Find the area of a rectangle with length 26 and width 9.174.

Step-by-step solution

1. 1

   Use the area formula for a rectangle. Area is length times width, with no dependence on which side is called which:

   $A=\ell w=26\times 9.174$

2. 2

   Split the decimal factor to keep the arithmetic exact. Writing $9.174=9+0.174$ turns one awkward multiplication into two easy ones (the distributive law):

   $26\times 9.174=26\times 9+26\times 0.174$

3. 3

   Compute the two pieces.

   $26\times 9=234,\qquad 26\times 0.174=4.524$

   The second product comes from $26\times 174=4524$ and then shifting three decimal places.

4. 4

   Add them for the area.

   $234+4.524=238.524$

   So the area is $238.524$ square units. There are exactly three decimal places, matching the three in the width — length $26$ is exact.

5. 5

   Sanity-check the size. The width lies between $9$ and $10$, so the area must lie between $26\times 9=234$ and $26\times 10=260$; $238.524$ sits comfortably inside that band and close to the lower end, as expected since $9.174$ is near $9$.