Precision Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

Multiply

3.4

\times

2.15

cm, applying the significant figures rule for multiplication.

1
$3.4$ cm has $2$ significant figures; $2.15$ cm has $3$ significant figures.
2
In multiplication, the result has as many significant figures as the factor with the fewest: $2$ .
3
Product: $3.4 \times 2.15 = 7.31$ cm $^2$ . Round to $2$ significant figures: $7.3$ cm $^2$ .

Answer

3.4 \times 2.15 \approx 7.3

^2

For multiplication and division, limit the result's significant figures to those of the least precise factor. This prevents false precision:

3.4

cm is only known to

2

significant figures, so the product cannot be claimed to

3

About Precision

The degree of exactness in a measurement or calculation, reflected in the number of significant digits reported.

A student measures a pencil three times and gets [formula] cm, [formula] cm, [formula] cm. Another i

Add [formula] cm and [formula] cm, applying the rule for precision in addition.

Which measurement is more precise: [formula] m, [formula] m, or [formula] m? How many significant fi