Welcome to decimal multiplication! Today we'll learn how to multiply decimals using the vertical multiplication method, also known as the column method. Our problem is 0.29 times 1.7. We'll set up the numbers vertically with 0.29 on top and 1.7 below it. The key strategy is to first treat these as whole numbers - 29 times 17 - and then correctly place the decimal point in our final answer.
Now let's set up our vertical multiplication format properly. The key is to align the numbers from right to left, just like we do with whole number multiplication. We start with 0.29 on top and 1.7 below it, with a multiplication symbol and horizontal line. For now, we'll ignore the decimal points and treat these as whole numbers: 29 times 17. This right-alignment is crucial for accurate calculation, as each digit must be in its proper place value position.
Now let's calculate our first partial product by multiplying 29 by 7, which is the ones digit of 17. We start from the right: 7 times 9 equals 63. We write down 3 and carry the 6. Next, 7 times 2 equals 14, plus our carried 6 gives us 20. We write down 0 and carry the 2. This gives us our first partial product of 203. Notice how we show the carrying numbers above to keep track of our calculation.
Now for our second partial product, we multiply 29 by 1, which is the tens digit of 17. This is simpler: 1 times 9 equals 9, and 1 times 2 equals 2, giving us 29. However, since we're multiplying by the tens digit, we must shift this result one position to the left, making it 290. This shift is crucial because the 1 represents 10, not just 1. So we now have our two partial products: 203 and 290.
Now we add our two partial products together: 203 plus 290. We add column by column from right to left. In the ones place: 3 plus 0 equals 3. In the tens place: 0 plus 9 equals 9. In the hundreds place: 2 plus 2 equals 4. This gives us our sum of 493. This is our result when treating the original numbers as whole numbers, but we still need to place the decimal point correctly.