Which expressions are equivalent to 3.64? Check the THREE that apply.

Question

(3 points)
Responses

36.4÷10
36 point 4 divided by 10

0.0364×100
0 point 0 3 6 4 times 100

(3×1)+(6×0.1)+(4×0.01)
open paren 3 times 1 close paren plus open paren 6 times 0 point 1 close paren plus open paren 4 times 0 point 0 1 close paren

36.4×10
36 point 4 times 10

[(3×1)+(6×0.1)+(4×0.01)]×100
open bracket open paren 3 times 1 close paren plus open paren 6 times 0 point 1 close paren plus open paren 4 times 0 point 0 1 close paren close bracket times 100

Answer 1

To determine which expressions are equivalent to 3.64, let's analyze each response:

1. 36.4 ÷ 10:

   • This expression simplifies to \(36.4 \div 10 = 3.64\).
   • Equivalent.

2. 0.0364 × 100:

   • This expression simplifies to \(0.0364 \times 100 = 3.64\).
   • Equivalent.

3. (3×1) + (6×0.1) + (4×0.01):

   • This simplifies to \(3 + 0.6 + 0.04 = 3.64\).
   • Equivalent.

4. 36.4 × 10:

   • This expression simplifies to \(36.4 \times 10 = 364\).
   • Not Equivalent.

5. [(3×1) + (6×0.1) + (4×0.01)] × 100:

   • This expression simplifies to \((3 + 0.6 + 0.04) \times 100 = 3.64 \times 100 = 364\).
   • Not Equivalent.

Thus, the three expressions that are equivalent to 3.64 are:

1. 36.4 ÷ 10
2. 0.0364 × 100
3. (3×1) + (6×0.1) + (4×0.01)