What is 1/(sqrt(2pi))e^{-1/2 0.1^2} ?

The solution to 1/(sqrt(2pi))e^{-1/2 0.1^2} is 0.39695…

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simplify 1/(sqrt(2pi))e^{-1/2 0.1^2}

simplify

\frac{1}{2 π} e^{- \frac{1}{2} 0. 1^{2}}

0.39695 \dots

Solution steps

\frac{1}{2 π} e^{- \frac{1}{2} \cdot 0. 1^{2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{2 π} \cdot \frac{1}{e ^{0. 1^{2} \cdot \frac{1}{2}}}

\frac{1}{2 π} = \frac{1}{2 π}

= \frac{1}{2 π} \cdot \frac{1}{e ^{0. 1^{2} \cdot \frac{1}{2}}}

\frac{1}{e ^{\frac{1}{2} \cdot 0. 1^{2}}} = \frac{1}{e ^{0.005}}

= \frac{1}{e ^{0.005}} \cdot \frac{1}{2 π}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 π e ^{0.005}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 e ^{0.005} π}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{1}{1.41421 \dots e ^{0.005} π}

Convert element to a decimal form

π = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{0.005}}

e^{0.005} = 1.00501 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots \cdot 1.00501 \dots}

Multiply the numbers:

1.41421 \dots \cdot 1.77245 \dots \cdot 1.00501 \dots = 2.51919 \dots

= \frac{1}{2.51919 \dots}

Divide the numbers:

\frac{1}{2.51919 \dots} = 0.39695 \dots

= 0.39695 \dots

7^{6}

12 e^{- 3}

2.3 \cdot 1 0^{- 2}

What is 1/(sqrt(2pi))e^{-1/2 0.1^2} ?
The solution to 1/(sqrt(2pi))e^{-1/2 0.1^2} is 0.39695…