Understanding Decimals & Place Value

What You’ll Learn

In this lesson you’ll learn what decimal numbers represent, how to read and write them correctly, and the place value of digits after the decimal point (tenths, hundredths, thousandths).

The Concept

Decimals are another way to show parts of a whole, like fractions but using powers of 10. The decimal point separates whole numbers from fractional parts.

Place value after the decimal (left to right):

Tenths (first digit after point): $0.1 = \frac{1}{10}$
Hundredths (second): $0.01 = \frac{1}{100}$
Thousandths (third): $0.001 = \frac{1}{1000}$

Example: $3.456$ means:

3 whole units
4 tenths ( $4 \times 0.1 = 0.4$ )
5 hundredths ( $5 \times 0.01 = 0.05$ )
6 thousandths ( $6 \times 0.001 = 0.006$ )

Total: $3 + 0.4 + 0.05 + 0.006 = 3.456$

To read: Say “and” at the decimal point, then name the last place. $3.456$ = “three and four hundred fifty-six thousandths”

Worked Examples

Write and read $0.875$

8 tenths, 7 hundredths, 5 thousandths
As fraction: $\frac{875}{1000} = \frac{7}{8}$
Read: “eight hundred seventy-five thousandths”

Compare $0.875$ and $0.87$ :

$0.875$ has 5 thousandths extra → $0.875 > 0.87$

Real-World Applications

Decimals are everywhere in money (42 dollars and 75 cents = 42.75), gas prices (3.89 per gallon), measurements (5.25 feet), or batting averages (0.312). Understanding place value helps you read receipts, price tags, or sports stats accurately without confusion.

Quiz

In 4.827, what place is the digit 2 in?

A.Tenths
B.Hundredths
C.Thousandths
D.Ones

What is 0.65 in words?

A.Sixty-five hundredths
B.Sixty-five thousandths
C.Six and five tenths
D.Sixty-five tenths

Which is larger: 3.09 or 3.1?

A.3.09
B.3.1
C.They are equal
D.Cannot tell

A gas price is 3.789 per gallon. What is the value of the 8?

A.8 tenths
B.8 hundredths
C.80 hundredths
D.8 thousandths

Write 0.025 in words.

A.Twenty-five thousandths
B.Twenty-five hundredths
C.Two and five tenths
D.Two hundred fifty thousandths