Question

multiply
14.3
×1.76
————

Explanation:

Step1: Multiply 14.3 by 6 (from 1.76)

$14.3\times6 = 85.8$

Step2: Multiply 14.3 by 70 (from 1.76, note 7 is in tenths place, so 7×10 = 70)

$14.3\times70 = 1001$ (shift one decimal place, actually 14.3×7 = 100.1, then ×10 = 1001? Wait, no, 1.76 is 1 + 0.7 + 0.06. So better to do 14.3×1.76 = 14.3×(1 + 0.7 + 0.06) = 14.3×1 + 14.3×0.7 + 14.3×0.06. Wait, or do decimal multiplication: ignore decimals, multiply 143×176, then place decimals.

143×176:
143×6 = 858
143×70 = 10010
143×100 = 14300
Sum: 858 + 10010 = 10868 + 14300 = 25168

Now, 14.3 has 1 decimal place, 1.76 has 2 decimal places, total 3 decimal places. So 25168 ÷ 1000 = 25.168.

Wait, let's do step by step decimal multiplication:

14.3
×1.76
------
First, 14.3 × 0.06 = 0.858 (6 hundredths)
Then, 14.3 × 0.7 = 10.01 (7 tenths, shift one decimal)
Then, 14.3 × 1 = 14.3 (1 unit, shift two decimals? Wait, no, when multiplying decimals, we can align the numbers:

14.3
×1.76
------
858 (14.3 × 6, note 6 is in hundredths place, so 14.3×0.06 = 0.858, but when writing, we can do 143×6 = 858, then since 14.3 has 1 decimal and 1.76 has 2, total 3, so later we'll place 3 decimals. Wait, maybe better to do:

14.3 × 1.76:

Multiply 143 × 176 = 25168 (as above). Now, 14.3 is 143 × 10⁻¹, 1.76 is 176 × 10⁻². So product is 143×176 × 10⁻³ = 25168 × 10⁻³ = 25.168.

So step by step:

Step1: Multiply 14.3 by 0.06

$14.3\times0.06 = 0.858$

Step2: Multiply 14.3 by 0.7 (shift one decimal)

$14.3\times0.7 = 10.01$ (wait, no, 14.3×0.7 = 10.01? 14×0.7=9.8, 0.3×0.7=0.21, total 10.01. Correct.

Step3: Multiply 14.3 by 1 (shift two decimals? No, 1.76 is 1 + 0.7 + 0.06, so 14.3×1 = 14.3, and since 1 is in the units place, when we add, we need to shift the positions. Wait, actually, the standard method is:

14.3
×1.76
------
858 (14.3 × 6, but since 6 is in the hundredths place, this is 14.3×0.06 = 0.858, but we write it as 858 with the last digit in the hundredths place, so:

14.3
×1.76
------
858 (14.3 × 0.06)
1001 (14.3 × 0.7, shifted one place to the left, so 14.3×0.7 = 10.01, but written as 1001 with last digit in tenths place)
143 (14.3 × 1, shifted two places to the left, so 14.3×1 = 14.3, written as 143 with last digit in units place)
------
Now, add them up:

858
10010 (wait, I think I messed up the shifting. Let's do it properly. When multiplying by 0.06, it's 14.3×0.06 = 0.858 (3 decimal places). When multiplying by 0.7 (which is 7×0.1), it's 14.3×0.7 = 10.01 (2 decimal places? No, 14.3×0.7 = 10.01, which is two decimal places? Wait, 14.3 has 1 decimal, 0.7 has 1, so product has 2 decimals? No, 14.3×0.7 = 10.01 (correct, 14×0.7=9.8, 0.3×0.7=0.21, sum 10.01). Then multiplying by 1 (1.0), 14.3×1 = 14.3 (1 decimal place). Now, to add them, we need to align the decimal places:

0.858 (from 14.3×0.06)
10.010 (from 14.3×0.7, add a zero at the end to make 3 decimal places)
14.300 (from 14.3×1, add two zeros to make 3 decimal places)

Now sum: 0.858 + 10.010 = 10.868 + 14.300 = 25.168.

Yes, that's correct. So the product is 25.168.

Answer:

25.168