What is the scientific notation of 0.0002?

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What is the scientific notation of 0.0002?

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Answer 1 · 2015-03-25T02:42:31

$2 \times 10^{- 4}$ $2xx10^(-4)$

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

$2 \times 10^{some number}$ $2xx10^"some number"$ . (We don't write " $2 .$ $2.$ ", just " $2$ $2$ ")

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

This of this:

$2 \times 10^{1} = 20$ $2xx10^1=20$ (decimal moved one to the right)
$2 \times 10^{- 1} = 0.2$ $2xx10^(-1)=0.2$ (decimal moved one to the left)

$2 \times 10^{- 2} = 0.02$ $2xx10^(-2)=0.02$ (decimal moved one to the left)

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$2 \times 10^{- 4} = 0.0002$ $2xx10^(-4)=0.0002$

Extra example:

What is the scientific notation for $0.0000037$ $0.0000037$ ?

I know it starts as $3.7 \times 10^{some number}$ $3.7xx10^"some number"$

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

So we need to multiply $\times 10$ $xx10$ to what power?

.

.#3.7xx10^(-6)

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

.

$4.7 \times 10^{some number}$ $4.7xx10^"some number"$

.

.Did you get $4.7 \times 10^{4}$ $4.7xx10^4$ ? Congratulatons! You can do it now.

Answer 2 · 2015-03-25T02:47:48

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 $0.0002$ $0.0002$ 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 $0.0002$ $0.0002$ in scientific notation is $2 \times 10^{- 4}$ $2xx10^(-4)$ .

Answer 3 · 2015-03-25T02:57:04

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 $0.0002$ $0.0002$ 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 $0.0002$ $0.0002$ in scientific notation is $2 \times 10^{- 4}$ $2xx10^(-4)$ .

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What is the scientific notation of 0.0002?

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