Subtracting Scientific Notation: 3.3e-3 minus 9.4e-4

Evaluate the difference between two numbers in scientific notation, 3.3 x 10^-3 and 9.4 x 10^-4, and express the final answer in standard scientific notation.

Answer

The problem asks to evaluate the expression

and express the answer in scientific notation.

To subtract these two numbers, we need to have the same power of 10 for both terms. We can convert one of the terms so that both have the power of

or both have the power of

Method 1: Convert to

We want to express

as a multiple of

.
Since

, we have:

Now, substitute this back into the original expression:

Factor out

Calculate the difference:

So the result is:

This is already in scientific notation since

Method 2: Convert to

We want to express

as a multiple of

.
Since

, we have:

Now, substitute this back into the original expression:

Factor out

Calculate the difference:

So the result is:

We need to express this in scientific notation, where the coefficient must be between 1 and 10 (inclusive of 1, exclusive of 10).

Substitute this back:

Both methods yield the same result.

The evaluation of the expression in scientific notation is:

Subtracting Scientific Notation: 3.3e-3 minus 9.4e-4

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