Understand Powers of 10 Patterns - 5th Grade Math
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What is $1200\div 10^2$?
What is $1200\div 10^2$?
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$12$. Remove 2 zeros from $1200$ to get $12$.
$12$. Remove 2 zeros from $1200$ to get $12$.
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What does $10^n$ mean when $n$ is a whole number?
What does $10^n$ mean when $n$ is a whole number?
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$10^n$ means $10$ multiplied by itself $n$ times. The exponent shows how many times to use $10$ as a factor.
$10^n$ means $10$ multiplied by itself $n$ times. The exponent shows how many times to use $10$ as a factor.
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Which expression is equal to $3.6\times 1000$: $3.6\times 10^3$ or $3.6\times 10^2$?
Which expression is equal to $3.6\times 1000$: $3.6\times 10^3$ or $3.6\times 10^2$?
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$3.6\times 10^3$. $1000 = 10^3$, so use the first expression.
$3.6\times 10^3$. $1000 = 10^3$, so use the first expression.
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Find and correct the error: $4.2\times 10^2=4.200$.
Find and correct the error: $4.2\times 10^2=4.200$.
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Correct: $4.2\times 10^2=420$. Decimal moves 2 places right, not adds zeros after decimal.
Correct: $4.2\times 10^2=420$. Decimal moves 2 places right, not adds zeros after decimal.
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What is the value of $10^0\times 7.3$?
What is the value of $10^0\times 7.3$?
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$7.3$. Since $10^0 = 1$, this equals $1 \times 7.3 = 7.3$.
$7.3$. Since $10^0 = 1$, this equals $1 \times 7.3 = 7.3$.
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What exponent $n$ makes $10^n=100000$?
What exponent $n$ makes $10^n=100000$?
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$n=5$. Count the zeros: $100000$ has 5 zeros.
$n=5$. Count the zeros: $100000$ has 5 zeros.
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What is $4.005\times 10^2$?
What is $4.005\times 10^2$?
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$400.5$. Move decimal 2 places right: $4.005 → 400.5$.
$400.5$. Move decimal 2 places right: $4.005 → 400.5$.
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What is $0.56\times 10^3$?
What is $0.56\times 10^3$?
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$560$. Move decimal 3 places right: $0.56 → 560$.
$560$. Move decimal 3 places right: $0.56 → 560$.
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What is $47\times 10^3$?
What is $47\times 10^3$?
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$47000$. Append 3 zeros to $47$ to get $47000$.
$47000$. Append 3 zeros to $47$ to get $47000$.
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What is $600\times 10^2$?
What is $600\times 10^2$?
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$60000$. Append 2 zeros to $600$ to get $60000$.
$60000$. Append 2 zeros to $600$ to get $60000$.
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What is $8.4\times 10^2$?
What is $8.4\times 10^2$?
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$840$. Move decimal 2 places right: $8.4 → 840$.
$840$. Move decimal 2 places right: $8.4 → 840$.
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What are the values of $10^0$, $10^1$, $10^2$, and $10^3$?
What are the values of $10^0$, $10^1$, $10^2$, and $10^3$?
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$10^0=1$, $10^1=10$, $10^2=100$, $10^3=1000$. Each power of $10$ adds one more zero to the previous value.
$10^0=1$, $10^1=10$, $10^2=100$, $10^3=1000$. Each power of $10$ adds one more zero to the previous value.
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What is the rule for multiplying a whole number by $10^n$?
What is the rule for multiplying a whole number by $10^n$?
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Multiply by $10^n$: append $n$ zeros to the whole number. Each power of $10$ adds that many zeros to the end.
Multiply by $10^n$: append $n$ zeros to the whole number. Each power of $10$ adds that many zeros to the end.
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What is the rule for multiplying a decimal by $10^n$?
What is the rule for multiplying a decimal by $10^n$?
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Multiply by $10^n$: move the decimal point $n$ places right. Each power of $10$ shifts digits left by that many places.
Multiply by $10^n$: move the decimal point $n$ places right. Each power of $10$ shifts digits left by that many places.
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What is the rule for dividing a decimal by $10^n$?
What is the rule for dividing a decimal by $10^n$?
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Divide by $10^n$: move the decimal point $n$ places left. Division shifts digits right, making the number smaller.
Divide by $10^n$: move the decimal point $n$ places left. Division shifts digits right, making the number smaller.
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What is the pattern in the number of zeros in $10^n$?
What is the pattern in the number of zeros in $10^n$?
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$10^n$ has exactly $n$ zeros for $n\ge 1$. The exponent equals the zero count (except $10^0=1$).
$10^n$ has exactly $n$ zeros for $n\ge 1$. The exponent equals the zero count (except $10^0=1$).
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What is $0.9\div 10^3$?
What is $0.9\div 10^3$?
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$0.0009$. Move decimal 3 places left: $0.9 → 0.0009$.
$0.0009$. Move decimal 3 places left: $0.9 → 0.0009$.
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What is $67\div 10^2$?
What is $67\div 10^2$?
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$0.67$. Move decimal 2 places left: $67 → 0.67$.
$0.67$. Move decimal 2 places left: $67 → 0.67$.
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What is $5.2\div 10^1$?
What is $5.2\div 10^1$?
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$0.52$. Move decimal 1 place left: $5.2 → 0.52$.
$0.52$. Move decimal 1 place left: $5.2 → 0.52$.
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What is $52.08\times 10^1$?
What is $52.08\times 10^1$?
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$520.8$. Move decimal 1 place right.
$520.8$. Move decimal 1 place right.
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