Question

Dylan and Lucas know that the digits in the product

6 x 3.01 are 1806. Dylan says the decimal should be placed between the 8 and 0. Lucas says the decimal should be placed between the 1 and 8.

Decide which student is correct. Explain your thinking. Use estimation and place value in your response. (Please help.)

Answer 1

Dylan is correct

Explanation:

Answer 2

Dylan is correct

The answer computed is the number of hundredths in the product, so the decimal point should be placed to reflect that fact.

Explanation:

3.01 is 301/100

When you multiply by 6, you get 1806/100. The number 1806 is the number of hundredths in the answer. When you put the 6 of 1806 in the hundredths place of the number, the decimal point falls between the 8 and the 0, as Dylan says.

_____

The answer can be estimated as 6×3 = 18. So, it is appropriate to place the decimal point so the resulting value is near 18: 18.06. (Not 1.806 or 180.6.)

_____

The multiplication algorithm for decimal numbers can be described as ...

1. multiply the numbers as though they were integers
2. count the total number of decimal places in the multiplicands
3. place the decimal point in the answer so it has that number of decimal places.

Here, the only number with decimal places is 3.01, and it has 2. Thus, the answer should have 2 decimal places: 18.06.