how do you express 0.00248 in scientific notation?

Hi TJM,

I'm sorry but this is not correct.    

$${\frac{{\mathtt{1}}}{\left({\mathtt{2.48}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}}\right)}} = {\mathtt{0.002\: \!48}}$$

This is correct

$$\frac{1}{(2.48*10^3)}=\frac{1}{2.48}\times \frac{1}{10^3} =\frac{1}{2.48}\times 10^{-3}$$

• Scientific Notation for decimal numbers

To express any decimal number in scientific notation, you count the numbers of zero after the decimal point until you find a non-zero number. This number will be the exponent of the power 10. The exponent must be negative. For the first part(the non-zero number), you will take the first non-zero number, followed by a decimal point, and adding the last numbers to it.

$${\mathtt{0.002\: \!48}} = {\mathtt{2.48}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{3}}}$$

Another examples:

$${\mathtt{0.253}} = {\mathtt{2.53}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{1}}}$$

$${\mathtt{0.000\: \!200\: \!85}} = {\mathtt{2.008\: \!5}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{4}}}$$

• Scientific Notation for whole Numbers. It applies the same rule but, the exponent will be positive.$${\mathtt{200}} = {\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{2}}}$$

  $${\mathtt{2\,085}} = {\mathtt{2.085}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}}$$

 $${\mathtt{35\,000}} = {\mathtt{3.5}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{4}}}$$

its $${\mathtt{2.48}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{3}}}$$ . negative exponents work like this: $${{\mathtt{x}}}^{{\mathtt{\,-\,}}{\mathtt{y}}} = {\frac{{\mathtt{1}}}{{{\mathtt{x}}}^{{\mathtt{y}}}}}$$ that is, x to the power of negative y equals 1 divided by x to the yth blah blah.

$${\frac{{\mathtt{1}}}{\left({\mathtt{2.48}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}}\right)}} = {\mathtt{0.002\: \!48}}$$

as for why it isnt $${\mathtt{248}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{5}}}$$ even though its the same value:

the rule for scientific notation is that the number being multiplied by $${{\mathtt{10}}}^{{\mathtt{something}}}$$ is supposed to be equal to or greater than 1 [i think] but less than 10 [im sure of this part].

hope this helps