I once worked at a company that priced everything with a .95 ending. The bestselling software package was $999.95. Add-on products were $9.95, or $19.95, or $49.95. Everything ended with a .95. It had been this way for more than twenty years.

One day, one of the VPs suggested we change all prices to end in .99. The rationale was that raising prices from .95-endings to .99-endings would net an extra four cents for every transaction.

But would that really happen? According to traditional economics, no. That’s because traditional economics predicts that raising a price results in fewer units—and fewer units, even at a higher price, means less revenue.

Flash forward a few years. Different company, same question. We’re sitting around a conference table discussing pricing strategy for an upcoming product. The VP leading the meeting smacks our competitor’s catalog onto the table. As we review our competitor’s products, we notice they price some of their products with .99-endings and others with .00-endings.

Why? Did they know something we didn’t? Do .99-ending prices make more money—but only some of the time?

To answer these questions, we need to take a deep dive into how the mind perceives numbers—and how that affects consumer behavior.

## 3 ways .99-ending prices affect your spending habits

### 1. .99-ending prices make you spend more money

In one of the first-ever studies on 9-ending prices, a national mail order company sent out their catalog to three group of people. Each group got a slightly different version of the catalog.

- The first group saw 9-ending prices for the four dresses, such as $39.
- The second group saw prices that were $5 more—$44 instead of $39.
- The third group saw prices that were $5
*less*—or $34 instead of $39.

These tests were run with four dresses at four prices: $39, $49, $59, $69.

The group that saw the 9-ending prices purchase more dresses and spent more money. The 9-ending prices earned 48% more revenue over prices that were $5 *more*, and 53% more revenue over prices that were $5 *less*.

Prices |
|||

Item |
9-ending prices |
$5 less |
$5 more |

Dress #1 | $ 39.00 | $ 34.00 | $ 44.00 |

Dress #2 | $ 49.00 | $ 44.00 | $ 54.00 |

Dress #3 | $ 59.00 | $ 54.00 | $ 64.00 |

Dress #4 | $ 79.00 | $ 74.00 | $ 84.00 |

Units purchased |
|||

Item |
9-ending prices |
$5 less |
$5 more |

Dress #1 | 21 | 16 | 17 |

Dress #2 | 14 | 8 | 10 |

Dress #3 | 7 | 7 | 6 |

Dress #4 | 24 | 12 | 15 |

TOTAL | 66 | 43 | 48 |

Revenue |
|||

Item |
9-ending prices |
$5 less |
$5 more |

Dress #1 | $ 819.00 | $748.00 | $ 544.00 |

Dress #2 | $686.00 | $352.00 | $ 540.00 |

Dress #3 | $413.00 | $ 378.00 | $ 384.00 |

Dress #4 | $1,896.00 | $1,008.00 | $ 1,110.00 |

TOTAL | $3,814.00 | $2,486.00 | $ 2,578.00 |

9-ending: +53% |
9-ending: +48% |

*9-ending prices led to a 48% more revenue, even when the price was higher.*

A second study tried the same thing, but with a much larger sample size. In this study, catalogs promoting 169 items were sent to two groups of 45,000 people. One group saw .00-endings and the other group saw .99-endings. **The group that saw the .99-ending prices spent 8% more**.

### 2. .99-ending prices make you more likely to spend money

In another study, conducted in France, researchers watched people buying cheese at a grocery store. They changed the prices of the cheese at 2-hour intervals and watched how people responded. First, they priced cheeses with .99-ending prices. Two hours later, they switched the prices to .00-ending prices.

They ran the experiment for two days. During this time, 241 people bought cheese. When they saw .00-ending prices, they bought cheese 44.1% of the time. But when they saw .99-ending prices, they bought cheese 51.2% of the time.

This study not only confirmed that .99-ending prices lead to more revenue, but they are also more likely to trigger a sale.

That’s not all. Experimenters also learned that the overall transaction amount went up when customers bought cheeses with .99-ending prices. For .00-ending prices, the mean purchase amount was €5.08, but with .99-ending prices, the mean purchase amount was €6.53.

This study revealed that .99-ending prices leads consumers to miscalculate their overall spend.

### 3. .99-ending prices make it harder to keep track of what you spend

In another study, researchers split people into two groups, and gave each group $73 and a list of products to buy.

The first group saw products with .00-ending prices, such as $3.00. This group bought an average of 23.9 items and spent $71.70 of the $73. They spent *less* than they intended.

But the story was different for the second group. When the researchers dropped prices by one cent—from $3.00 to $2.99, for example—this group bought an average of 25.21 items and spent $75.38.

