Lesson 2: Thousandths and Place Value Relationships

Property

A decimal number is a number that includes a decimal point, separating the whole number part from the fractional part.
The digits to the right of the decimal point represent fractions with denominators that are powers of ten (tenths, hundredths, thousandths, etc.).
For example, a number $a.bcd$ can be written in expanded form as:

Examples

• The decimal $0.6$ is equivalent to the fraction $\frac{6}{10}$.
• The decimal $5.42$ can be written as $5 + \frac{4}{10} + \frac{2}{100}$, which is equal to the mixed number $5\frac{42}{100}$.
• In money, $1.75$ dollars represents one whole dollar and seventy-five hundredths of a dollar, or $1 + \frac{75}{100}$ dollars.

Explanation

A decimal is a way to write a number that is not whole. The decimal point acts as a separator between the whole part on the left and the fractional part on the right. Each place value to the right of the decimal point is ten times smaller than the place value to its left. Understanding this structure is key to performing arithmetic with decimals, especially in financial contexts like calculating costs and change.

Property

Decimal place values are related by a factor of 10. Composing means bundling 10 smaller units to make 1 larger unit. Decomposing is the reverse.

Examples

Property

Dividing a place value unit by 10 results in the next smaller unit to its right. This pattern extends the place value chart to include decimals such as tenths, hundredths, and thousandths.

Examples

• $1000000 \times \frac{1}{10} = 100000$ (one million ÷ 10 = one hundred thousand)
• $100000 \times \frac{1}{10} = 10000$ (one hundred thousand ÷ 10 = ten thousand)
• $10000 \times \frac{1}{10} = 1000$ (ten thousand ÷ 10 = one thousand)
• $1 \times \frac{1}{10} = 0.1$ (one ÷ 10 = one tenth)
• $0.1 \times \frac{1}{10} = 0.01$ (one tenth ÷ 10 = one hundredth)
• $0.01 \times \frac{1}{10} = 0.001$ (one hundredth ÷ 10 = one thousandth)