Trigonometry Examples

$\sqrt{\frac{5.4 + 9.5 \cdot 10^{- 3}}{6000} \cdot (1.1)}$

Step 1

Convert $5.4$ to scientific notation.

$\sqrt{\frac{5.4 \cdot 10^{0} + 9.5 \cdot 10^{- 3}}{6000} \cdot 1.1}$

Step 2

Move the decimal point in $9.5$ to the left by $3$ places and increase the power of $10^{- 3}$ by $3$ .

$\sqrt{\frac{5.4 \cdot 10^{0} + 0.0095 \cdot 10^{0}}{6000} \cdot 1.1}$

Step 3

Factor $10^{0}$ out of $5.4 \cdot 10^{0} + 0.0095 \cdot 10^{0}$ .

$\sqrt{\frac{(5.4 + 0.0095) \cdot 10^{0}}{6000} \cdot 1.1}$

Step 4

Add $5.4$ and $0.0095$ .

$\sqrt{\frac{5.4095 \cdot 10^{0}}{6000} \cdot 1.1}$

Step 5

Divide using scientific notation.

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Step 5.1

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

$\sqrt{(\frac{5.4095}{6000}) (\frac{10^{0}}{1}) \cdot 1.1}$

Step 5.2

Divide $5.4095$ by $6000$ .

$\sqrt{0.00090158 \frac{10^{0}}{1} \cdot 1.1}$

Step 5.3

Divide $10^{0}$ by $1$ .

$\sqrt{0.00090158 \cdot 10^{0} \cdot 1.1}$

Step 6

Multiply $0.00090158$ by $1.1$ .

$\sqrt{0.00099174 \cdot 10^{0}}$

Step 7

Rewrite $\sqrt{0.00099174 \cdot 10^{0}}$ as $\sqrt{0.00099174} \cdot \sqrt{10^{0}}$ .

$\sqrt{0.00099174} \cdot \sqrt{10^{0}}$

Step 8

Evaluate the root.

$0.03149193 \cdot \sqrt{10^{0}}$

Step 9

Rewrite $10^{0}$ as ${(10^{0})}^{2}$ .

$0.03149193 \cdot \sqrt{{(10^{0})}^{2}}$

Step 10

Pull terms out from under the radical, assuming positive real numbers.

$0.03149193 \cdot 10^{0}$

Step 11

Move the decimal point in $0.03149193$ to the right by $2$ places and decrease the power of $10^{0}$ by $2$ .

$3.14919301 \cdot 10^{- 2}$

Step 12

The result can be shown in multiple forms.

Scientific Notation:

$3.14919301 \cdot 10^{- 2}$

Expanded Form:

$0.03149193$