Algebra Examples

$\frac{4.16 \cdot 10^{3} + 2.58 \cdot 10^{2}}{5.377 \cdot 10^{4}}$

Step 1

Move the decimal point in $2.58$ to the left by $1$ place and increase the power of $10^{2}$ by $1$ .

$\frac{4.16 \cdot 10^{3} + 0.258 \cdot 10^{3}}{5.377 \cdot 10^{4}}$

Step 2

Factor $10^{3}$ out of $4.16 \cdot 10^{3} + 0.258 \cdot 10^{3}$ .

$\frac{(4.16 + 0.258) \cdot 10^{3}}{5.377 \cdot 10^{4}}$

Step 3

Add $4.16$ and $0.258$ .

$\frac{4.418 \cdot 10^{3}}{5.377 \cdot 10^{4}}$

Step 4

Divide using scientific notation.

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Step 4.1

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

$(\frac{4.418}{5.377}) (\frac{10^{3}}{10^{4}})$

Step 4.2

Divide $4.418$ by $5.377$ .

$0.82164775 \frac{10^{3}}{10^{4}}$

Step 4.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$0.82164775 \cdot 10^{3 + 4 \cdot - 1}$

Step 4.4

Multiply $4$ by $- 1$ .

$0.82164775 \cdot 10^{3 - 4}$

Step 4.5

Subtract $4$ from $3$ .

$0.82164775 \cdot 10^{- 1}$

Step 5

Move the decimal point in $0.82164775$ to the right by $1$ place and decrease the power of $10^{- 1}$ by $1$ .

$8.21647758 \cdot 10^{- 2}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$8.21647758 \cdot 10^{- 2}$

Expanded Form:

$0.08216477$