Question Find the equation that shows how to multiply $1,000,000$ and $1,000,000$ using scientific notation: $A. (1 \times 10^{6}) \times (1 \times 10^{6}) = 1 \times 10^{12}$

Studdy Solution

STEP 1

Assumptions
1. We are working with the number $1,000,000$ .
2. We want to express $1,000,000$ in scientific notation.
3. We want to find the product of two $1,000,000$ numbers using scientific notation.
4. We need to apply the rules of exponents when multiplying numbers in scientific notation.

STEP 2

Express $1,000,000$ in scientific notation. Scientific notation is of the form $a \times 10^{n}$ , where $1 \leq a < 10$ and $n$ is an integer.
$1,000,000 = 1 \times 10^{6}$

STEP 3

Write the product of $1,000,000$ and $1,000,000$ using their scientific notation forms.
$1,000,000 \times 1,000,000 = \left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)$

STEP 4

Apply the rule for multiplying powers with the same base: $a^{m} \times a^{n} = a^{m+n}$ .
$\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right) = 1 \times 10^{6+6}$

STEP 5

Add the exponents.
$1 \times 10^{6+6} = 1 \times 10^{12}$

STEP 6

The final expression in scientific notation for the product of $1,000,000$ and $1,000,000$ is:
$1 \times 10^{12}$

STEP 7

Compare the result with the given options. The correct equation that shows how to find the product of $1,000,000$ and $1,000,000$ using scientific notation is:
$1,000,000 \times 1,000,000=\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)=1 \times 10^{(6+6)}=1 \times 10^{12}$
This corresponds to option A.
The correct answer is A. $1,000,000 \times 1,000,000=\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)=1 \times 10^{(6+6)}=1 \times 10^{12}$ .

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Question Find the equation that shows how to multiply $1,000,000$ and $1,000,000$ using scientific notation: $A. (1 \times 10^{6}) \times (1 \times 10^{6}) = 1 \times 10^{12}$

Studdy Solution

STEP 1

Assumptions
1. We are working with the number $1,000,000$ .
2. We want to express $1,000,000$ in scientific notation.
3. We want to find the product of two $1,000,000$ numbers using scientific notation.
4. We need to apply the rules of exponents when multiplying numbers in scientific notation.

STEP 2

Express $1,000,000$ in scientific notation. Scientific notation is of the form $a \times 10^{n}$ , where $1 \leq a < 10$ and $n$ is an integer.
$1,000,000 = 1 \times 10^{6}$

STEP 3

Write the product of $1,000,000$ and $1,000,000$ using their scientific notation forms.
$1,000,000 \times 1,000,000 = \left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)$

STEP 4

Apply the rule for multiplying powers with the same base: $a^{m} \times a^{n} = a^{m+n}$ .
$\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right) = 1 \times 10^{6+6}$

STEP 5

Add the exponents.
$1 \times 10^{6+6} = 1 \times 10^{12}$

STEP 6

The final expression in scientific notation for the product of $1,000,000$ and $1,000,000$ is:
$1 \times 10^{12}$

STEP 7

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Question Find the equation that shows how to multiply 1,000,0001,000,0001,000,000 and 1,000,0001,000,0001,000,000 using scientific notation: A.(1×106)×(1×106)=1×1012A. (1 \times 10^{6}) \times (1 \times 10^{6}) = 1 \times 10^{12}A.(1×106)×(1×106)=1×1012

Studdy Solution

STEP 1

STEP 2

Express 1,000,0001,000,0001,000,000 in scientific notation. Scientific notation is of the form a×10na \times 10^{n}a×10n, where 1≤a<101 \leq a < 101≤a<10 and nnn is an integer.1,000,000=1×1061,000,000 = 1 \times 10^{6}1,000,000=1×106

STEP 3

Write the product of 1,000,0001,000,0001,000,000 and 1,000,0001,000,0001,000,000 using their scientific notation forms.1,000,000×1,000,000=(1×106)×(1×106)1,000,000 \times 1,000,000 = \left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)1,000,000×1,000,000=(1×106)×(1×106)

STEP 4

Apply the rule for multiplying powers with the same base: am×an=am+na^{m} \times a^{n} = a^{m+n}am×an=am+n.(1×106)×(1×106)=1×106+6\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right) = 1 \times 10^{6+6}(1×106)×(1×106)=1×106+6

STEP 5

Add the exponents.1×106+6=1×10121 \times 10^{6+6} = 1 \times 10^{12}1×106+6=1×1012

STEP 6

The final expression in scientific notation for the product of 1,000,0001,000,0001,000,000 and 1,000,0001,000,0001,000,000 is:1×10121 \times 10^{12}1×1012

STEP 7

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Studdy solves anything!

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Question Find the equation that shows how to multiply $1,000,000$ and $1,000,000$ using scientific notation: $A. (1 \times 10^{6}) \times (1 \times 10^{6}) = 1 \times 10^{12}$

Express $1,000,000$ in scientific notation. Scientific notation is of the form $a \times 10^{n}$ , where $1 \leq a < 10$ and $n$ is an integer.
$1,000,000 = 1 \times 10^{6}$

Write the product of $1,000,000$ and $1,000,000$ using their scientific notation forms.
$1,000,000 \times 1,000,000 = \left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right)$

Apply the rule for multiplying powers with the same base: $a^{m} \times a^{n} = a^{m+n}$ .
$\left(1 \times 10^{6}\right) \times\left(1 \times 10^{6}\right) = 1 \times 10^{6+6}$

Add the exponents.
$1 \times 10^{6+6} = 1 \times 10^{12}$

The final expression in scientific notation for the product of $1,000,000$ and $1,000,000$ is:
$1 \times 10^{12}$