# What is the scientific notation of 0.0002?

Mar 25, 2015

$2 \times {10}^{- 4}$

I know scientific notation has one non-0 digit before the decimal point. So I know the scientific notation for $0.0002$ is

$2 \times {10}^{\text{some number}}$. (We don't write "$2.$", just "$2$")

Multiplying by $10$ to a positive whole number moves the decimal to the right. I need to multiply $2$ to move the decimal to the left. To "recover" the number $0.0002$ from $2$, I need to move the decimal 4 to the left. That means I multiply by ${10}^{- 4}$

This of this:

$2 \times {10}^{1} = 20$ (decimal moved one to the right)
$2 \times {10}^{- 1} = 0.2$ (decimal moved one to the left)

$2 \times {10}^{- 2} = 0.02$ (decimal moved one to the left)

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$2 \times {10}^{- 4} = 0.0002$

Extra example:

What is the scientific notation for $0.0000037$ ?

I know it starts as $3.7 \times {10}^{\text{some number}}$

To "recover $0.0000037$ from $3.7$, we need to move the decimal how far, in which direction?

So we need to multiply $\times 10$ to what power?

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.

.#3.7xx10^(-6)

Last extra example
Write $47 , 000$ in scientific notation.

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$4.7 \times {10}^{\text{some number}}$

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.Did you get $4.7 \times {10}^{4}$? Congratulatons! You can do it now.

Mar 25, 2015

Scientific notation includes a coefficient consisting of a single digit in front of the decimal, numbers 1 - 9 inclusive, multiplied times the base 10 raised to some power. When a number is not already written in scientific notation, we need to move the decimal to the right or to the left so that there is a single digit in front of the decimal. The power of 10 is the same number as the decimal places that were moved. If the decimal is moved to the right, the exponent (power) is negative, and if the decimal is moved to the left, the exponent is positive.

To change $0.0002$ to scientific notation, move the decimal to the right 4 places so that you get 2. The exponent on the base 10 will be -4 because the decimal was moved to the right 4 places. So $0.0002$ in scientific notation is $2 \times {10}^{- 4}$.

Mar 25, 2015

Scientific notation includes a coefficient consisting of a single digit in front of the decimal, numbers 1 - 9 inclusive, multiplied times the base 10 raised to some power.

When a number is not already written in scientific notation, we need to move the decimal to the right or to the left so that there is a single digit in front of the decimal. The power of 10 is the same number as the decimal places that were moved. If the decimal is moved to the right, the exponent (power) is negative, and if the decimal is moved to the left, the exponent is positive.

To change $0.0002$ to scientific notation, move the decimal to the right 4 places so that you get 2. The exponent on the base 10 will be -4 because the decimal was moved to the right 4 places. So $0.0002$ in scientific notation is $2 \times {10}^{- 4}$.