*Dropping the price by one cent led to an increase in sales of 5.1%.*

The second group, which saw .99-ending prices couldn’t budget as well as the first group. As we’ve seen, .99-ending prices makes it more likely you will spend money *and* that you will spent more overall. It seems the reason for this is that .99-ending prices cause you to miscalculate how much you’re spending.

Why are we tricked by .99-ending prices?

To answer this, we need to understand how your mind perceives and compares numbers.

## When your brain quantifies subjective stimuli, 1 + 3 = 2

If you have one light bulb, and you want to double the number of light bulbs, all you need is one more: one plus one equals two.

Pretty obvious, right?

Now, let’s say you’ve hung a 15-watt light bulb, and you want the room to be twice as bright. How would you do this?

Well, the easy answer is that you simply add one more light bulb. One 15-watt light bulb plus another 15-watt light bulb gives you 30 watts–a room that’s twice as bright.

Right?

Wrong.

Actually, if you have a 15-watt light bulb, and you want to double the brightness of your room, you would need 60 watts. **You need to quadruple your wattage in order to double your perception of brightness.**

(If you’re hanging Christmas lights and want to be twice as bright as your neighbor, then you need to buy four times as many Christmas lights.)

This is known as Steven’s Power Law, and it predicts how our scales of magnitude differ when we perceive various stimuli. Stevens Power Law says that to double the perception of brightness, add 4 times more wattage.

This law is true other perceptions, too, but at different constants:

- To double the perception of sweetness, add 1.7 times more sugar
- To double the perception of heaviness, add 1.7 times more weight
- To double the perception of shock, add 1.2 times more electricity

And it even works for more than just physical stimuli:

- To double your happiness, you need 4 times more money.
- To get a watch twice as nice, you need to spend 8.7 times more.
- To double your social status, you need to earn 2.6 times more money.
- To double the seriousness of theft, you need to steal 60 times more. (If someone steals $100 from you, you’re only half as angry as if they had stolen $6,000 instead.)

And, of course, it happens for how you perceive numbers, too. As soon as your mind needs to compute and compare numbers, the scales of magnitude bend and warp, just like they do when you need to quantify changes in physical stimuli.

## How your mind perceives numbers

Your mind doesn’t process numbers on a neat, objective scale.

Just like doubling the wattage of your light bulbs doesn’t double the perception of brightness, doubling the number doesn’t necessarily mean doubling your perception of twice-as-much.

Sometimes it takes more. Sometimes less.

That’s because your brain processes numbers on an internal, subjective scale that bends and warps. Most people have in their minds a visual number scale; it’s likely you do, too.

More than a century ago, Francis Galton attempted to draw the ways people view numbers. Here is what he found:

Some numbers lie in rows or blocks. Others are in three dimensions. One person’s visualization even looks like a clock for the numbers one through twelve, and then as the numbers increase beyond twelve they arc to the left, before turning clockwise again for numbers 101 through 112.

When we talk about numbers, what we are really talking about is something more complicated. Numbers don’t exist in our mind in the same definite, objective way they exist in the world.

Numbers don’t always lie on neat, linear scales. Instead, they often lie on warped scales of magnitude. How we process and compare numbers is affected by how we perceive them.

For example, in the real, objective world, a number scale might look like this:

But in the subjective world of your brain, you perceive the same numbers like this:

On a scale like this, the space between 2.99 and 3.00 is greater than one cent. When you see a price of $2.99, it feels like less than $2.99 because something is warping the scale and affecting your perception of the number. It feels closer to $2.90 or even $2.00.

But why?

*What makes our mind perceive the number scale incorrectly? How do .99-endings trick our brains into thinking they’re smaller numbers than they really are—and trick us into spending more?*

It would be impossible to give a full account of what’s going on in the brain. But we do know that two key mechanisms are at play: one is the **anchor effect**, and the other is the **left-digit effect**.

Let’s take a look at each of these.

## The anchor effect

The first reason you perceive numbers incorrectly is related to the anchoring effect. To illustrate this, let’s borrow a famous example from Richard Thaler and Cass Sunstein.

If I ask you to guess the population of Milwaukee, how would you decide?

- If you’re from
**Chicago**, you might think to yourself,*well, I know 3 million people live in Chicago, and Milwaukee seems quite a bit smaller, but it’s still a big city, so let’s say 1 million people.* - But if you’re from
**Green Bay**you might think,*I know around 100,000 people live in Green Bay, and Milwaukee seems quite a bit bigger—and probably more than twice as big—so let’s say 300,000 people*.

In the first instance—you’re from Chicago—the number 3 million is your anchor, and you adjust downward. No matter what number you choose, the initial number of 3 million exerts a powerful effect on your prediction.

