Consider the product, 872 multiplied by 0.082. Estimate the product by rounding each number to its greatest place value. Calculate the product.
We have to calculate 872 multiplied by 0.082. First, we have to estimate the product by rounding each of our two numbers to its greatest place value. Let’s start by rounding 872 to its greatest place value. 872 is a three-digit number. So its greatest place value is its hundreds digit. We know that 872 has eight hundreds. But to help us round, we need to look at the digit to the right, the tens digit. If this is five or more, we have to round up to the next 100. It’s a seven. So we need to round up to 900. 872 rounded to its greatest place value is 900. Now, we need to round 0.082 to its greatest place value. Its greatest place value is the eight digit, which is worth eight hundredths. To round to the nearest hundredths, we need to look to the digit to the right. It’s a two. This means that we need to round down. 0.082 rounded to the nearest hundredth is 0.08.
So now, we can multiply 900 by 0.08. We know that nine times eight is 72. We can use this fact to help us. We can use this fact to calculate nine multiplied by 0.08, which is 0.72. 90 times 0.08 will be 10 times more, which is 7.2. So 900 multiplied by 0.08 will be 72. So the estimated product is 72. We rounded 872 to 900 and 0.082 to 0.08. 900 multiplied by 0.08 is 72. Now, we have to actually calculate the product of 872 multiplied by 0.082. To help us calculate the product, we can imagine that 0.082 has no decimals. 0.082 has three decimal places. So if we calculate 872 multiplied by 82, we could add the three decimal places back in the end.
So let’s start by multiplying 872 by the eight in 82. We’ve put a zero down as a placeholder because we’re multiplying by 80. Now, we just need to multiply each of the digits in 872 by eight. Eight times two is 16. Eight times seven is 56 plus the one we exchanged makes 57. And eight eights are 64 plus the five we exchanged make 69. Next, we need to multiply 872 by two. We know that two times two is four. Two times seven is 14. Two times eight is 16 plus the one we exchanged makes 17. Now, we just need to add both of these totals together to find the final answer. Zero and four is four. Six plus four is 10. Seven plus seven is 14 plus the one we exchanged is 15. Nine plus one is 10 plus one more makes 11. Six and one make seven. Now, we just need to remember to add the three decimal places. Because we’re not multiplying by 82, we’re supposed to multiply by 0.082. So this is where the decimal should go.
The product of 872 multiplied by 0.082 is 71.504, which is very close to our estimate of 72.