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

Question

(3 points)
Responses

36.4×10
36 point 4 times 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

[(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

36.4÷10
36 point 4 divided by 10

Answer 1

To determine which expressions are equivalent to 3.64, we can evaluate each option:

1. 36.4 × 10: This equals 364, which is NOT equivalent to 3.64.
2. 0.0364 × 100: This equals 3.64, which IS equivalent to 3.64.
3. (3 × 1) + (6 × 0.1) + (4 × 0.01): This breaks down as follows:
   • 3 × 1 = 3
   • 6 × 0.1 = 0.6
   • 4 × 0.01 = 0.04 Thus, 3 + 0.6 + 0.04 = 3.64, which IS equivalent to 3.64.
4. [(3 × 1) + (6 × 0.1) + (4 × 0.01)] × 100: Since we determined that (3 × 1) + (6 × 0.1) + (4 × 0.01) = 3.64, multiplying this by 100 gives 364. Therefore, this is NOT equivalent to 3.64.
5. 36.4 ÷ 10: This equals 3.64, which IS equivalent to 3.64.

Therefore, the THREE expressions that are equivalent to 3.64 are:

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