Intro to Decimals: Decimal Form, Examples, and Meaning
So, it’s time to work with decimals, huh? Gone are the days of simple, whole numbers — but that’s okay! We have to keep life interesting, right?
Pro tip: If you find yourself having trouble navigating this page on decimals, it might help to read this page about fractions to shed some more basic light on the fundamental concepts of non-whole numbers.
What is a decimal?
A decimal is a representation of a number that is more (or less) than a whole number. We’ll get into decimal form in a little bit, but essentially, a decimal is a number comprised of three pieces: a whole number piece, a fractional piece, and a dot (a.k.a. the decimal!).
How do we describe decimal numbers at Photomath? Like this:
A decimal number is a number consisting of a whole number part, the decimal separator, and a fractional part.
Decimals vs fractions
You may have noticed that we’re referring to a “fractional part” of decimal numbers. That doesn’t mean that we have an actual fraction in our number — it just means that the decimal number includes a quantity that is less than one whole, just like in fractions.
In the case of decimals, the “fractional part” — or the part less than one whole — is the piece to the right of the decimal point.
BTW: You can convert decimals to fractions (and fractions to decimals) using denominators that are multiples of ten. In other words, the decimal part of a number is actually equal to a fraction! The difference is really the format, and you can decide which makes the most sense to use in any given situation.
So, what does working with decimal numbers really mean?
As you’ve seen, it means you’re dealing with a quantity that is less than or greater than a whole. But why is it important that we can work with numbers like this?
Well, what if you need to weigh something that’s not just a whole number? Let’s say you need $$5.5$$ lbs of bird feed to keep all the little birdies in your backyard coming back! You find a bag of $$7.3$$ lbs of bird feed — you’ll need to know your decimals in order to see if you have enough (and calculate how much you might have left over!).
How do we know when we’re working with a decimal? We can tell by the form of the number!
Some people will refer to the way we write decimal numbers as “decimal notation,” but no matter how you spin it, you’ll know a decimal when you see one.
The main tip-off should be the “.” In this case, it’s a decimal point, not a period. You’ll see a number (or a few) to the left of the decimal point, and then at least one other number to the right of the decimal point, like this:
Let’s dive a little deeper into the foundation of why we write decimal numbers the way that we do:
The decimal system — or “decimal numeral system,” if you’re feeling fancy — uses $$10$$ as its base. That’s why it’s also called a “base-ten” (or “base-10”) positional numeral system.
Whoah, whoah, whoah. That was a lot. Let’s break it down:
- Base-10: There are 10 different numerals (including $$0$$) used to represent numbers. The digits are $$0, 1, 2, 3, 4, 5, 6, 7, 8$$, and $$9$$.
- Positional numeral system: In our case, this means that the position of digits (and how we reference them) is related to their distance from the decimal point.
Because the decimal system is a base-10 system, the names of place values are all based on the number $$10$$ and its multiples.
You’ll notice that we differentiate the left side of the decimal from the right side by adding “th” to the end when referencing the fractional part. For example, the “thousands place” is to the left of the decimal, but the “thousandths place” is to the right.
Where is the tenths place in a decimal?
The tenths place is one place to the right of the decimal point, actually right next to it on the right side. We know it’s to the right of the decimal because “tenths” ends in “ths.”
When working with place values to the right of the decimal, the names are still based on $$10$$ and its multiples; for place values to the right of the decimal, you can use the number of zeroes in the name to tell how many places away from the decimal it is.
For instance, there’s one $$0$$ in $$10$$, so the tenths place is one place to the right!
Where is the hundreds place in a decimal?
The hundreds place is three places to the left of the decimal point. This place value doesn’t have “ths” at the end, so we know it’s on the left side of the decimal.
Think of how you would write three-hundred: $$300$$. We say it as “three-hundred” because the $$3$$ is in the hundreds place!
Generally, when working to the left of the decimal point, the number of digits of the place value name will tell you how many places to move to the left (NOT the number of zeroes like after the decimal). That’s because the place immediately to the left of the decimal is the “ones” place.
In the example of the “hundreds” place, we can tell that’s based on $$100$$, which has three digits total; so, the hundreds place is three to the left.
Place values in numbers with decimals
We already know that place values to the right of our decimal — in other words, place values in the fractional part of our decimal number — will end in “ths,” like “hundredths.”
We also know that the naming of place values is slightly different depending on which side of the decimal point you’re on.
So, to sum it all up, let’s think of it this way:
- If the place value name does not have “ths” at the end, use the number of digits of the name and move that many places to the left of the decimal.
- Ex: The thousands place —> 1000 —> four digits —> four places to the left of the decimal
- If the place value name has a “th” at the end, use the number of zeroes implied in the name to move that number of spaces to the right of the decimal.
- Ex: The hundredths place —> 100 —> two zeroes —> two places to the right of the decimal
Reading a scale with decimal intervals
Picture a ruler: It has evenly spaces markings to help us measure more precisely. We see the whole numbers labeled very clearly, but the little lines in-between are not.
Those little lines can be used to find the fractional part of a decimal number when measuring!
Because they’re evenly spaced and based on tenths, we can refer to the distance between the scaled markings as “decimal intervals.”
For example, let’s say our ruler measures in inches, and there are 10 decimal intervals (spaces) between the whole numbers. If we measure a piece of cardboard whose edge lines up with the fourth tick after the whole number $$6$$, we know that length is $$6.4$$ inches.
Decimal example problems
We know it’s hard to just read about decimals, so let’s put all those words into action and try some examples of real math!
- Round the decimal number $$352.081$$ to the nearest hundredth.
- What number is in the ones place in $$36.5$$?
- What number is in the tens place in $$4,732.98$$?
- Convert $$4.25$$ into a fraction.
- Rewrite $$.01$$ as a percentage.
Want to keep playing around with decimals? Scan a decimal number with your Photomath app to see how to convert, round, and more!
Here’s how we solve the first problem in the app:
What are the 3 types of decimals?
Three types of decimals are non-recurring (non-repeating or terminating, like $$4.32$$); recurring (repeating or non-terminating, like $$3.14159…$$); and decimal fractions (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).
How do you explain decimals to children?
We can explain decimals as representing parts of a whole, with the left side representing how many “wholes” we have, and the numbers after the decimal point telling us how many pieces of a whole we have. It might help to start with fractions and then relate decimals accordingly!
What are the four rules of decimals?
The four “rules” of decimals are just the four arithmetic operations: addition, subtraction, multiplication, and division. Heads-up: in addition and subtraction, you’ll need to line up the decimal points in order to perform the operation correctly!