How do I convert 3427 into scientific notation?

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How do I convert 3427 into scientific notation?

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Answer 1 · 2014-10-11T15:06:11

A number in scientific notation is in the form

$a \cdot 10^{b}$ $a * 10^b$

Generally,

$1 \leq a < 10$ $1 <= a < 10$

For $3427$ $3427$ , the decimal point is on the right of 7

$3427.0$ $3427.0$

We need to move the decimal such that $1 \leq a < 10$ $1 <= a < 10$ will be satisfied.

However, we also need to retain its value.
For each movement of the decimal place to the left, multiply the number by 10.

To satisfy $1 \leq a < 10$ $1 <= a < 10$ , the decimal place needs to move by 3 places to the left.

Hence, we have

$3.427 \cdot 10^{3}$ $3.427 * 10^3$

For the longer version of converting to scientific notation, we have
$3427 \cdot (1) = 3427$ $3427 * (1) = 3427$
$3427 \cdot (\frac{1}{10} \cdot 10) = 3427$ $3427 * (1/10 * 10) = 3427$
$(3427 \cdot \frac{1}{10}) \cdot 10 = 3427$ $(3427 * 1/10) * 10 = 3427$
$342.7 \cdot 10 = 3427$ $342.7 * 10 = 3427$

$342.7 \cdot 1 \cdot 10 = 3427$ $342.7 * 1 * 10 = 3427$
$342.7 \cdot (\frac{1}{10} \cdot 10) \cdot 10 = 3427$ $342.7 * (1/10 * 10) * 10 = 3427$
$(342.7 \cdot \frac{1}{10}) \cdot (10 \cdot 10) = 3427$ $(342.7 * 1/10) * (10 * 10) = 3427$
$34.27 \cdot (10^{2}) = 3427$ $34.27 * (10^2) = 3427$

$34.27 \cdot 1 \cdot (10^{2}) = 3427$ $34.27 * 1 * (10^2) = 3427$
$34.27 \cdot (\frac{1}{10} \cdot 10) \cdot (10^{2}) = 3427$ $34.27 * (1/10 * 10) * (10^2) = 3427$
$(34.27 \cdot \frac{1}{10}) \cdot (10 \cdot 10^{2}) = 3427$ $(34.27 * 1/10) * (10 * 10^2) = 3427$
$3.427 \cdot 10^{3} = 3427$ $3.427 * 10^3 = 3427$

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How do I convert 3427 into scientific notation?

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