What is the scientific notation of 0.0002?

3 Answers
Mar 25, 2015

2xx10^(-4)2×104

I know scientific notation has one non-0 digit before the decimal point. So I know the scientific notation for 0.00020.0002 is

2xx10^"some number"2×10some number. (We don't write "2.2.", just "22")

Multiplying by 1010 to a positive whole number moves the decimal to the right. I need to multiply 22 to move the decimal to the left. To "recover" the number 0.00020.0002 from 22, I need to move the decimal 4 to the left. That means I multiply by 10^(-4)104

This of this:

2xx10^1=202×101=20 (decimal moved one to the right)
2xx10^(-1)=0.22×101=0.2 (decimal moved one to the left)

2xx10^(-2)=0.022×102=0.02 (decimal moved one to the left)

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2xx10^(-4)=0.00022×104=0.0002

Extra example:

What is the scientific notation for 0.00000370.0000037 ?

I know it starts as 3.7xx10^"some number"3.7×10some number

To "recover 0.00000370.0000037 from 3.73.7, we need to move the decimal how far, in which direction?

So we need to multiply xx10×10 to what power?

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.#3.7xx10^(-6)

Last extra example
Write 47,00047,000 in scientific notation.

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4.7xx10^"some number"4.7×10some number

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.Did you get 4.7xx10^44.7×104? 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 0.00020.0002 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 0.00020.0002 in scientific notation is 2xx10^(-4)2×104.

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 0.00020.0002 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 0.00020.0002 in scientific notation is 2xx10^(-4)2×104.