Question

chronika stated that 20.534 divided by 10 is 2,053.4. select the explanation for her
she divided by 100 instead of multiplying by 100
she multiplied by 10 instead of multiplying by 100
she divided by 100 instead of multiplying by \\(\frac{1}{10}\\)
she multiplied by 100 instead of multiplying by \\(\frac{1}{10}\\)

Explanation:

Step1: Calculate correct result of division

$29,854 \div 10 = 2,985.4$

Step2: Analyze Claudia's error

Claudia got 2,985.4, but let's check each option:

• Option1: $29,854 \div 100 = 298.54

eq 2,985.4$

• Option2: $29,854 \times 10 = 298,540

eq 2,985.4$

• Option3: Multiplying by $\frac{1}{10}$ is same as dividing by 10: $29,854 \times \frac{1}{10}=2,985.4$, but dividing by 100 gives 298.54, so this is wrong.
• Option4: Multiplying by $\frac{1}{10}$ is $29,854 \times \frac{1}{10}=2,985.4$. Multiplying by 100 gives $29,854 \times 100=2,985,400$, which is not her answer. Wait, correction: Wait, Claudia said 29,854 divided by 10 is 2,985.4? No, wait 29,854 ÷10 is 2,985.4, that is correct? No, wait the options: Wait no, maybe I misread. Wait 29,854 ÷10 = 2,985.4, that is correct. But the options are about her mistake. Wait no, maybe the question is that she said 29,854 divided by 10 is 298.54? No, the image says she said 29,854 divided by 10 is 2,953.4? No, image says 2,953.4? No, image says 2,983.4? Wait no, let's recheck: 29,854 ÷10 = 2,985.4. If she got 298.54, that is dividing by 100. Wait the first option: "She divided by 100 instead of multiplying by 10"? No. Wait no, the question is: Claudia stated that 29,854 divided by 10 is 2,985.4? That is correct. No, maybe the number is 29,854 divided by 10 is 298.54, which is wrong. Oh, maybe the image has a typo, but let's re-express:

Wait, dividing a number by 10 moves the decimal left 1 place: 29854.0 → 2985.4. Dividing by 100 moves left 2 places: 298.54. Multiplying by 10 moves right 1: 298540. Multiplying by $\frac{1}{10}$ is same as dividing by 10.

Wait the only option that makes sense: If she thought dividing by 10 is dividing by 100, but no. Wait no, the correct answer is the first option? No, wait no. Wait let's re-express each option:

1. She divided by 100 instead of multiplying by 10: $29854 ÷100=298.54$, $29854×10=298540$ → not matching.
2. She multiplied by 10 instead of multiplying by 100: $29854×10=298540$, $29854×100=2985400$ → no.
3. She divided by 100 instead of multiplying by $\frac{1}{10}$: $29854 ÷100=298.54$, $29854×\frac{1}{10}=2985.4$ → if her answer was 298.54 instead of 2985.4, this is the mistake.
4. She multiplied by 100 instead of multiplying by $\frac{1}{10}$: $29854×100=2985400$, $29854×\frac{1}{10}=2985.4$ → no.

Wait, the question says Claudia stated that 29,854 divided by 10 is 2,985.4? That is correct. But the options are about her mistake, so maybe the number she said is 298.54. Assuming that, the mistake is she divided by 100 instead of dividing by 10 (which is multiplying by $\frac{1}{10}$). So option 3.

Wait no, let's correct:

Step1: Correct operation result

$29854 \div 10 = 29854 \times \frac{1}{10} = 2985.4$

Step2: Analyze incorrect result

If Claudia got $298.54$, that is $29854 \div 100 = 298.54$, which means she divided by 100 instead of multiplying by $\frac{1}{10}$ (the correct operation for dividing by 10).

Answer:

C. She divided by 100 instead of multiplying by $\frac{1}{10}$