Lesson 35: Writing Decimal Numbers as Fractions, Part 1

New Concept

Decimal numbers are actually fractions. Their denominators come from the sequence $10$, $100$, $1000$, ...

What’s next

This is your introduction to the world of decimals. Next, you’ll work through examples converting between decimals and fractions, and practice reading and writing them.

Property

Decimal numbers are fractions where the denominator is indicated by the number of decimal places. One decimal place means the denominator is $10$, two places mean $100$, and three places mean $1000$. The number of zeros in the denominator equals the number of decimal places.

Examples

$0.25 = \frac{25}{100}$
$0.57 = \frac{57}{1000}$
$0.1 = \frac{1}{10}$

Explanation

Think of decimal places as a secret code for the number of zeros in a fraction's denominator. One spot after the dot? One zero ($10$). Two spots? Two zeros ($100$). This trick helps you unmask any decimal and reveal its fraction identity. The number you see becomes the numerator, and the place value provides the denominator!

Property

To read a decimal, read the number to the right of the decimal point as a whole number, then say the place value of the last digit. For a mixed decimal like $20.04$, read the whole number, say "and," then read the decimal part.

Examples

$0.057$ is read as "fifty-seven thousandths".
$2.54$ is read as "two and fifty-four hundredths".
$15.2$ is read as "fifteen and two tenths".

Explanation

Reading decimals is like telling a two-part story. First, state the whole number. The decimal point is your cue to say the magic word "and." Then, read the number to the right of the decimal as a group and finish by naming the place value of the very last digit, like 'tenths,' 'hundredths,' or 'thousandths.'