Decimal Place Value to Thousandths

In our base-10 number system, place value doesn't stop at the ones place. When we move to the right of the decimal point, we enter the world of fractions: tenths, hundredths, and thousandths.

The Decimal Place Value Chart

Just like whole numbers, every digit in a decimal has a specific value based on its position.

• Tenths: One place to the right of the decimal point ($\frac{1}{10}$ or $0.1$).
• Hundredths: Two places to the right ($\frac{1}{100}$ or $0.01$).
• Thousandths: Three places to the right ($\frac{1}{1000}$ or $0.001$).

The Golden Rule: Each place value is $10$ times greater than the place to its right, and $\frac{1}{10}$ of the value of the place to its left.

Finding the Value of a Digit

Let's look at the number $2.386$:

• 2 is in the ones place $\rightarrow$ Value is $2$
• 3 is in the tenths place $\rightarrow$ Value is $0.3$
• 8 is in the hundredths place $\rightarrow$ Value is $0.08$
• 6 is in the thousandths place $\rightarrow$ Value is $0.006$

Reading and Writing Decimals

Decimals can be written in three main ways:

Standard Form

This is the normal way we write numbers using digits: $4.235$

Word Form

When writing a decimal in words, the decimal point is read aloud as "and". You read the decimal part as if it were a whole number, followed by the name of the last place value.

$4.235$ is written as: Four and two hundred thirty-five thousandths.

Expanded Form

Expanded form breaks the number apart to show the value of every single digit added together.

For $4.235$: $4 + 0.2 + 0.03 + 0.005$

Using fractions and multiplication, it looks like this: $(4 \times 1) + \left(2 \times \frac{1}{10}\right) + \left(3 \times \frac{1}{100}\right) + \left(5 \times \frac{1}{1000}\right)$

Practice Examples

Example 1: Write "five and twenty-three thousandths" in standard form.

• "Five" is the whole number: $5$
• "And" is the decimal point: $'$
• "Twenty-three thousandths" means the number 23 must end in the thousandths place. We need a placeholder zero in the tenths place.
• Answer: $5.023$

Example 2: What is the value of the digit 8 in $2.386$?

• The 8 is two spaces to the right of the decimal point, which is the hundredths place.
• Answer: $0.08$ (or $\frac{8}{100}$)