Basic Math Examples

$10^{- 6} - 2.4 \cdot 10^{- 7}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10^{6}} - 2.4 \cdot 10^{- 7}$

Step 1.2

Raise $10$ to the power of $6$ .

$\frac{1}{1000000} - 2.4 \cdot 10^{- 7}$

Step 2

To write $- 2.4 \cdot 10^{- 7}$ as a fraction with a common denominator, multiply by $\frac{1000000}{1000000}$ .

$\frac{1}{1000000} - 2.4 \cdot 10^{- 7} \cdot \frac{1000000}{1000000}$

Step 3

Combine fractions.

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Step 3.1

Combine $- 2.4 \cdot 10^{- 7}$ and $\frac{1000000}{1000000}$ .

$\frac{1}{1000000} + \frac{- 2.4 \cdot 10^{- 7} \cdot 1000000}{1000000}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1 - 2.4 \cdot 10^{- 7} \cdot 1000000}{1000000}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 2.4$ by $1000000$ .

$\frac{1 - 2400000 \cdot 10^{- 7}}{1000000}$

Step 4.2

Move the decimal point in $- 2400000$ to the left by $6$ places and increase the power of $10^{- 7}$ by $6$ .

$\frac{1 - 2.4 \cdot 10^{- 1}}{1000000}$

Step 4.3

Convert $1$ to scientific notation.

$\frac{1 \cdot 10^{0} - 2.4 \cdot 10^{- 1}}{1000000}$

Step 4.4

Move the decimal point in $- 2.4$ to the left by $1$ place and increase the power of $10^{- 1}$ by $1$ .

$\frac{1 \cdot 10^{0} - 0.24 \cdot 10^{0}}{1000000}$

Step 4.5

Factor $10^{0}$ out of $1 \cdot 10^{0} - 0.24 \cdot 10^{0}$ .

$\frac{(1 - 0.24) \cdot 10^{0}}{1000000}$

Step 4.6

Subtract $0.24$ from $1$ .

$\frac{0.76 \cdot 10^{0}}{1000000}$

Step 4.7

Move the decimal point in $0.76$ to the right by $1$ place and decrease the power of $10^{0}$ by $1$ .

$\frac{7.6 \cdot 10^{- 1}}{1000000}$

Step 4.8

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{7.6 \cdot \frac{1}{10}}{1000000}$

Step 5

Combine $7.6$ and $\frac{1}{10}$ .

$\frac{\frac{7.6}{10}}{1000000}$

Step 6

Simplify by dividing numbers.

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Step 6.1

Divide $7.6$ by $10$ .

$\frac{0.76}{1000000}$

Step 6.2

Divide $0.76$ by $1000000$ .

$0.00000076$