#49
Top 50 Mistake
Using wrong sign for small numbers
"The Sign Slip"
The Mistake in Action
Write 0.00045 in standard form.
Wrong: $4.5 \times 10^4$
Why It Happens
Students move the decimal point correctly but use a positive power instead of negative. They confuse the direction of movement.
The Fix
For numbers less than 1, the power is negative.
Think of it this way:
- Big numbers (≥10) → positive power (×10 makes things bigger)
- Small numbers (<1) → negative power (×10^{-n} makes things smaller)
$$0.00045 = 4.5 \times 10^{-4}$$
Check: $10^{-4} = 0.0001$, and $4.5 \times 0.0001 = 0.00045$ ✓
Spot the Mistake
Can you identify where this student went wrong?
Write 0.00045 in standard form
$4.5 \times 10^4$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: