Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Numerical Calculations

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...

Significant Figures in Calculations

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:

Accuracy, limits, and approximation

Accuracy, limits, and approximation

Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...

Vector Representation of Complex Numbers

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...

Routh-Hurwitz Criterion II

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

ManyNumbers 3: A Multi-Lab Study of Demographic Correlates of Early Number Knowledge.

Developmental science·2026

Same author

Ensemble size perception as a case study of the bounds of adaptation.

Psychonomic bulletin & review·2026

Same author

Can we "see" value? Spatiotopic "visual" adaptation to an imperceptible dimension.

Cognition·2025

Same author

Seven reasons to (still) doubt the existence of number adaptation: A rebuttal to Burr et al. and Durgin.

Cognition·2024

Same author

Size adaptation: Do you know it when you see it?

Attention, perception & psychophysics·2024

Same author

Born to Count: As Plato anticipated, babies do math.

Scientific American·2024

Same journal

Evidence for abstract spatial concept learning in young animals.

Cognition·2026

Same journal

Blurred lines or clear boundaries? Synchrony and social dominance shape domain-specific self-other processing.

Cognition·2026

Same journal

Knowability predicts curiosity and learning.

Cognition·2026

Same journal

Throwing good effort after bad: Evidence for a sunk-cost effect in cognitive effort-based decision-making.

Cognition·2026

Same journal

Cross-linguistic differences in incremental planning under uncertainty.

Cognition·2026

Same journal

Sensory attenuation scales with the strength of action-outcome coupling: A psychophysical study.

Cognition·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 24, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Published on: August 28, 2021

Rational number representation by the approximate number system.

Chuyan Qu¹, Sam Clarke², Francesca Luzzi¹

¹Department of Psychology, University of Pennsylvania, United States of America.

|June 13, 2024

Summary

This summary is machine-generated.

The approximate number system (ANS) can represent rational numbers, not just natural numbers. This study shows ANS uses part-whole representations, supporting the idea that the ANS processes fractions.

Keywords:

Approximate number system Connectedness illusion Numerosity perception Ratio Rational number

More Related Videos

The Optical Fractionator Technique to Estimate Cell Numbers in a Rat Model of Electroconvulsive Therapy

The Optical Fractionator Technique to Estimate Cell Numbers in a Rat Model of Electroconvulsive Therapy

Published on: July 9, 2017

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Related Experiment Videos

Last Updated: Jun 24, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

Published on: August 28, 2021

The Optical Fractionator Technique to Estimate Cell Numbers in a Rat Model of Electroconvulsive Therapy

The Optical Fractionator Technique to Estimate Cell Numbers in a Rat Model of Electroconvulsive Therapy

Published on: July 9, 2017

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Area of Science:

Cognitive Science
Numerical Cognition
Psychology

Background:

The approximate number system (ANS) allows estimation of quantities without counting.
Recent hypotheses suggest the ANS represents rational numbers, extending beyond natural numbers.
Prior research shows ratio discrimination consistent with ANS properties.

Purpose of the Study:

To investigate if ratio discrimination by the ANS is based on perceived numerosity.
To determine if ANS ratio discrimination relies on verbal working memory or counting.
To ascertain if the ANS represents ratios in a part-whole (fraction) or part-part format.

Main Methods:

Utilized a "connectedness illusion" to manipulate perceived numerosity.
Assessed ratio discrimination tasks in adults and children.
Employed tasks designed to isolate numerical processing from verbal memory and counting.

Main Results:

Ratio-dependent discriminations were confirmed to be based on perceived item counts, not confounds.
These discriminations were independent of verbal working memory and explicit counting.
Evidence suggests representations are in a part-whole (fraction) format, not part-part (ratio).

Conclusions:

The findings support the hypothesis that the approximate number system represents rational numbers.
The ANS appears to process quantities using a part-whole representation, akin to fractions.
This extends our understanding of the ANS beyond natural number representation.