Understanding Decimals

Decimals extend place value to parts smaller than one.

Place Value with Decimals

The decimal point separates whole numbers from fractional parts.

Ones	.	Tenths	Hundredths	Thousandths
1	.	1/10	1/100	1/1000
$1$		$0.1$	$0.01$	$0.001$

Reading Decimals

$3.47$ is read as:

• "Three and forty-seven hundredths"
• "Three point four seven"

Decimals and Fractions

Every decimal can be written as a fraction:

$0.5 = \frac{5}{10} = \frac{1}{2}$

$0.25 = \frac{25}{100} = \frac{1}{4}$

$0.125 = \frac{125}{1000} = \frac{1}{8}$

Common Decimal-Fraction Equivalents

Decimal	Fraction
0.5	$\frac{1}{2}$
0.25	$\frac{1}{4}$
0.75	$\frac{3}{4}$
0.2	$\frac{1}{5}$
0.1	$\frac{1}{10}$
0.125	$\frac{1}{8}$

Comparing Decimals

Line up the decimal points and compare digit by digit:

Compare 0.45 and 0.405:

• 0.45 = 0.450
• 0.405 = 0.405
• Compare: 450 vs 405
• So $0.45 > 0.405$

Rounding Decimals

Same rules as whole numbers:

• Round 3.847 to tenths → 3.8
• Round 3.847 to hundredths → 3.85