Estimate With Powers of 10 - 8th Grade Math
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What is $10^0$?
What is $10^0$?
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$10^0=1$. Any number to the zero power equals 1.
$10^0=1$. Any number to the zero power equals 1.
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What is $10^{-3}$ written as a decimal?
What is $10^{-3}$ written as a decimal?
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$0.001$. Move decimal 3 places left: $\frac{1}{1000}=0.001$.
$0.001$. Move decimal 3 places left: $\frac{1}{1000}=0.001$.
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Estimate $6.7\times10^8$ to one significant digit in the form $a\times10^n$.
Estimate $6.7\times10^8$ to one significant digit in the form $a\times10^n$.
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$7\times10^8$. Round 6.7 to nearest whole number.
$7\times10^8$. Round 6.7 to nearest whole number.
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Which is greater: $3\times10^{-6}$ or $7\times10^{-7}$?
Which is greater: $3\times10^{-6}$ or $7\times10^{-7}$?
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$3\times10^{-6}$. Less negative means larger; $-6 > -7$.
$3\times10^{-6}$. Less negative means larger; $-6 > -7$.
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Which number is larger: $6\times10^4$ or $5\times10^5$?
Which number is larger: $6\times10^4$ or $5\times10^5$?
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$5\times10^5$. Compare exponents first; $10^5 > 10^4$.
$5\times10^5$. Compare exponents first; $10^5 > 10^4$.
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What is $\frac{8\times10^9}{2\times10^3}$ in scientific notation?
What is $\frac{8\times10^9}{2\times10^3}$ in scientific notation?
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$4\times10^6$. Divide coefficients $(8÷2=4)$ and subtract exponents $(9-3=6)$.
$4\times10^6$. Divide coefficients $(8÷2=4)$ and subtract exponents $(9-3=6)$.
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What is $(2\times10^6)(3\times10^2)$ in scientific notation?
What is $(2\times10^6)(3\times10^2)$ in scientific notation?
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$6\times10^8$. Multiply coefficients $(2×3=6)$ and add exponents $(6+2=8)$.
$6\times10^8$. Multiply coefficients $(2×3=6)$ and add exponents $(6+2=8)$.
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What does a negative exponent mean in $a\times10^n$ when $n<0$?
What does a negative exponent mean in $a\times10^n$ when $n<0$?
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A small number; the decimal moves left $|n|$ places. Negative powers of 10 divide by 10 repeatedly, creating fractions.
A small number; the decimal moves left $|n|$ places. Negative powers of 10 divide by 10 repeatedly, creating fractions.
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What does a positive exponent mean in $a\times10^n$ when $n>0$?
What does a positive exponent mean in $a\times10^n$ when $n>0$?
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A large number; the decimal moves right $n$ places. Positive powers of 10 multiply by 10 repeatedly, making larger values.
A large number; the decimal moves right $n$ places. Positive powers of 10 multiply by 10 repeatedly, making larger values.
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What is the meaning of writing a number in the form $a\times10^n$ with $1\le a<10$?
What is the meaning of writing a number in the form $a\times10^n$ with $1\le a<10$?
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Scientific notation using a single digit times a power of $10$. Ensures the coefficient is between 1 and 10 for standard form.
Scientific notation using a single digit times a power of $10$. Ensures the coefficient is between 1 and 10 for standard form.
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State the quotient rule for powers of $10$: $\frac{10^a}{10^b}=?$
State the quotient rule for powers of $10$: $\frac{10^a}{10^b}=?$
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$10^{a-b}$. When dividing powers, subtract the exponents.
$10^{a-b}$. When dividing powers, subtract the exponents.
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Find and correct the scientific notation error: $0.52\times10^6$.
Find and correct the scientific notation error: $0.52\times10^6$.
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$5.2\times10^5$. Coefficient must be $≥1$; shift decimal right.
$5.2\times10^5$. Coefficient must be $≥1$; shift decimal right.
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Estimate $6.2\times10^7+3.9\times10^7$ as a single digit times $10^n$.
Estimate $6.2\times10^7+3.9\times10^7$ as a single digit times $10^n$.
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$1\times10^8$. Sum is $10.1×10^7 ≈ 1×10^8$ when rounded.
$1\times10^8$. Sum is $10.1×10^7 ≈ 1×10^8$ when rounded.
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How many times as much is $4\times10^6$ as $2\times10^4$?
How many times as much is $4\times10^6$ as $2\times10^4$?
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$200$ times. $(4÷2)×10^{6-4} = 2×10^2 = 200$.
$200$ times. $(4÷2)×10^{6-4} = 2×10^2 = 200$.
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What does $10^n$ mean when $n$ is a positive integer?
What does $10^n$ mean when $n$ is a positive integer?
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$10^n$ is $1$ followed by $n$ zeros. Positive exponents show how many zeros follow the 1.
$10^n$ is $1$ followed by $n$ zeros. Positive exponents show how many zeros follow the 1.
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What is the standard form pattern for a number written as a single digit times a power of $10$?
What is the standard form pattern for a number written as a single digit times a power of $10$?
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$a\times 10^n$ where $1\le a<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with integer exponent.
