Advertisement

Expanded form calculator

Choose expansion or combine terms. Decimal expansion uses the entered number's numeric value, so insignificant trailing zeros are not retained.

Calculator

Number
305.0700000000
Expanded form
300 + 5 + 0.07
Non-zero digit places
3 at 10^2; 5 at 10^0; 7 at 10^-2

Advertisement

How this calculator works

Each decimal digit contributes its value times a power of ten. Digits left of the decimal have non-negative exponents, while digits to the right have negative exponents. Zero contributions are omitted. Negative values put one minus sign around the full expansion. Combine mode sums numeric place-value contributions before expanding.

Formula

x = sign(x) × sum(digit_k × 10^k). For example, the hundredths place has k = -2.

Worked example

305.07 = 300 + 5 + 0.07 = 3 × 10^2 + 5 × 10^0 + 7 × 10^-2. Combining 400, 20 and 6 gives 426.

Advertisement

Frequently asked questions

Why are zero digits omitted?

A zero contributes nothing to the sum. Its position is still reflected in the powers of ten of the other digits.

Can I expand a negative number?

Yes. The minus sign applies to the entire positive-magnitude expansion.

Will 1.20 keep its final zero?

No. Numeric inputs treat 1.20 and 1.2 as the same value. This tool explains place value rather than significant-figure notation.

Sources

Advertisement