Math - Decimal Numbers

A decimal number consists of a whole part and a fractional part, separated by a decimal point.

Base 10

The decimal number system is a base-10 system where each place value is a power of 10. It uses ten digits (0-9) to represent all numbers.

Example:

The number 9547.735 in base 10 is interpreted as:

Whole Part:

• $9*10^3 = 9000$
• $5*10^2 = 500$
• $4*10^1 = 40$
• $7*10^0 = 7$

Fractional Part:

• $7*10^{-1} = 0.7$
• $3*10^{-2} = 0.03$
• $5*10^{-3} = 0.005$

Decimal Number:

• $9547.735 = 9000 + 500 + 40 + 7 + 0.7 + 0.03 + 0.005$

Place value

Every place in a decimal number carries a place value.

Example:

The number 1249547.735:

• 1 Million
• 2 Hundred Thousands
• 4 Ten Thousands
• 9 Thousands
• 5 Hundreds
• 4 Tens
• 8 Ones
• . Decimal Point
• 7 Tenths
• 3 Hundredths
• 5 Thousandths