Solve 3.6-1.8left(2.5-1right)+0.6(2.5-1)(2.5-2)-0.15(2.5-1)(2.5-2)(2.5-3)+0.03(2.5-1)(2.5-2)(2.5-3)(2.5-4)

$$3.6-1.8 \left( 2.5-1 \right) +0.6(2.5-1)(2.5-2)-0.15(2.5-1)(2.5-2)(2.5-3)+0.03(2.5-1)(2.5-2)(2.5-3)(2.5-4)$$

Evaluate

$$1.423125$$

Solution Steps

Subtract 1 from 2.5 to get 1.5.

$$3.6-1.8\times 1.5+0.6\left(2.5-1\right)\left(2.5-2\right)-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 1.8 and 1.5 to get 2.7.

$$3.6-2.7+0.6\left(2.5-1\right)\left(2.5-2\right)-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 2.7 from 3.6 to get 0.9.

$$0.9+0.6\left(2.5-1\right)\left(2.5-2\right)-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 1 from 2.5 to get 1.5.

$$0.9+0.6\times 1.5\left(2.5-2\right)-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.6 and 1.5 to get 0.9.

$$0.9+0.9\left(2.5-2\right)-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 2 from 2.5 to get 0.5.

$$0.9+0.9\times 0.5-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.9 and 0.5 to get 0.45.

$$0.9+0.45-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Add 0.9 and 0.45 to get 1.35.

$$1.35-0.15\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 1 from 2.5 to get 1.5.

$$1.35-0.15\times 1.5\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.15 and 1.5 to get 0.225.

$$1.35-0.225\left(2.5-2\right)\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 2 from 2.5 to get 0.5.

$$1.35-0.225\times 0.5\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.225 and 0.5 to get 0.1125.

$$1.35-0.1125\left(2.5-3\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 3 from 2.5 to get -0.5.

$$1.35-0.1125\left(-0.5\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.1125 and -0.5 to get -0.05625.

$$1.35-\left(-0.05625\right)+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

The opposite of -0.05625 is 0.05625.

$$1.35+0.05625+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Add 1.35 and 0.05625 to get 1.40625.

$$1.40625+0.03\left(2.5-1\right)\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 1 from 2.5 to get 1.5.

$$1.40625+0.03\times 1.5\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.03 and 1.5 to get 0.045.

$$1.40625+0.045\left(2.5-2\right)\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 2 from 2.5 to get 0.5.

$$1.40625+0.045\times 0.5\left(2.5-3\right)\left(2.5-4\right)$$

Multiply 0.045 and 0.5 to get 0.0225.

$$1.40625+0.0225\left(2.5-3\right)\left(2.5-4\right)$$

Subtract 3 from 2.5 to get -0.5.

$$1.40625+0.0225\left(-0.5\right)\left(2.5-4\right)$$

Multiply 0.0225 and -0.5 to get -0.01125.

$$1.40625-0.01125\left(2.5-4\right)$$

Subtract 4 from 2.5 to get -1.5.

$$1.40625-0.01125\left(-1.5\right)$$

Multiply -0.01125 and -1.5 to get 0.016875.

$$1.40625+0.016875$$

Add 1.40625 and 0.016875 to get 1.423125.

$$1.423125$$

Factor

$$\frac{11 \cdot 23 \cdot 3 ^ {2}}{2 ^ {6} \cdot 5 ^ {2}} = 1\frac{677}{1600} = 1.423125$$