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How do you write 0.00437 in scientific notation?

Dec 5, 2015

$4.37 \times {10}^{- 3}$

Explanation:

$\textcolor{b l u e}{\text{This method is very important as it avoids some very common}}$ $\textcolor{b l u e}{\text{mistakes.}}$

Imagine keeping the decimal point in the same place and sliding the number to the left until you got $4.37$.

This is the notation type you are aiming for but as it stands at the moment it is a different value to that in the question. So we need to show how to change it back without actually doing the maths.

We 'slid' the given number to the left by 3 digits so we simply write:

$\frac{4.37}{{10}^{3}}$ but this is still not in scientific form.

If we have, say $\frac{1}{10}$ this can be written as ${10}^{- 1}$

But we have $\frac{1}{{10}^{3}}$. This can be written as ${10}^{- 3}$

So we write $\frac{4.37}{{10}^{3}} \text{ as } 4.37 \times {10}^{- 3}$

Once you have grasped the idea how this works it will become second nature to you.

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