Decimals Calculator

To multiply decimals without a calculator, multiply the numbers as whole integers by ignoring the decimal points, count the total number of decimal places across both original factors, and place the decimal point that same count of digits from the right in the final product. For example, to multiply 2.4 (1 decimal place) by 1.35 (2 decimal places), compute 24 × 135 = 3240, and insert the decimal point 3 places from the right to obtain 3.240, which simplifies to 3.24.

To divide decimals without a calculator, shift the decimal point in the divisor to the right until the divisor becomes a whole integer, shift the decimal point in the dividend to the right by the same number of places, and perform standard long division. For example, to divide 14.72 by 3.2, multiply both numbers by 10 to obtain 147.2 ÷ 32, carry the decimal point directly upward into the quotient, and divide 147.2 by 32 to yield 4.6.

To add decimals using a calculator, enter the first decimal number, press the addition (+) button, enter the second decimal number, and press the equals (=) button. For multi-number additions, continue pressing the addition operator after each term before pressing equals to receive the final sum with preserved place value alignment.

To calculate the square root of a decimal number, convert the decimal into a fraction with a base-10 denominator, compute the square root of the numerator and denominator, or apply the iterative Babylonian method x_{n+1} = (x_n + S / x_n) / 2. For example, to find the square root of 0.49, rewrite the decimal as 49/100, calculate √49 / √100 = 7/10, which equals 0.7.

To calculate decimal exponents, convert the decimal exponent into an irreducible fraction p/q to express the power as the q-th root of the base raised to the p-th power (b^(p/q) = (q√b)^p), or compute the natural logarithm expansion e^(x · ln(b)). For example, to evaluate 16^0.75, convert 0.75 to 3/4 to calculate (⁴√16)³ = 2³ = 8.

To calculate the log of a decimal number, express the decimal in scientific notation m × 10^c to separate the integer characteristic c from the fractional mantissa log10(m), or use the change of base formula log_b(x) = ln(x) / ln(b). For example, to calculate log10(0.05), rewrite 0.05 as 5 × 10⁻² to compute -2 + log10(5) = -2 + 0.69897 = -1.30103.

To subtract decimals without a calculator, align the decimal points vertically, pad the shorter decimal with trailing zeros so both values have equal decimal places, and subtract each column from right to left while borrowing 10 from the adjacent left column when a top digit is smaller than a bottom digit. For example, to subtract 17.85 from 32.40, align columns, borrow 1 from tenths to compute 10 - 5 = 5 in hundredths, borrow 1 from ones to compute 13 - 8 = 5 in tenths, and subtract whole parts to yield 14.55.

To round decimals using a calculator, select your target precision (tenths, hundredths, thousandths, or significant figures), identify the deciding digit immediately to the right of your target place, and apply the round-half-up convention where digits 5 through 9 increase the target place by 1 and digits 0 through 4 leave the target place unchanged.

Yes, this decimal calculator converts decimals to fractions by placing terminating decimals over their corresponding power of 10 and dividing both the numerator and denominator by their Greatest Common Factor (GCF) to simplify the ratio. For repeating decimals, the calculator uses the algebraic subtraction method (10^n x - 10^m x) to produce exact integer fractions.

Yes, this decimal calculator generates step-by-step solutions for arithmetic operations, long division brackets, fraction simplifications, and exponent evaluations. Every step includes place value alignment, carry and borrow logs, and verification proofs.

Yes, you can use this decimal calculator online for free with no account registration, software installation, or payment required. All tools run directly in modern web browsers across desktop, tablet, and mobile devices.