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Mathematics · pattern A, Numeric fields

Decimal arithmetic, with the place-value check.

Enter two decimals for all four operations, with rounding to a chosen number of places and the decimal-place count that verifies a multiplication.

Inputs

The formula used

align the points for addition; add the place counts for multiplication

The number of decimal places in a product is the sum of the places in the two factors, which is the fastest check available on a multiplication.

Sum

16.15000000

Difference
9.35000000
Product
43.35000000
Quotient
3.75000000
Sum rounded
16.150000
Product rounded
43.350000
Decimal places in the product
3

Rounding early is how answers drift.

Every rounding step introduces a small error, and rounding at each intermediate stage lets those errors accumulate past the tolerance of the final answer. Carry full precision through the working and round once, at the end, to the precision the question asks for.

Questions about decimal

Why does 0.1 + 0.2 not give exactly 0.3 on a computer?
Because binary floating point cannot represent 0.1 exactly. The residue is around 10⁻¹⁷ and shows up when testing equality.
How many places should I give?
As many as the question asks, or as many as the least precise input justifies. Extra digits are not extra accuracy.
What is the rule for multiplying decimals?
Multiply as whole numbers, then place the point so the answer has as many decimal places as both factors combined.

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A calculator handles the arithmetic. It cannot teach you the method.

If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.