Scientific vs Engineering Notation, SI Prefixes and Significant Figures

Avogadro's number is 602,214,076,000,000,000,000,000 and the elementary charge is 0.0000000000000000001602176634 C. Written out like that, it is easy to miscount the zeros. Science and engineering therefore separate the size of a number into a power of ten. This guide covers scientific and engineering notation, SI prefixes, entering exponents on a calculator, and significant-figure rules.

1. Scientific notation (SCI)

Write the number as a × 10ⁿ with 1 ≤ |a| < 10.

• 6.02214076 × 10²³ (Avogadro's number)
• 1.602176634 × 10⁻¹⁹ C (elementary charge)
• 0.00047 = 4.7 × 10⁻⁴

Two benefits: the magnitude (n) is visible at a glance, and the number of significant figures (the digits in a) is unambiguous.

2. Engineering notation (ENG)

Restrict the exponent to multiples of 3 and keep 1 ≤ |a| < 1000.

• 0.000047 → 47 × 10⁻⁶ (= 47 μ)
• 123456789 → 123.456789 × 10⁶ (= 123.456789 M)
• 3386.28 → 3.38628 × 10³ (= 3.38628 k)

With exponents in steps of three, you can read the SI prefix directly: 47×10⁻⁶ F is 47 μF and 3.38628×10³ Ω is 3.38628 kΩ. That is why circuit work prefers engineering notation.

3. SI prefix table

Kilo is a lowercase k and mega an uppercase M. m (milli) and M (mega) differ by a factor of 10⁹, so case matters.

4. Entering exponents: E notation

In SciKey, E (or e) followed by an integer, written directly after a number, means × 10ⁿ.

• 6.02E23 = 6.02 × 10²³
• 1.6e-19 = 1.6 × 10⁻¹⁹
• 47E-6 = 0.000047

6.02E23 has the same value as 6.02×10^23, but E notation is treated as a single number. So 1/6.02E23 correctly means 1/(6.02×10²³), whereas 1/6.02×10^23 is evaluated left to right as (1/6.02)×10²³ = 1.66×10²², because multiplication and division share the same precedence. Get into the habit of typing exponents with E.

One catch: if no integer follows, as in 2e, it means 2 × e (Euler's number, 2.71828…) = 5.43656365692. For E notation, always put the digits after the E.

5. Worked examples

Example 1: checking the Faraday constant. F = N_A × e. NA×qe → 96485.3321233 (C/mol), or 9.64853321233×10⁴ in SCI.

Example 2: capacitive reactance. At 1 kHz and 47 nF, X = 1/(2πfC):

1/(2π×1E3×47E-9) → 3386.27538493 Ω

In ENG that is 3.38627538493×10³, about 3.39 kΩ. Note the brackets around the entire denominator. 1/2π×1E3×47E-9 is evaluated left to right and gives something entirely different (7.38×10⁻⁵).

Example 3: switching display formats. For a result of 0.000000512:

• NORM: 0.000000512 (at least 1e−9 and below 1e12, so plain notation)
• SCI: 5.12 × 10⁻⁷
• ENG: 512 × 10⁻⁹ (= 512 n)

Example 4: a light-year in metres. A light-year is the distance light travels in a Julian year (365.25 days): c0×365.25×86400 → 9.46073047258×10¹⁵ m. Since it exceeds 10¹², NORM also shows it in scientific form. The exponent 15 is already a multiple of 3, so ENG looks the same; with a prefix it reads about 9.46 Pm (petametres).

Example 5: molecules in 9 g of water. Taking water's molar mass as 18.015 g/mol, 9/18.015×NA → 3.00856324396×10²³ molecules. Multiplication and division run left to right, so this is (9/18.015)×N_A as intended.

6. Significant figures

The digits in a measurement show how precisely it was measured. 2.50 cm was measured to 0.01 cm; 2.5 cm only to 0.1 cm.

Which digits count

1. All nonzero digits count: 123 → 3
2. Zeros between nonzero digits count: 1.005 → 4
3. Leading zeros do not count: 0.0047 → 2
4. Trailing zeros after a decimal point count: 2.50 → 3
5. Trailing zeros in a whole number without a decimal point are ambiguous: 1200 → 2 to 4. Scientific notation removes the doubt: 1.2 × 10³ (2) or 1.20 × 10³ (3).

Digits in a result

• Multiplication and division: match the value with the fewest significant figures. 2.50 × 3.1 = 7.75 → 2 significant figures → 7.8
• Addition and subtraction: match the value with the fewest decimal places. 12.0 + 0.345 = 12.345 → one decimal place → 12.3

Round once, at the end

Rounding at every step compounds error. Keep intermediate values in Ans or stored variables and round only the final answer. SciKey's round(x, n) rounds to n decimal places, e.g. round(3.14159, 2) = 3.14.

7. How this differs from the calculator's digit setting

SciKey's display digit setting (6 to 15, default 12) only controls how many digits appear on screen; it does not apply significant-figure rules. Compute 2.50 × 3.1 and the calculator shows 7.75. Deciding to report 7.8 is your job. Since the setting's minimum is 6 and each problem needs a different precision, leave the setting generous and round the final answer yourself.

8. Common mistakes

• Reading 10E5 as 10⁵. 10E5 is 10 × 10⁵ = 10⁶; 10⁵ is 1E5.
• Appending ×10^n to a denominator without brackets. Use E notation or bracket it.
• Confusing μ (10⁻⁶) and m (10⁻³), a factor of 1,000.
• Copying all 12 displayed digits into the answer. Three-digit measurements give roughly three-digit answers.

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Last updated: 2026-09-24