Author

Tony Phung

Published

September 11, 2025

1. Scentific Notation

Assumptions:

Trailing zeros in a whole number with no decimal are not significant

2. Form

\([significand]*10^{exponent}\)

2.1 Positive Exponent for larger numbers:

\(1.2 \times 10^{4}:\)
- = \(12,000\) since (\(10^{4}=10,000\))
  - \(1.2\) is the \(significand\)
  - \(4\) is the \(exponent\)
- using \(e\):
  - = \(1.2e4\)

2.2 Negative Exponent for numbers smaller than 1:

\(5e^{-2}\)
- = \(5 / (10^{2})\)
- = \(5 / (100)\)
- = \(0.05\)

3. Significant Digits

Significant Digits are the digits before the \(e\).

3.1 Problem 1: \(600.410\)

\(600.410e0\)
\(60.0410e1\)
\(6.00410e2\)
\(6.0041e2 \ [Wrong!]\)
\(6.00410e2\)
- \(6\) significant figures, numbers before \(e\).

Do not trim trailing zeros.
Only trim if there are no decimal places.

3.2 Problem 2: \(0.0078900\)

\(0.0078900e0\)
\(00.078900e-1\)
\(000.78900e-2\)
\(0007.8900e-3\)
\(7.8900e-3\)

3.3 Problem 3: \(42030\)

\(42030e0\)
\(4203.0e1\)
\(420.30e2\)
\(42.030e3\)
\(4.203e4\)
- 4 significant figures

3.4 Problem 4: \(34.50\)

\(34.50e0\)
\(3.450e1\)
- 4 sig figs

3.5 Problem 5: \(0.004000\)

\(0.004000e0\)
\(00.04000e-1\)
\(000.4000e-2\)
\(0004.000e-3\)
\(4.000e-3\)
- 4 sig figs

3.6 Problem 6: \(123.005\)

\(123.005e0\)
\(12.3005e1\)
\(1.23005e2\)
- 6 sig figs

3.7 Problem 7: \(146000\)

\(146000e0\)
\(14600.0e1\)
\(1460.00e2\)
\(146.000e3\)
\(14.6000e4\)
\(1.46000e5\)
\(1.46e5\)
- 3 sig figs

3.8 Problem 8: \(146000.001\)

\(146000.001e0\)
\(14600.0001e1\)
\(1460.00001e2\)
\(146.000001e3\)
\(14.6000001e4\)
\(1.46000001e5\)
- 10 sig figs

3.9 Problem 9: \(0.0000000008\)

\(0.0000000008e0\)
\(00.000000008e-1\)
\(000.00000008e-2\)
\(0000.0000008e-3\)
\(00000.000008e-4\)
\(000000.00008e-5\)
\(0000000.0008e-6\)
\(00000000.008e-7\)
\(000000000.08e-8\)
\(0000000000.8e-9\)
\(00000000008e-10\)
\(8e-10\)
- 1 sig fig

3.10 Problem 10: \(34500.0\)

\(34500.0e0\)
\(3450.00e1\)
\(345.000e2\)
\(34.5000e3\)
\(3.45000e4\)
- 6 sig fig

3.11 Problem 11: \(146000\)

Assume knowledge that zeros are significant:

\(146000e0\)
\(14600.0e1\)
\(1460.00e2\)
\(146.000e3\)
\(14.6000e4\)
\(1.46000e5\)
- 6 sig figs