Murder By Numbers: Killing your Own Idea with Rounding Errors.

Updated: Sep 6, 2020

Our minds are brimming with numbers - passwords, measurements, forecasts, averages, weights, prices, dates, telephone numbers, bills and budgets.

And there are so many types of numbers - whole, fractional, natural, odd, rational, real, irrational, complex and imaginary. Head-spinning for a right-brainer!

Human behaviour has long been irrational around numbers. New research now finds that round numbers can be more influential than whether you use a decimal point or not.

Caution is required. You may be killing your own idea by communicating with the wrong type of number. Or missing opportunities to influence voters, patients, regulators, analysts, employees and customers.

A Digital Difference​

Some people love numbers, others fear them. But do they really influence our attitude to information?

Smart consumers know that whether data is presented visually, graphically or verbally dictates how they receive it. Smart presenters know that incorporating numbers conveys incremental authority, precision and accuracy [1].

Even 44% of media news reports contain data, numbers or percentages [2]. And forecasters using exact numbers rather than ‘some’, ‘many’ or ‘few’ are seen as more credible [3].

But the framing of numbers matters more than absolute value.

Attributes can be framed positively or negatively. Imagine that your surgeon advises you to have a heart operation. The average survival expectancy is either positioned as ’75% of patients live’ or ‘25% of patients die’.

It’s the same probability but gain or loss framing influences your decision.

While the framing matters, using any number simply won’t do.

It must be a certain type of number - according to a new study published in the Journal of Organisation Behaviour & Human Decision Processes. Is it a rounded whole number like 2 or a precise number like 2.84 - what mathematicians call ‘real’ numbers.

Counter-intuitively, this study found that people prefer whole numbers and negatively evaluate propositions when precise numbers are used [4]. In other words, precision created a less favourable perception of the message.

Let’s revisit the heart operation. Would hearing ‘76.45% of patients live’ make you more likely to interpret this less favourably than ‘75% of patients live’, even though the survival expectancy is higher?

Intuitively, the laser precision of 76.45% should enhance your attention and confidence. But human perception is predictably irrational! Normally, positive attribute framing generates more favourable evaluations but, in this research, positive framing with exact numbers generated a negative evaluation.

Testing With A Coronovirus Message:

Researchers tested communications messaging with 1,500 consumers about the potential effectiveness of a coronavirus vaccine - comparing ‘the vaccine is 91.27% effective’ with ‘the vaccine is 90% effective’.

They found that the higher ‘91.27% effective’ message decreased evaluations more than the lower ‘90% effective’ message. Clearly, a 91.27% vaccine success probability carries a more positive mortality outcome than 90%.

This matters.

High-stake risks and unintended backfire effects occur if surgeons, economists, traders, marketers or businesses fail to communicate effectively. People may misinterpret important purchases, investments or decisions.

Let’s consider an employee’s annual pay rise. Finance and HR typically calculate figures based on a central budget. Your manager then communicates your 3.12% or 4.86% rise. Rarely is this a round number. Your manager expects appreciation for this inflation-busting gesture but instead, you are disappointed and irritated. Why can’t companies just give 3% or 5%? They kill the gesture.

Similarly, sales teams pitch for budget hikes, convinced that a 16.23% request conveys more calculated logic than appeal. But over-reliance on logic just kills their request. When did you last invest in something based on data over sentiment? Female investors are also consistently put off by complicated messages with precise numerical content. Firms unintentionally kill opportunity.

Why? Several psychological factors help explain this negative perception:

Narrow Framing: People tend to narrow frame in decisions rather than incorporate all relevant information.[5] This risk climbs in uncertainty as eyes are narrowly focus on a pandemic.

Familiarity: Science shows the more familiar we are with something, the more we like it. As 91.27% deviates from the more standard benchmark of 90%, attributes are perceived less favourably. [6]

Emotion: Businesses overweight logical argument more than psychologically-based argument. Yet we are far less moved by fact than emotion, unless loss-inducing. Emotion decides and reason justifies.

✅ Cognitive Effort: Precise numbers are salient but hard to comprehend. This is effortful and people are cognitively lazy. In a 24/7 world, many are overloaded, distracted and don’t have time to compute. They may be responding to the effort required more than the message itself.

Suggestions for Numbers 101:

Context matters. Certain situations demand precision of course. Precision drives consumer spending decisions, market trading, Libor submissions, currency calculations and Olympic games scoring.

Sometimes, round numbers can also lower trust in negotiation offers which appear as random guesstimates. Three factors should be considered when choosing between numerical communications.

1. Storytelling: Statistics are most compelling when combined with a story. This was evidenced in a large experiment which compared the effect of using statistics only, story only or statistics with a story [8].

2. Framing: Framing with precise numbers can be powerful if used carefully in complex communications requiring behaviour change. Note how negative framing is more effortful than positive framing.

3. Simplicity: Like numbers, simple words matter. Psychologist Robert Cialdini [7] cites an American Museum of Natural History survey testing interest in the ‘fields of botany, anthropology and zoology’. The results were 39%, 44% and 59% respectively. But, when the words were changed to ‘plants and trees,’ ‘people of the world’ and ‘animals,’ interest rose to 77%, 81% and 87%.

So what’s in a number?

Apparently far more than its intrinsic value. And potentially a lot more when you give it meaning within a context-based, simple, well-framed story.

Of that, you should be 100% confident! Don't kill your own idea.

Changing behaviour requires scientific principles and frameworks. To discuss this further or any organisational communications, culture and reputation challenges which might benefit from behaviourally-informed solutions, feel free to reach out at


[1] Koetsenruijter, A. W. M. (2011). Using numbers in news increases story credibility. Newspaper research journal, 32(2), 74-82.

[2] Zillman, D., & Brosius, H. (2000). Exemplification in communication: The influence of case reports on the perception of issues. Mahwah, NJ: Erlbaum


[4] Gaurav Jain, Gary J. Gaeth, Dhananjay Nayakankuppam, Irwin P. Levin. Revisiting attribute framing: The impact of number roundedness on framing. Organizational Behavior and Human Decision Processes, 2020; 161: 109 DOI:

[5] Kahneman, D., & Lovallo, D. (1993). Timid choices and bold forecasts: A cognitive perspective on risk-taking. Management science, 39(1), 17-31.


[7] Cialdini, R. (2016). Pre-suasion: A revolutionary way to influence and persuade. Simon and Schuster.

[8] Allen, M., Bruflat, R., Fucilla, R., Kramer, M., McKellips, S., Ryan, D. J., & Spiegelhoff, M. (2000). Testing the persuasiveness of evidence: Combining narrative and statistical forms. Communication Research Reports, 17(4), 331-336.

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