How this calculator works
In a decimal number each position is worth ten times the position on its right. Reading left to right from the decimal point the places are ones, tens, hundreds and so on; reading right from the decimal point they are tenths, hundredths and thousandths. The expanded form writes each nonzero digit multiplied by its place value and joins the parts with plus signs. Zeros are place holders: in 3,406 the zero keeps the 4 in the hundreds place even though nothing sits in the tens place.
Formula
A number such as 3406.58 equals 3 × 1000 + 4 × 100 + 0 × 10 + 6 × 1 + 5 × 0.1 + 8 × 0.01. Each integer place k is worth 10^k and each decimal place j is worth 10^-j.
Worked example
The number 3,406 has a 3 in the thousands place worth 3,000, a 4 in the hundreds place worth 400, a 0 in the tens place worth 0 and a 6 in the ones place worth 6. Its expanded form is 3,000 + 400 + 6.
Advertisement
Frequently asked questions
Why is the zero in 3,406 not shown in the expanded form?
Zero times ten is zero, so the term adds nothing. The zero still matters for reading the number, because it holds the tens place open and keeps the 4 in the hundreds place.
How do decimal places work?
The first digit after the point counts tenths, the second hundredths, the third thousandths, and so on. Each step right divides the place value by ten, mirroring the integer places that multiply by ten.
Are trailing zeros kept?
Numeric input does not retain a trailing zero, so 2.50 arrives as 2.5 and only two decimal places are reported. To show a specific precision, use a rounding tool after the calculation.
Can the number be negative?
Yes. The sign applies to the whole number and is placed outside the expanded sum, as in -(3,000 + 400 + 6).