Basic Math Examples

$0.3513 \cdot (10^{27} \div 10^{23}) = 0.3513 \cdot 10^{r}$

Step 1

Rewrite the equation as $0.3513 \cdot 10^{r} = 0.3513 \cdot 10^{27} \div 10^{23}$ .

$0.3513 \cdot 10^{r} = 0.3513 \cdot 10^{27} \div 10^{23}$

Step 2

Simplify.

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Step 2.1

Move the decimal point in $0.3513$ to the right by $1$ place and decrease the power of $10^{27}$ by $1$ .

$0.3513 \cdot 10^{r} = 3.513 \cdot 10^{26} \div 10^{23}$

Step 2.2

Reduce the expression $3.513 \cdot 10^{26} \div 10^{23}$ by cancelling the common factors.

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Step 2.2.1

Factor $10^{23}$ out of $3.513 \cdot 10^{26}$ .

$0.3513 \cdot 10^{r} = 10^{23} \cdot 3.513 \cdot 10^{3} \div 10^{23}$

Step 2.2.2

Multiply by $1$ .

$0.3513 \cdot 10^{r} = 10^{23} \cdot 3.513 \cdot 10^{3} \div 10^{23} \cdot 1$

Step 2.2.3

Cancel the common factor.

$0.3513 \cdot 10^{r} = 10^{23} \cdot 3.513 \cdot 10^{3} \div 10^{23} \cdot 1$

Step 2.2.4

Rewrite the expression.

$0.3513 \cdot 10^{r} = \frac{3.513 \cdot 10^{3}}{1}$

Step 2.3

Divide $3.513 \cdot 10^{3}$ by $1$ .

$0.3513 \cdot 10^{r} = 3.513 \cdot 10^{3}$

Step 3

Divide each term in $0.3513 \cdot 10^{r} = 3.513 \cdot 10^{3}$ by $0.3513$ and simplify.

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Step 3.1

Divide each term in $0.3513 \cdot 10^{r} = 3.513 \cdot 10^{3}$ by $0.3513$ .

$\frac{0.3513 \cdot 10^{r}}{0.3513} = \frac{3.513 \cdot 10^{3}}{0.3513}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.3513$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.3513 \cdot 10^{r}}{0.3513} = \frac{3.513 \cdot 10^{3}}{0.3513}$

Step 3.2.1.2

Divide $10^{r}$ by $1$ .

$10^{r} = \frac{3.513 \cdot 10^{3}}{0.3513}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide using scientific notation.

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Step 3.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$10^{r} = (\frac{3.513}{0.3513}) (\frac{10^{3}}{1})$

Step 3.3.1.2

Divide $3.513$ by $0.3513$ .

$10^{r} = 10 \frac{10^{3}}{1}$

Step 3.3.1.3

Divide $10^{3}$ by $1$ .

$10^{r} = 10 \cdot 10^{3}$

Step 3.3.2

Multiply $10$ by $10^{3}$ by adding the exponents.

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Step 3.3.2.1

Multiply $10$ by $10^{3}$ .

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Step 3.3.2.1.1

Raise $10$ to the power of $1$ .

$10^{r} = 10^{1} \cdot 10^{3}$

Step 3.3.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10^{r} = 10^{1 + 3}$

Step 3.3.2.2

Add $1$ and $3$ .

$10^{r} = 10^{4}$

Step 3.3.3

Raise $10$ to the power of $4$ .

$10^{r} = 10000$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$10^{r} = 10^{4}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$r = 4$