A student claims that $$ 0.403=0.43 $$. How do you respond? Choose the correct answer below. A. Since $$ 0.403=\frac{403}{1000}, 0.43=\frac{43}{100}=\frac{430}{1000} $$, and $$ 403
eq 430 $$, the decimals are not equal. B. Since $$ 0.403=\frac{403}{1000}, 0.43=\frac{43}{1000} $$, and $$ 403
eq 43 $$, the decimals are not equal. C. Since both decimals are formed from the digits 0,4 , and 3 , they are equal. D. Since adding a zero to a number does not change the number, the decimals are equal.

Question

A student claims that $$ 0.403=0.43 $$. How do you respond? Choose the correct answer below. A. Since $$ 0.403=\frac{403}{1000}, 0.43=\frac{43}{100}=\frac{430}{1000} $$, and $$ 403 
eq 430 $$, the decimals are not equal. B. Since $$ 0.403=\frac{403}{1000}, 0.43=\frac{43}{1000} $$, and $$ 403 
eq 43 $$, the decimals are not equal. C. Since both decimals are formed from the digits 0,4 , and 3 , they are equal. D. Since adding a zero to a number does not change the number, the decimals are equal.

UpStudy AI · Accepted Answer

1. Convert $$0.403$$ to a fraction:
   $$
   0.403 = \frac{403}{1000}.
   $$
2. Convert $$0.43$$ to a fraction by recognizing that:
   $$
   0.43 = \frac{43}{100}.
   $$
3. Express $$\frac{43}{100}$$ with a denominator of $$1000$$:
   $$
   \frac{43}{100} = \frac{43 \times 10}{100 \times 10} = \frac{430}{1000}.
   $$
4. Compare the two fractions:
   $$
   \frac{403}{1000} \quad \text{and} \quad \frac{430}{1000}.
   $$
   Since $$403 \neq 430$$, the two fractions (and therefore the decimals) are not equal.

Thus, the correct answer is:

A. Since $$ 0.403=\frac{403}{1000}, 0.43=\frac{43}{100}=\frac{430}{1000} $$, and $$ 403 \neq 430 $$, the decimals are not equal.
The decimals $$0.403$$ and $$0.43$$ are not equal because $$0.403 = \frac{403}{1000}$$ and $$0.43 = \frac{430}{1000}$$, and $$403 \neq 430$$.

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