People use the decimal point system worldwide, but sometimes it’s easy to confuse numbers with the same numerals. This is especially true in a system where the order of the numbers is so important. This can leave you a bit baffled and asking, “Which one is greater: 0.1 or 1.0?”
1.0 is greater than 0.1 in every circumstance. This is because the numeral 1.0 represents the whole number “one” (1), while the numeral 0.1 represents one-tenth (1/10). So, not only is 1.0 bigger than 0.1, it is ten times bigger! Both 1.0 and 0.1 are numbers we express using y a base-10 system.
The decimal point and the position of the decimal point play a crucial role in determining the value each of these numbers represents.
Let’s check these two numerals and learn more about the features of numbers with decimal points. Then, we’ll take a greater look at the base-10 decimal system and how to read and make sense of numbers with decimal points.
Which Is Bigger: 0.1 or 1.0?
The numeral 1.0 is bigger than 0.1, especially when you are measuring something with a specific scale or unit of measure. This is because 1.0 represents one whole unit, while 0.1 represents only 1/10th of that unit (source).
Consider it this way: imagine you have a pizza. You have one whole pizza, and someone divides it into 10 slices. In this case, 1.0 would represent the whole pizza with all 10 slices.
However, if your friends came and ate some pizza, leaving you with just one slice, then you are left with 1/10th of a pizza. In this and all other cases, 1/10th is the same as the decimal form 0.1.
From this illustration, you can see how 1.0 is significantly bigger than 0.1. When you’re talking about a pizza, it’s the difference between one measly slice and the whole pie!
You can also think about it in terms of money. If you have 1.0 dollar, then you have $1.00. However, if you have one-tenth of a dollar, you have only $0.10. In this case, “1.0” represents a whole dollar, while 0.1 represents only a dime.
The Decimal System
The decimal system is the name given to a base-10 numeral system. This system employs 10 different numerals; you’re probably most familiar with the system that uses zero (0) to nine (9) with the Hindu-Arabic numerals (source).
In the decimal system, the value of the number these numerals represent relies on the position of the numeral. So, for example, when you see 365, you know that the 3 actually represents three hundred, the 6 actually means 60, and the 5 means 5.
So, just based on the position of the numerals, you can easily see that the number 365 doesn’t mean 3-6-5, but it actually represents “three hundred and sixty-five.”
Another essential feature of the decimal system is the decimal point (.). The decimal point marks the position where whole numbers start and where fractions or parts of whole numbers begin.
All of the numerals to the left of the decimal point represent whole numbers, while all of the numerals to the right of the decimal point represent a fraction of a number or unit.
What Is the Base-10 System?
The base-10 system is the official name of the number system you’re probably most familiar with. This is the system that most countries use to count money and produce, and we learn about it from the time we are in pre-school or even younger.
The base-10 system is a place-value number system because the actual value of the number we represent by the numeral depends on the placement of that number (source). The digit “zero” acts as a placeholder if there are no numbers corresponding to the value of a certain placement.
For more information about the digit “zero” and its special place in our number system, check out our article “Is 0 an Irrational or Rational Number?”
Have a look at these examples:
Here you can see how the position of each digit corresponds to the real value of the unit that each digit represents. For example, a 5 in the “hundreds” position represents 500, while a 7 in the “tenths” position represents 0.7.
For more information about determining if numbers are bigger and smaller in the decimal system, check out our article “Which Is Greater: 0.2 or 0.02?”
Should I Use a Decimal Point or Comma?
In the United States, we always use a decimal point (.). So, you’ll see $46.72 (forty-six dollars and seventy-two cents) and not $42,76.
However, some countries that use the decimal system use a comma (,) instead of a decimal point (.) to show the separation between whole numbers and fractions of numbers. This is especially prevalent when they write amounts of money.
Thus, in some countries in Europe, it is much more common to see a price with the comma (,) instead. This means that it isn’t strange to see a price such as 42,76€ (forty-two euros and seventy-six cents).
Commas in Large Numbers
In the American system, though, there is a place for the comma. Usually, we use the comma to show the spot where the “hundreds” end and the “thousands” begin. For instance, we write the number “thirty-two thousand, four hundred and seventy-two” as 32,472.
From that example, you can see that the comma (,) comes in between the “thousands” and “hundreds” positions. Even when we say the number aloud, you can hear a slight pause. And when we write the number out, we include a comma there as well.
We use the comma in the same way between “millions” and “hundreds of thousands” and between “hundreds of millions” and “trillions” as well. Basically, for every three digits before the decimal point, we use a comma to make reading the number easier on our eyes.
Take a look at the commas and decimal points in these examples to get a feel for how we use them in large numbers:
- 54,306.25 = fifty-four thousand, three hundred and six point twenty-five
- 8,402,840 = eight million, four hundred and two thousand, eight hundred and forty
- 3,193.54 = three thousand, one hundred and ninety-three point fifty-four
Remember, when you’re adding these commas, it’s important to start counting from the decimal point, continuing to the left. Don’t add commas based on the position of the first digits in the number!
Greater Than and Less Than Symbols
Like most expressions in our number system, we use special symbols to show if one number is greater than or less than another number. The “greater than” symbol looks like this: >. The “less than” symbol looks like this: <.
It can be a bit confusing at first to remember which one is which. An easy way to use the correct symbol every time is first to set up the two numbers or values that you are comparing. For instance, if you want to compare 1.0 and 0.1, write them down first:
Now, determine which one is bigger. We know that 1.0 is greater than 0.1, so now it’s time to choose the right symbol to express that. So, should we use > or <?
Imagine that the symbol is an alligator with its mouth open wide. This alligator wants to “eat” the biggest value, so the symbol should always be open towards the greater number.
In our example, the expression should look like this:
1.0 > 0.1
We can read this expression as “1.0 is greater than 0.1.” We can express the same thing like this:
0.1 < 1.0
We can read this expression as “0.1 is less than 1.0.” Both of these expressions have the same meaning. This article was written for strategiesforparents.com.
The important thing to remember when you’re using the greater than (>) and less than (<) symbols is to make sure that the symbols open up towards the greater number. Just remember that hungry alligator, and you’ll get it correct every time!
No matter how you slice it, 1.0 is greater than 0.1 in every situation. That’s because 1.0 represents the number “one”: it is a whole unit. On the other hand, 0.1 represents 1/10th — it is only a part of a whole unit.
We base this distinction on the decimal system, which uses the position of 10 different digits to determine their value in the larger number.
There are two key players in the decimal system. The first one is the decimal point (.), which denotes the place where whole numbers end and where fractions begin. The second one is the digit “zero” (0), which is a placeholder.