$a\times 10^n$ where $1\le a<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with integer exponent.
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What does $10^{-n}$ mean when $n$ is a positive integer?
What does $10^{-n}$ mean when $n$ is a positive integer?
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$10^{-n}=\frac{1}{10^n}$. Negative exponents create fractions with positive exponents in denominator.
$10^{-n}=\frac{1}{10^n}$. Negative exponents create fractions with positive exponents in denominator.
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What is $4\times 10^5$ written in standard decimal form?
What is $4\times 10^5$ written in standard decimal form?
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$400000$. Move decimal 5 places right from 4.
$400000$. Move decimal 5 places right from 4.
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What is $7\times 10^{-4}$ written in standard decimal form?
What is $7\times 10^{-4}$ written in standard decimal form?
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$0.0007$. Move decimal 4 places left from 7.
$0.0007$. Move decimal 4 places left from 7.
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What is $6{,}200{,}000$ written as $a\times 10^n$ with $1\le a<10$?
What is $6{,}200{,}000$ written as $a\times 10^n$ with $1\le a<10$?
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$6.2\times 10^6$. Move decimal left until one non-zero digit remains before it.
$6.2\times 10^6$. Move decimal left until one non-zero digit remains before it.
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What is $0.000045$ written as $a\times 10^n$ with $1\le a<10$?
What is $0.000045$ written as $a\times 10^n$ with $1\le a<10$?
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$4.5\times 10^{-5}$. Count 5 decimal places from first non-zero digit.
$4.5\times 10^{-5}$. Count 5 decimal places from first non-zero digit.
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What is the product $(3\times 10^6)(2\times 10^4)$ written in scientific notation?
What is the product $(3\times 10^6)(2\times 10^4)$ written in scientific notation?
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$6\times 10^{10}$. Multiply coefficients $(3×2=6)$ and add exponents $(6+4=10)$.
$6\times 10^{10}$. Multiply coefficients $(3×2=6)$ and add exponents $(6+4=10)$.
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What is the quotient $\frac{8\times 10^7}{2\times 10^3}$ written in scientific notation?
What is the quotient $\frac{8\times 10^7}{2\times 10^3}$ written in scientific notation?
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$4\times 10^4$. Divide coefficients $(8÷2=4)$ and subtract exponents $(7-3=4)$.
$4\times 10^4$. Divide coefficients $(8÷2=4)$ and subtract exponents $(7-3=4)$.
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What is $(5\times 10^9)+(2\times 10^9)$ written in scientific notation?
What is $(5\times 10^9)+(2\times 10^9)$ written in scientific notation?
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$7\times 10^9$. Add coefficients when exponents match: $5+2=7$.
$7\times 10^9$. Add coefficients when exponents match: $5+2=7$.
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Which is larger: $6\times 10^5$ or $4\times 10^6$?
Which is larger: $6\times 10^5$ or $4\times 10^6$?
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$4\times 10^6$. Compare exponents first; $10^6>10^5$ regardless of coefficients.
$4\times 10^6$. Compare exponents first; $10^6>10^5$ regardless of coefficients.
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What is $3.4\times 10^7$ rounded to $1$ significant digit in scientific notation?
What is $3.4\times 10^7$ rounded to $1$ significant digit in scientific notation?
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$3\times 10^7$. Round 3.4 down to 3 for one significant digit.
$3\times 10^7$. Round 3.4 down to 3 for one significant digit.
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What is the estimate of $5.1\times 10^6+2.9\times 10^6$ to $1$ significant digit?
What is the estimate of $5.1\times 10^6+2.9\times 10^6$ to $1$ significant digit?
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$8\times 10^6$. Sum is $8×10^6$; both round to same power for easy addition.
$8\times 10^6$. Sum is $8×10^6$; both round to same power for easy addition.
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What is the estimate of $\frac{6\times 10^8}{2\times 10^6}$ as a whole number?
What is the estimate of $\frac{6\times 10^8}{2\times 10^6}$ as a whole number?
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$300$. Divide coefficients and subtract exponents: $6÷2×10^{8-6}=3×10^2$.
$300$. Divide coefficients and subtract exponents: $6÷2×10^{8-6}=3×10^2$.
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How many times as large is $7\times 10^9$ compared to $3\times 10^8$ (nearest whole number)?
How many times as large is $7\times 10^9$ compared to $3\times 10^8$ (nearest whole number)?
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$23$ times. Calculate $\frac{7×10^9}{3×10^8}=\frac{7}{3}×10^1≈23.3$, round to 23.
$23$ times. Calculate $\frac{7×10^9}{3×10^8}=\frac{7}{3}×10^1≈23.3$, round to 23.
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What is the value of $\frac{9\times 10^{-2}}{3\times 10^{-5}}$ written in scientific notation?
What is the value of $\frac{9\times 10^{-2}}{3\times 10^{-5}}$ written in scientific notation?
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$3\times 10^3$. Divide coefficients ($9 \div 3 = 3$) and subtract exponents ($-2 - (-5) = 3$)
$3\times 10^3$. Divide coefficients ($9 \div 3 = 3$) and subtract exponents ($-2 - (-5) = 3$)
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