But in the second instance—you’re from Green Bay—the number 100,000 is your anchor, and you adjusted upward. Again, your initial anchor influences your choice.

It turns out neither guess is correct. The real population of Milwaukee is just under 600,000 people.

Let’s take a few real-life examples of how this works.

### Your brain wants a reference point

Anchors are powerful because you have a hard time assigning values to objects. Your brain searches for a reference point—*any *reference point. The problem is that anchors exert a powerful influence on how we perceive value—*and we don’t even know it. *Even when you know you can be tricked by anchors, they *still* affect your answers. It is impossible for us to ignore anchors.

You can try this right now on yourself. In three seconds, can you guess the answers to these two simple math problems?

- 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
- 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Have your answer?

Amos Tversky and Daniel Kahneman, in their famous paper, “Judgment under Uncertainty: Heuristics and Biases,” found that for the first sequence, the average guess is 512. For the second sequence, the average guess is 2,250.

In the first sequence, the number 1 serves as an anchor, and the average guess is low. But in the second sequence, the number 8 serves as an anchor. The average guess is much higher.

Not only are these two numbers wildly divergent from each other–because of their different anchors–but they’re also completely wrong. The correct answer to both math problems is 40,320.

### Anchors can be *anything*

In one study, Dan Ariely found that completely random numbers can function as anchors. He asked his students to write down the last two digits of their social security number before placing bids in an auction. In other words, if the auctioneer held up a bottle of wine, students would write down the two digits—say, 88—and then place their bid.

He found that students who had above-median social security numbers placed bids that were ** 57 to 107 percent higher **than students who had below-median social security numbers.

He also found that one-fifth of students with the highest social security numbers placed bids that were more than ** 3 times the average**. In one example, students in the top-fifth bid $56 on average for a cordless computer keyboard, compared with students in the bottom-fifth, who bid $16 on average.

Students were unaware that their willingness-to-pay was significantly affected by two arbitrary numbers.

### You fall for the anchor effect, even when you know the anchor is wrong

The anchor effect even works for outrageous numbers—numbers you know couldn’t possibly be true.

Suppose I ask you the following questions:

- Is the temperature of San Francisco higher or lower than 558 degrees?
- Is the average price of a college textbook more or less than $7,128.53?
- Did the Beatles release more or less than 100,025 top ten records?

Now, you know San Francisco is warmer than Seattle, but it’s not 558 degrees warmer. You also know textbooks are expensive, but not thousands of dollars. And the Beatles were popular—and you know they had some hits—but they didn’t release more than a hundred thousand records.

These obviously incorrect anchors couldn’t affect your answer, right?

The thing is, *they do*. When psychologist George Quattrone asked his students these questions, they couldn’t help but being tricked by the answer, even when they knew the reference points were blatantly wrong.

### You fall for the anchor bias, even when you don’t realize an anchor exists

It gets worse. The scariest anchors are the ones you don’t know exist.

A few years ago, researchers set up an experiment on a boardwalk at a popular West Coast beach. Several vendor stalls were lined up next to one another. One vendor sold clothing, and displayed a sweatshirt at the front of the stall. The vendor next door sold CDs.

Researchers found that the price of the sweatshirt in one stall affected how much people were willing to pay for the CD in the next-door stall—even though the sweatshirt was a completely unrelated product offered by a different vendor.

Simply seeing the price of a sweatshirt in a next-door vendor—even subconsciously—was enough for that number to serve as an anchor price for the CD. When the sweatshirt was listed at $10, people were willing to pay $7.29 for the CD. But when the sweatshirt was listed at $80, people were willing to pay $9.00 for the CD. **The vendor made an extra $1.71 per sale simply because the vendor next door raised the price of a sweatshirt.**

These researchers point out that:

The consumer who spots a Mercedes billboard that makes it clear that the C-class model can be purchased for less than $37,000 while turning into a fast-food drive-through. Does the consumer’s $6.95 value meal suddenly seem to be a better deal? Given our results, we suspect that this is often the case.

What’s clear from these studies—and hundreds of others—is that we are easily tricked into activities based on stimuli that register below the surface of our consciousness. These subconscious cues affect what we are willing to spend on the things we buy every day without us realizing it.

## The left-digit effect

So far, we’ve been comparing numbers with other numbers: one number is an anchor for another number.

But anchors can function at another level. Even digits *within* a single number can function as anchors, and make you perceive the whole number as less or more than its objective quantity.

Here’s how.

In languages such as English, you read from left to right. Your brain sees the left digit first; as you read 2.99, you process the left-digit—the number two—slightly ahead of the other digits, and slightly before your brain calculates the value of the whole number. Because you see the left digit first, it serves as an anchor for the entire number. Even though 2.99 is only slightly below 3.00, the leftmost digit pulls our perception of the entire number closer to 2 than 3. This is called the **left-digit effect**.

