Measurement and Uncertainty

What is the difference between SI units and Non-SI units?

• SI (Metric) Units: International standard units used worldwide for science and measurement.

  • Examples: meter (m), kilogram (kg), second (s)

• Non-SI Units: Units that are not part of the SI system.

  • Examples: inch (in), pound (lb), mile (mi)

What are the basic MKS units?

MKS = Meter, Kilogram, Second

Why are SI units important?

SI units provide a worldwide standard for recording, communicating, and comparing data accurately.

Match the fundamental quantity to its SI unit:

Length = ______

meter (m)

What is a derived quantity?

A derived quantity is a quantity that is calculated from one or more fundamental quantities.

Match the derived quantity to its unit:

• Speed = ?

m s⁻¹

Tera (T)

10¹²

What is scientific notation?

A way of writing very large or very small numbers using a number between 1 and 10 multiplied by a power of 10.

What is the general form of scientific notation?

a × 10ⁿ

where:

• 1 ≤ a < 10

• n is an integer

What happens when the exponent is positive?

The decimal point moves to the right.

Example:
6.4 × 10⁶ = 6,400,000

What happens when the exponent is negative?

The decimal point moves to the left.

Example:
5 × 10⁻¹¹ = 0.00000000005

Is the exponent positive or negative for large numbers?

Positive

Example:
45,000 = 4.5 × 10⁴

Is the exponent positive or negative for very small numbers?

Negative

Example:
0.003 = 3 × 10⁻³

What must be true about the first number (coefficient) in scientific notation?

It must be greater than or equal to 1 and less than 10.

Example:
✅ 6.4 × 10⁶
❌ 64 × 10⁵

Are non-zero digits significant?

Yes, always.

Example: In 347, all 3 digits are significant.

Are zeros between non-zero digits significant?

Yes.

Example:

• 101 → 3 significant figures

• 5006 → 4 significant figures

Are leading zeros significant?

No.

Leading zeros only show the position of the decimal point.

Example:

• 0.0025 → 2 significant figures

What are leading zeros?

Zeros that come before the first non-zero digit.

Example:

0.0042 (The three zeros are leading zeros and are not significant).

Are trailing zeros to the right of a decimal point significant?

Yes.

Example:

• 2.00 → 3 significant figures

• 5.400 → 4 significant figures

Are trailing zeros to the left of a decimal point always significant?

Not always.

Use scientific notation to avoid confusion.

Example:

• 1500 could be 2, 3, or 4 significant figures depending on how it was measured.

Why is scientific notation useful when working with significant figures?

It clearly shows how many digits are significant and avoids ambiguity.

Example:

• 1500 = ambiguous

• 1.5 × 10³ = 2 significant figures

• 1.500 × 10³ = 4 significant figures

What are the four main rules for significant figures?

1. Non-zero digits are significant.

2. Zeros between non-zero digits are significant.

3. Leading zeros are not significant.

4. Trailing zeros are significant if to the right of a decimal point; otherwise, be careful and use scientific notation.

When multiplying or dividing, what determines the number of significant figures in the answer?

The value with the fewest significant figures.

For multiplication and division, should the answer have more, fewer, or the same number of significant figures as the least precise measurement?

The same number of significant figures as the least precise measurement.

Why can't you leave the answer to 2.86 ÷ 1.5 × 10⁻⁴ as 19066.66?

Because the input data only contains 2 significant figures, so the answer appears more precise than the measurements justify.

True or False: Calculator answers should always be written exactly as displayed.

❌ False

Answers must be rounded according to the significant-figure rules

What does "least precise data" mean?

The measurement with the fewest significant figures.

What is the significant-figure rule for multiplication and division?

✅ Perform the calculation normally.
✅ Identify the value with the fewest significant figures.
✅ Round the answer to that number of significant figures.

Example:
2.86 ÷ 1.5 × 10⁻⁴ = 19066.66... ≈ 1.9 × 10⁴ (2 sig figs).

When adding or subtracting, what do you round based on?

The decimal place of the least precise measurement.

For addition and subtraction, do you use significant figures or decimal places?

Decimal places, not the total number of significant figures.

What is the rule for addition and subtraction?

Round the answer to the same decimal place as the least precise measurement.

What is the most important rule for addition and subtraction?

✅ Calculate first.
✅ Find the measurement with the fewest decimal places.
✅ Round the answer to that same decimal place.

Match the fundamental quantity to its SI unit:

Mass = ______

kilogram (kg)

Match the fundamental quantity to its SI unit:

Time = ______

second (s)

Match the fundamental quantity to its SI unit:

Temperature = ______

kelvin (K)

Match the fundamental quantity to its SI unit:

Current = ______

ampere (A)

Match the fundamental quantity to its SI unit:

Amount of substance = ______

mole (mol)

Match the fundamental quantity to its SI unit:

Luminous intensity = ______

candela (cd)

Match the derived quantity to its unit:

• Density = ?

kg m⁻³

Match the derived quantity to its unit:

• Area = ?

m²

Match the derived quantity to its unit:

• Force = ?

N (kg m s⁻²)

Match the derived quantity to its unit:

• Pressure = ?

Pa (kg m⁻¹ s⁻²)

Match the derived quantity to its unit:

• Energy = ?

J (kg m² s⁻²)

Match the derived quantity to its unit:

• Momentum = ?

kg m s⁻¹

Giga (G)

10⁹

Mega (M)

10⁶

kilo (k)

10³

hecto (h)

10²

deka (da)

10¹

deci (d)

10⁻¹

centi [c]

10^-2

milli (m)

10^-3

micro (μ)

10^-6

nano (n)

10^-9

pico (p)

10^-12