Question

Mary says the digits in the quotient of 381.109 ÷ 0.86 are 4 4 3 1 5,but she doesn’t know where to place the decimal point. How can Mary uses number sense to place the decimal point?

Answer 1

Mary can use her understanding of number sizes to determine that the decimal in the quotient of 381.109 ÷ 0.86 should be placed to make the result a little larger than 381, leading to 443.15.

Step-by-step explanation:

Mary can use number sense to correctly place the decimal point in the quotient by considering the relative sizes of the numbers involved in the division. Since 0.86 is close to 1, if we were to divide 381.109 by 1, the quotient would simply be 381.109.

As 0.86 is slightly smaller than 1, dividing by 0.86 will produce a slightly larger quotient, but the order of magnitude will remain the same.

Therefore, Mary should place the decimal point in such a way that the quotient is a little bit larger than 381 - this makes the correct placement for the decimal point after the first two digits, resulting in a quotient of 443.15.