Decimals

What is a Decimal Fraction?

A decimal fraction is a fraction where the denominator is a power of ten (e.g., 10, 100, 1000).

Understanding Place Value

Each digit in a number has a place value:

• Thousands | Hundreds | Tens | Units | Tenths | Hundredths | Thousandths
• Example: In 808.713, the first 8 represents 800, while the second 8 represents 8.

Decimal Place Values

• 1 ÷ 10 = 0.1 (One tenth, $\frac{1}{10}$)
• 1 ÷ 100 = 0.01 (One hundredth, $\frac{1}{100}$)
• 1 ÷ 1000 = 0.001 (One thousandth, $\frac{1}{1000}$)

Multiplying and Dividing by 10, 100, and 1000

• To multiply by 10: Move digits one place to the left (or move the decimal one place right).
• To multiply by 100: Move digits two places to the left (or move the decimal two places right).
• To multiply by 1000: Move digits three places to the left (or move the decimal three places right).

Converting Between Decimals and Fractions

• 0.1 = $\frac{1}{10}$
• 0.5 = $\frac{1}{2}$
• 0.25 = $\frac{1}{4}$