How is 0.00124 expressed in proper scientific notation?

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How is 0.00124 expressed in proper scientific notation?

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Answer 1 · 2016-08-11T00:25:50

$1.24 \cdot 10^{- 3}$ $1.24 * 10^(-3)$

Explanation:

A number expressed in scientific notation must have the form

$a a m \times 10^{n a a a a a a a \leftarrow -- -} a the a exponent a a$ $color(white)(aa)color(blue)(m) xx 10^(color(purple)(n) color(white)(a)stackrel(color(white)(aaaaaa))(larr))color(white)(acolor(black)("the")acolor(purple)("exponent")aa)$
$\frac{a}{a} ↑ ⏐ ⏐ ⏐ a a a a$ $color(white)(a/acolor(black)(uarr)aaaa)$
$the a mantissa a$ $color(white)(color(black)("the")acolor(blue)("mantissa")a)$

For normalized scientific notation, the mantissa must satisfy the condition

$1 \leq | m | < 10$ $1 <= |m| < 10$

Your starting number can be written as

$0.00124 \cdot 10^{0}$ $color(blue)(0.00124) * 10^color(purple)(0)$

Your goal here will be to move the decimal place to the right until the mantissa satisfies the above condition. For every position that you move the decimal to the right you must subtract $1$ $1$ from the value of the exponent, which starts at $0$ $0$ .

So, start moving the decimal place to the right

$0.0124 \cdot 10^{- 1} \to$ $color(blue)(0.0124) * 10^color(purple)(-1) ->$ one position

$0 0.124 \cdot 10^{- 2} \to$ $color(white)(0)color(blue)(0.124) * 10^color(purple)(-2) ->$ two positions

$00 1.24 \cdot 10^{- 3} \to$ $color(white)(00)color(blue)(1.24) * 10^color(purple)(-3) ->$ three positions

At this point, the mantissa satisfies the required condition

$1 \leq 1.24 < 1$ $1 <= color(blue)(1.24) < 1$

which means that you have found the scientific notation for your original number

$0.00124 = 1.24 \cdot 10^{- 3}$ $0.00124 = 1.24 * 10^(-3)$

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How is 0.00124 expressed in proper scientific notation?

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