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

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

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

simplify

\frac{1}{2 π} e^{- \frac{( 0.1 ) ^{2}}{2}}

0.39695 \dots

Solution steps

\frac{1}{2 π} e^{- \frac{( 0.1 ) ^{2}}{2}}

Apply exponent rule:

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

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

\frac{1}{2 π} = \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

0. 1^{2} = 0.01

= \frac{1}{2 ^{\frac{1}{2}} e ^{\frac{0.01}{2}} π ^{\frac{1}{2}}}

Convert element to a decimal form

2^{\frac{1}{2}} = 1.41421 \dots

= \frac{1}{1.41421 \dots e ^{\frac{0.01}{2}} π ^{\frac{1}{2}}}

Convert element to a decimal form

π^{\frac{1}{2}} = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{\frac{0.01}{2}}}

e^{\frac{0.01}{2}} = 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

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