Jameela is learning about binary numbers. She leaves her mom an “encoded” shopping list that says she needs “101” notebooks and a bag of “1111” apples for her field trip. What does she really need?

Question

(1 point)
Responses

four notebooks and 10 apples
four notebooks and 10 apples

five notebooks and 15 apples
five notebooks and 15 apples

101 notebooks and 1,111 apples
101 notebooks and 1,111 apples

25 notebooks and eight apples

Answer 1

To decode Jameela's shopping list:

1. The binary number "101" converts to decimal as follows:

   • \(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5\) So, she needs 5 notebooks.

2. The binary number "1111" converts to decimal as follows:

   • \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 4 + 2 + 1 = 15\) So, she needs 15 apples.

Therefore, Jameela really needs 5 notebooks and 15 apples.

The correct answer is: five notebooks and 15 apples.