Place Value Explorer & Expanded Form

Our modern numeral system is a base-10 positional notation system (Hindu-Arabic system). In this system, the value of a digit is determined entirely by its position relative to the decimal point, with each position representing a power of 10.

Moving ONE step left → Multiplies the value by 10 (×10)
Moving ONE step right → Divides the value by 10 (÷10 or ×0.1)

Place Value Name	Numerical Power of 10	Value (Decimal / Fraction)
Billions	109	1,000,000,000
Hundred Millions	108	100,000,000
Ten Millions	107	10,000,000
Millions	106	1,000,000
Hundred Thousands	105	100,000
Ten Thousands	104	10,000
Thousands	103	1,000
Hundreds	102	100
Tens	101	10
Ones (Units)	100	1
• Decimal Point •	—	—
Tenths	10−1	0.1 (1/10)
Hundredths	10−2	0.01 (1/100)
Thousandths	10−3	0.001 (1/1000)
Ten-Thousandths	10−4	0.0001 (1/10,000)
Millionths	10−6	0.000001 (1/1,000,000)

• Standard Form: The conventional numeral (e.g. 5,432.85).
• Expanded Form: The sum of the value of each digit: (5 × 1,000) + (4 × 100) + (3 × 10) + (2 × 1) + (8 × 0.1) + (5 × 0.01).
• Word Form: Written out in formal English: "Five thousand, four hundred thirty-two and eighty-five hundredths."

In science and engineering, extreme numbers (such as the speed of light or the size of an atom) are expressed using normalized power-of-10 scientific notation:

Speed of light: 299,792,458 m/s = 2.99792458 × 10⁸ m/s
Mass of electron: 0.0000000000000000000000000000009109 kg = 9.109 × 10⁻³¹ kg