

The practical implications stretch well beyond the laboratory. Financial behavior is riddled with round numbers: stock prices cluster at whole-dollar values, limit orders pile up at prominent levels, and studies of equity crowdfunding and German real estate transactions have documented the same attraction to round figures. Survey researchers have long worried about heaping, the tendency of respondents to report their age, income, or financial expectations in round numbers, which distorts datasets and can mask real variation. The new findings suggest that heaping is not merely laziness or satisficing, the cognitive shortcut of giving a good-enough answer. It is a systematic output of uncertainty, which means that the amount of rounding in a dataset could itself serve as a diagnostic of how uncertain respondents are, a possibility that researchers studying inflation expectations and other economic beliefs may find valuable.

There are also implications for how we interpret the numbers other people give us. Work by Jerez-Fernandez, Angulo, and Oppenheimer showed that listeners use precision as a cue to a speaker’s confidence, treating a precise estimate as a sign of expertise. The new study adds the flip side of that coin: when someone hands you a round number, it may be a signal, whether intended or not, that their internal evidence was weak. In negotiations, market forecasts, or eyewitness estimates of time and distance, the shape of the number carries information about the mind that produced it. Conversely, the finding that larger magnitudes attract more rounding offers a useful corrective, since a round estimate of a large quantity may reflect nothing more than the ordinary scaling of noise rather than any special ignorance on the part of the estimator.

The authors are careful to frame their work as a step toward understanding rather than a final verdict. Because the analysis relied on secondary datasets, future studies can manipulate uncertainty directly and track rounding trial by trial, and researchers can explore whether the same uncertainty-to-rounding link appears in other magnitude domains such as line length, weight, or distance. Still, the core message is striking in its simplicity. The round numbers that saturate human communication, from price tags to promises of five more minutes, are not arbitrary cultural conventions. They are the visible fingerprints of an internal measurement system that knows, with remarkable sophistication, exactly how unsure it is, and chooses its numbers accordingly.

Subject of Research: The role of estimation uncertainty in producing the round-number bias in numerosity and temporal magnitude judgments

Article Title: Uncertainty levels in magnitude estimations predict round number bias

Article References: Öztel, T., Ünübol, H., & Balcı, F. (2026). Uncertainty levels in magnitude estimations predict round number bias. Current Psychology, 45(17), Article 1486. https://doi.org/10.1007/s12144-026-10027-6

Image Credits: AI Generated

DOI: 10.1007/s12144-026-10027-6

Keywords: round number bias, uncertainty, magnitude estimation, temporal estimation, numerosity estimation, metacognition, confidence, scalar property, Weber's law, behavioral economics, numerical cognition, Current Psychology