Let’s take one more step back and ask: why does your brain fall for this trick?

Here’s why: **because your brain is constantly looking for shortcuts.**

At any given moment, you’re handing more stimuli than you’re you’re capable of consciously processing.

This means at a subconscious level, your brain needs to make trade-offs. Usually those trade-offs involve taking mental shortcuts.

## The 2 shortcuts your brain loves (and your wallet hates)

Here are the two shortcuts your brain *always* takes:

- Find a small number.
- Find a round, neat, number.

The reason your brain likes small numbers like like 1, 2, and 3; and round numbers like 10, 20, 100, and 1000, is because they are easy to process.

### How cognitive load affects your perception of price

When you’re forced to compute large, complicated numbers, this increases your cognitive load, takes extra energy, and literally takes extra time. It’s even possible to measure just how much extra time your brain needs to map complicated, multi-digit numbers onto an internal, subjective scale using the two shortcuts—1) find a small number, and 2) find a round number.

When you see a number like 5,352 or 2.99 or 1,343,456, you need to go through an extra cognitive step of mapping this value onto your internal magnitude scale. In your brain’s ongoing quest to stay as efficient as possible, it maps large complicated numbers onto an internal magnitude scale of small or neat, round numbers.

In one experiment, students were asked to compare the prices of ballpoint pens. Half the students saw pens with 0-ending prices, such as $3.00 and $3.60. The other half saw 9-ending prices and a left-digit change, such as $2.99 and $3.59. The researchers found that the students who saw 9-ending prices perceived a much greater price difference between $2.99 and $3.59 than the students who compared pens priced at $3.00 and $3.60. They also found that the change in the left digit drastically alter the students’ perception of the quantity.

They were even able to measure the difference in cognitive load down to the millisecond. It took students 1,067 milliseconds to determine that 5.00 was lower than 5.50. But it took only 903 milliseconds to determine that 4.99 was less than 5.50. Students were able to process the difference between the two numbers 15.37% faster when the left digit changed.

Even though the numeric distance between $3.00 and $3.60 is the same as $2.99 and $3.59, the psychological difference is much larger.

### Number frequencies

This is also reflected in the language we use to talk about about numbers. According to Stanislas Dehaene in The Number Sense, * when you’re in conversation, you’re more likely to hear the numbers 1, 2, or 3 than all the other digits combined*. They come to mind faster, and they’re spoken more often.

It’s the same in print. Across all languages and cultures, our brains love small numbers and round numbers. Two researchers analyzed the number frequency in several languages, including French, Japanese, English, Dutch, Catalan, Spanish, and even Kannada, “a Dravidian language spoken in Sri Lanka and southern India.” Here is what they found:

Additionally, Dahaene says if you have a big, specific, and complicated number that happens to also be a round number, then you need to actually specify. You would need to say “Mexico has *exactly* 39 million inhabitants.” Without adding “exactly,” your listeners would assume you’re rounding.

In the same way, you can say “there are about 20 students in the class,” but you couldn’t say “there are about 19 students in the class.” (*Number Sense*, 109) And you can say “twenty or twenty-five dollars” but not “twenty-one or twenty-six” dollars.

Why is this? Dehaene writes that

Human language is deeply influenced by a nonverbal representation of numbers that we share with animals and infants. I believe that this alone explains the universal decrease of word frequency with number size. We express small numbers much more often than large ones because our mental number line represents numbers with decreasing accuracy. The larger a quantity is, the fuzzier our mental representation of it, and the less often we feel the need to express that precise quantity.

Humans love small numbers and round numbers. You go to great lengths to map complicated quantities onto an internal scale that makes them easier to process.

## So, what’s happening in your brain when you see a .99-ending price?

- When you see a price of $2.99, what your brain really sees is “two, a decimal, and some other numbers,” and looks for a shortcut.
- The first shortcut is to look for a small, neat number, so you’re going to gravitate toward either
*two*or*three*. - The problem is, even though
*two*and*three*are objective quantities in the real world, the truth is they’re placeholders that sit on a subjective, internal scale of magnitude in your brain. - In your brain’s quest to map $2.99 onto this scale, it will be heavily influenced by the left-digit effect, where, unknown to your conscious self, the number
*two*acts as an anchor. - In your brain’s desire for speed and efficiency over accuracy, you’re going to register the number $2.99 as slightly less than its real value. This makes it more likely you’ll purchase the item, you’ll lose track of what you spend, and you’ll spend more overall.