Question

solve the problem. use what you learned from the example.

stefan was finding the quotients of decimals and powers of ten.

here is what stefan wrote for two problems:

(0.2 \div 100 = 20) \t (0.02 \div 10 = 0.2)

what did stefan do correctly? what did he do wrong? what can to help him divide correctly with powers of ten the next time?

Explanation:

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<reasoning>

Analyze Stefan's work

Stefan wrote:

1. \(0.2 \div 100 = 20\)
2. \(0.02 \div 10 = 0.2\)

Let's check the actual math.

• For the first problem: \(0.2 \div 100 = 0.002\). Stefan got \(20\).
• For the second problem: \(0.02 \div 10 = 0.002\). Stefan got \(0.2\).

Identify what Stefan did correctly

Using the Decimal Place Value Relationships knowledge point, we look at the digits.
In both problems, Stefan kept the correct non-zero digit, which is \(2\). He also shifted the decimal point by the correct number of places:

• In \(0.2 \div 100\), he shifted the decimal point by \(2\) places (from \(0.2\) to \(20\) is a shift of \(2\) places to the right).
• In \(0.02 \div 10\), he shifted the decimal point by \(1\) place (from \(0.02\) to \(0.2\) is a shift of \(1\) place to the right).

Identify what Stefan did wrong

Stefan shifted the decimal point in the wrong direction.

• Division by powers of ten makes a number smaller, so the decimal point must shift to the left.
• Stefan shifted the decimal point to the right, which is what you do when multiplying by powers of ten.

Formulate advice for next time

To divide correctly by powers of ten:

• Count the number of zeros in the power of ten (or look at the exponent).
• Move the decimal point to the left by that many places to make the value smaller.
• Use placeholder zeros as needed.

</reasoning>

<answer>

• What Stefan did correctly: He kept the correct digit \(2\) and shifted the decimal point by the correct number of places (two places for dividing by \(100\), and one place for dividing by \(10\)).
• What Stefan did wrong: He shifted the decimal point in the wrong direction (to the right instead of to the left), which made the numbers larger instead of smaller.
• Advice for next time: When dividing by a power of ten, move the decimal point to the left by the number of zeros in the divisor to make the value smaller.

</answer>

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"Mathematics",
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"Dividing Decimals by Powers of Ten"
]
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Answer:

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<reasoning>

Analyze Stefan's work

Stefan wrote:

1. \(0.2 \div 100 = 20\)
2. \(0.02 \div 10 = 0.2\)

Let's check the actual math.

• For the first problem: \(0.2 \div 100 = 0.002\). Stefan got \(20\).
• For the second problem: \(0.02 \div 10 = 0.002\). Stefan got \(0.2\).

Identify what Stefan did correctly

Using the Decimal Place Value Relationships knowledge point, we look at the digits.
In both problems, Stefan kept the correct non-zero digit, which is \(2\). He also shifted the decimal point by the correct number of places:

• In \(0.2 \div 100\), he shifted the decimal point by \(2\) places (from \(0.2\) to \(20\) is a shift of \(2\) places to the right).
• In \(0.02 \div 10\), he shifted the decimal point by \(1\) place (from \(0.02\) to \(0.2\) is a shift of \(1\) place to the right).

Identify what Stefan did wrong

Stefan shifted the decimal point in the wrong direction.

• Division by powers of ten makes a number smaller, so the decimal point must shift to the left.
• Stefan shifted the decimal point to the right, which is what you do when multiplying by powers of ten.

Formulate advice for next time

To divide correctly by powers of ten:

• Count the number of zeros in the power of ten (or look at the exponent).
• Move the decimal point to the left by that many places to make the value smaller.
• Use placeholder zeros as needed.

</reasoning>

<answer>

• What Stefan did correctly: He kept the correct digit \(2\) and shifted the decimal point by the correct number of places (two places for dividing by \(100\), and one place for dividing by \(10\)).
• What Stefan did wrong: He shifted the decimal point in the wrong direction (to the right instead of to the left), which made the numbers larger instead of smaller.
• Advice for next time: When dividing by a power of ten, move the decimal point to the left by the number of zeros in the divisor to make the value smaller.

</answer>

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