- Understanding place value and decimals

Understanding Place Value

Place value is a fundamental concept in mathematics that helps us understand the value of each digit in a number based on its position. In our base-10 system, each place represents a power of ten.

How Place Value Works

• Ones: The rightmost digit represents units (100).
• Tens: The next digit to the left represents tens (101).
• Hundreds: The third digit from the right represents hundreds (102).
• Thousands: The fourth digit from the right represents thousands (103), and so on.

For example, in the number 3,482:

• 3 is in the thousands place (3 × 1,000 = 3,000)
• 4 is in the hundreds place (4 × 100 = 400)
• 8 is in the tens place (8 × 10 = 80)
• 2 is in the ones place (2 × 1 = 2)

Understanding Decimals

Decimals extend the place value system to represent values less than one. The decimal point separates whole numbers from fractional parts.

Decimal Place Values

• Tenths: The first digit to the right of the decimal point (1/10 or 10-1).
• Hundredths: The second digit to the right (1/100 or 10-2).
• Thousandths: The third digit to the right (1/1,000 or 10-3), and so on.

For example, in the number 56.789:

• 7 is in the tenths place (7 × 0.1 = 0.7)
• 8 is in the hundredths place (8 × 0.01 = 0.08)
• 9 is in the thousandths place (9 × 0.001 = 0.009)

Why Place Value and Decimals Matter

Understanding place value and decimals is essential for performing arithmetic, comparing numbers, and solving real-world problems involving measurements and money.

Mastery of place value and decimals builds a strong foundation for all future math learning.

For more practice and interactive activities, visit Khan Academy's place value resources.