Overview
This lecture explains how decimal place value extends the base 10 number system to represent fractions and values between whole numbers using decimal points and places.
Whole Number Place Value Review
- Base 10 uses digits 0–9 and number places to represent different group sizes.
- Each place to the left increases in value by ten times (ones, tens, hundreds, thousands, etc.).
- Whole numbers are counts without fractions, like 235, where 2 is hundreds, 3 is tens, and 5 is ones.
Introduction to Decimals
- Decimals represent values between whole numbers (parts or fractions).
- Decimal places are located to the right of the ones place.
- Decimal digits let us count parts of a whole, not just whole items.
The Decimal Point
- The decimal point separates whole number places (left) from decimal places (right).
- In whole numbers, the rightmost digit is in the ones place; decimals use the point when fractional digits are present.
- The digit immediately left of the decimal point is always the ones place.
Decimal Place Values
- Places to the right of the decimal point are called tenths, hundredths, thousandths, etc.
- Each place value to the right is ten times smaller than the previous one.
- The tenths place counts parts that are one out of ten (1/10) of a whole.
- The hundredths place counts parts that are one out of one hundred (1/100) of a whole.
- The thousandths place counts parts that are one out of one thousand (1/1000) of a whole.
Expanded Form with Decimals
- Each digit’s value is based on its place (e.g., a 2 in the tenths place = 2/10).
- 126.53 in expanded form: 100 + 20 + 6 + 5/10 + 3/100.
Key Terms & Definitions
- Whole Number — a number without fractions or decimals (e.g., 1, 2, 3).
- Decimal Point — the symbol that separates whole numbers from fractional values.
- Decimal Place — each position right of the decimal point representing tenths, hundredths, etc.
- Tenths — the first decimal place, representing one part out of ten (1/10).
- Hundredths — the second decimal place, representing one part out of one hundred (1/100).
- Expanded Form — a way of writing a number by showing the value of each digit.
Action Items / Next Steps
- Review videos or materials on fractions to deepen understanding.
- Practice converting decimal numbers into expanded form.