Decimal Place Value Calculator
Break down decimal numbers by place value with detailed explanations
Understanding Decimal Place Value
Place value in decimals extends the base-10 system to numbers smaller than one. Each position to the right of the decimal point represents a fraction with a denominator that's a power of 10.
Decimal Place Values
First place (tenths): 1/10 = 0.1
Second place (hundredths): 1/100 = 0.01
Third place (thousandths): 1/1000 = 0.001
Fourth place (ten thousandths): 1/10,000 = 0.0001
Example: 123.456
1 is in the hundreds place = 100
2 is in the tens place = 20
3 is in the ones place = 3
4 is in the tenths place = 0.4
5 is in the hundredths place = 0.05
6 is in the thousandths place = 0.006
Total: 100 + 20 + 3 + 0.4 + 0.05 + 0.006 = 123.456
Place Value Chart
| Hundreds | Tens | Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
| 100 | 10 | 1 | 0.1 | 0.01 | 0.001 |
Frequently Asked Questions
What is place value in decimals?
Place value in decimals represents the value of each digit based on its position. Positions to the right of the decimal point are tenths, hundredths, thousandths, etc.
What is the first decimal place called?
The first position to the right of the decimal point is called the tenths place, representing 1/10 or 0.1.
How do you read decimal place values?
Read from left to right: tenths (0.1), hundredths (0.01), thousandths (0.001), ten thousandths (0.0001), etc. Each position is 1/10 the value of the position to its left.
What's the difference between tenths and tens?
Tens is to the left of the ones place (10), while tenths is to the right of the decimal point (0.1). Tenths is 1/10, much smaller than tens which is 10.
How do you write decimals in expanded form?
Write each digit multiplied by its place value, then add them together. For example, 12.34 = 10 + 2 + 0.3 + 0.04.
Why is understanding place value important?
Place value is fundamental to understanding decimal operations, rounding, comparing decimals, and converting between decimals and fractions. It's essential for all decimal arithmetic.