Decimals made easy! The ins and outs of decimal place values – what they’re named, how they work, and applying them to real problems

Author

Tess Loucka

Published

November 7, 2023

Author

Tess Loucka

Published

Nov 1, 2023

Author

Tess Loucka

Published

Nov 7, 2023

Key takeaways

- Decimal numbers get smaller the farther away from the decimal point they are. Decimal places closer to the decimal point are bigger.
- Adding zeros after a decimal number does not change the number’s value.
- To round decimal places, look at the number that comes after the decimal place value you are rounding to. Numbers 5 or more are rounded up. Numbers 4 or less can be kept the same.

When you’re buying something from the store or measuring something with a ruler, you’ve probably noticed that you don’t always get whole numbers. For example, a candy bar might cost $1.98 or a shelf in your room might be 15.25 inches long.

But how do you work with numbers like this?

In this article, we’ll go over **decimal place values**, decimal comparison, rounding decimals, and the **decimal place value chart**.

Decimals are numbers made up of a whole number followed by a fractional number. These two numbers are separated by a dot called a decimal point.

For example, 13.5 is a decimal number because of the decimal point in the middle. The 13 is the whole number and the 5 is a fractional part.

Numbers that come after decimal points should be thought of as fractions. The position a number falls in relation to the decimal point is called its **decimals place value**.

Let’s take a look at a **decimal places chart** to better understand each decimal place.

Decimal place values have different names and values according to how close or far away they are from the decimal point. The **decimal places **are all powers of 10. This is visualized on the **decimal chart**.

**Place value chart with decimals:**

Take a look at the **decimals chart **above.

Decimal numbers get smaller as they move farther away from the decimal point, and larger as they move closer. Whole numbers are the opposite.

Let’s compare the tens place and the **tenths place**. When a whole number reaches the tens place, it means there are tens of something. When a decimal number reaches the** tenths place**, it means there is a tenth of something or a fraction of a whole.

The **tenths place** is **one decimal place **after the decimal point and is the largest value decimal place. Numbers in this place are called tenths because when turned into fractions, they are put over a 10.

Ex. 13.5 = 13 5/10 or 13 ½ when simplified

The **hundredths place **comes second after the decimal point. When decimal numbers reach this place, it means they will be written over 100 in fraction form.

Ex. 12.25 = 12 25/100 or 12 ¼

The **thousandths place** comes third after the decimal point. When turned into a fraction, these numbers will be written over 1,000.

Ex. 3.825 = 3 825/1,000 or 3 33/44

We already mentioned that negative numbers appear on thermometers to show us that the temperature is “below zero”, but that’s not the only real-life example of negative numbers.

Negative numbers are all around us! When we make purchases, the money or credit due is a negative number. Negative numbers also appear on elevation maps to indicate places that are “below sea level”.

Negative numbers can be used as penalties in games, quizzes, and tests. When you get an answer wrong, you may get -5 points, meaning 5 points are being taken away from your total score.

In sports, too, negative numbers can be used to denote the scores of teams. One great example is golf. The golfer with the lowest score, which represents the least amount of strokes, wins!

As you can see, there are many real-world applications of negative numbers. They may not be as common as positive numbers, but they’re just as important.

Now, let’s go over the rules for working with negative numbers.

Pi is a rare number that has 31.4 trillion **decimal place values **and counting!

When doing math with pi, mathematicians definitely don’t use 31.4 trillion decimal places. They round pi down to a more manageable number. At NASA, pi is rounded down to 15 digits: 3.14159265358979.

Let’s try **rounding to the one decimal place**.

What is 12.57 rounded to the nearest **tenths place**?

We’re rounding to the **tenths place**, so look at the **hundredths place**. In this case, that’s 7.

Next, determine whether this number is 5 or more, or 4 or less. Numbers 5 or more are rounded up. Numbers 4 or less are kept the same. In this case, round up since 7 falls under the category of 5 or more.

So, 12.57 rounded to the nearest tenth is 12.6.

Now let’s try to **round to three decimal places**. What is 2.4983 rounded to the nearest **thousandths place**?

The number that comes after the **thousandths place** is 3. Since 3 falls under the category of 4 or less, we will be keeping the number in the **thousandths place **the same.

So, 2.4983 rounded to the nearest thousandth is 2.498.

For more help with reading, writing, and rounding decimals, there are great online math apps and websites you can use that will provide you with detailed instruction, a **decimals place value chart**, practice questions, and explanations to strengthen your understanding of decimals.

*Click on the boxes below to see the answers!*

Question 1: How would you write 5.34 as a mixed number based on what you know about decimal place values?

Answer: 5 34/100.

Since the number 5.34 ends in the hundredths decimal place, the number after the decimal point can be written over 100 in fraction form.

Question 2: Look at the number 8.723. Round to 2 decimal places.

Answer: 8.72

To round to the second decimal place, look at the number that comes after it in the thousandths place, 3. Since 3 is smaller than 5, you keep the hundredths place the same. So, 8.723 rounded to the second decimal place is 8.72.

Question 3: Which is the larger number? 1.54 or 1.6?

Answer: 1.6

To compare the size of decimal numbers, start by comparing the whole numbers and work your way to the right. The number 1.54 has a 5 in the tenths place while 1.6 has a 6 in the tenths place. Six is larger than 5, so 1.6 is the larger number.

**Decimal place value** is the value of numbers according to how far away they are from a decimal point. Place values after a decimal point represent fractions of a whole number.

Place value in decimals starts with the tenths place and grows by powers of 10 as you move to the right. The second place value is the **hundredths place **and the third is the **thousandths place**.

No, negative numbers are not whole numbers. Whole numbers are only positive round numbers, including 0.

The **hundredths place **in a decimal is the second **decimal place value **after the decimal point.

Lesson credits

Tess Loucka

Tess Loucka discovered her passion for writing in high school and has not stopped writing since. Combined with her love of numbers, she became a math and English tutor, focusing on middle- and high-school-level topics. Since graduating from Hunter College, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.

Tess Loucka

Tess Loucka discovered her passion for writing in high school and has not stopped writing since. Combined with her love of numbers, she became a math and English tutor, focusing on middle- and high-school-level topics. Since graduating from Hunter College, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.

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