Question

Which expressions are equivalent to 3.64? Check the THREE that apply. (3 points)Responses36.4÷1036 point 4 divided by 1036.4×1036 point 4 times 100.0364×1000 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

Answer 1

To determine which expressions are equivalent to 3.64, let's evaluate each of the responses provided:

1. **36.4 ÷ 10**:
\[
36.4 ÷ 10 = 3.64
\]
This expression is equivalent to 3.64.

2. **36.4 × 10**:
\[
36.4 × 10 = 364
\]
This expression is NOT equivalent to 3.64.

3. **364 × 0.01**:
\[
364 × 0.01 = 3.64
\]
This expression is equivalent to 3.64.

4. **(3 × 1) + (6 × 0.1) + (4 × 0.01)**:
\[
(3 × 1) + (6 × 0.1) + (4 × 0.01) = 3 + 0.6 + 0.04 = 3.64
\]
This expression is equivalent to 3.64.

5. **[(3 × 1) + (6 × 0.1) + (4 × 0.01)] × 100**:
\[
[(3 × 1) + (6 × 0.1) + (4 × 0.01)] × 100 = 3.64 × 100 = 364
\]
This expression is NOT equivalent to 3.64.

Thus, the three expressions that are equivalent to 3.64 are:
- 36.4 ÷ 10
- 364 × 0.01
- (3 × 1) + (6 × 0.1) + (4 × 0.01)