Lessons 31: Reading and Writing Decimal Numbers

New Concept

A decimal number uses place value to represent parts of a whole. The digits to the right of the decimal point represent a fraction.

$0.3 = \frac{3}{10} \quad \text{three tenths}$

What’s next

Property

In a decimal fraction, we can see the numerator, but we cannot see the denominator. The denominator of a decimal fraction is indicated by place value. For example, $0.3 = \frac{3}{10}$ and $0.03 = \frac{3}{100}$.

Examples

$0.9$ is equivalent to the fraction $\frac{9}{10}$.
$0.41$ is equivalent to the fraction $\frac{41}{100}$.
$0.007$ is equivalent to the fraction $\frac{7}{1000}$.

Explanation

Think of decimal fractions as sneaky fractions in disguise! They don't show their denominator outright. Instead, you have to be a detective and count the digits after the decimal point. One digit means tenths, two means hundredths, and so on. It’s a secret code for the bottom number of a fraction, making big calculations much neater.

Property

In our number system, the place a digit occupies has a value called place value. Places to the left of the decimal point increase in value (ones, tens, hundreds), while places to the right decrease in value (tenths, hundredths, thousandths).

Examples

In the number $28.156$, the digit $5$ is in the hundredths place, so its value is $\frac{5}{100}$.
In the number $40.2$, the $4$ is in the tens place and the $2$ is in the tenths place.
In the number $3.14159$, the digit $9$ is in the hundred-thousandths place.

Explanation

Place value is like a number's home address! To the left of the decimal point live the big whole numbers, getting larger the further they go. To the right live the tiny fractions, getting smaller and smaller. The decimal point is the main street separating the two neighborhoods. Knowing the address tells you a digit's true worth.