What is 2.5*10^{-10} ?

The solution to 2.5*10^{-10} is 1/4000000000

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simplify 2.5*10^{-10}

simplify

2.5 \cdot 1 0^{- 10}

\frac{1}{4000000000}

Decimal Notation

2.5 E - 10

Solution steps

2.5 \cdot 1 0^{- 10}

Apply exponent rule:

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

1 0^{- 10} = \frac{1}{1 0 ^{10}}

= 2.5 \cdot \frac{1}{1 0 ^{10}}

2.5 \cdot \frac{1}{1 0 ^{10}} = \frac{2.5}{1 0 ^{10}}

= \frac{2.5}{1 0 ^{10}}

\frac{2.5}{1 0 ^{10}} = \frac{25}{10 \cdot 1 0 ^{10}}

= \frac{25}{10 \cdot 1 0 ^{10}}

10 \cdot 1 0^{10} = 1 0^{11}

= \frac{25}{1 0 ^{11}}

Factor the number:

25 = 5^{2}

= \frac{5 ^{2}}{1 0 ^{11}}

Factor

1 0^{11} : 5^{11} \cdot 2^{11}

= \frac{5 ^{2}}{5 ^{11} \cdot 2 ^{11}}

\frac{5 ^{2}}{5 ^{11}} = \frac{1}{5 ^{9}}

= \frac{1}{5 ^{9} \cdot 2 ^{11}}

5^{9} \cdot 2^{11} = 4000000000

= \frac{1}{4000000000}

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