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Where are we now and where might we be going - Measurement

Grade 7IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The International System of Units (SI) is the modern form of the metric system, ensuring global consistency. Base units include the meter (mm) for length, kilogram (kgkg) for mass, and second (ss) for time.

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Derived units are created by combining base units. For example, area is measured in m2m^2, volume in m3m^3, and density in kg/m3kg/m^3 or g/cm3g/cm^3.

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Scientific notation (a×10na \times 10^n) is essential for expressing very large distances (like the distance to the moon, ≈3.84×108 m\approx 3.84 \times 10^8\ m) or very small sizes (like an atom's diameter).

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Accuracy describes how close a measurement is to the true or accepted value, whereas Precision describes the consistency or reproducibility of multiple measurements.

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The Displacement Method is used to find the volume of irregular solids. The volume of the object is equal to the volume of fluid it displaces: Vobject=Vfinal−VinitialV_{object} = V_{final} - V_{initial}.

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Density is a fundamental property of matter that describes how much mass is contained in a given volume. An object will float in a fluid if its density is less than the fluid's density.

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Estimation is a critical skill in science used to verify if a measured value or calculation is 'reasonable' within the context of the problem.

📐Formulae

ρ=mV\rho = \frac{m}{V}

V=l×w×hV = l \times w \times h

W=m×gW = m \times g

Error=∣Experimental Value−True Value∣\text{Error} = |\text{Experimental Value} - \text{True Value}|

Percentage Error=ErrorTrue Value×100%\text{Percentage Error} = \frac{\text{Error}}{\text{True Value}} \times 100\%

💡Examples

Problem 1:

A metal cube has a mass of 160 g160\ g and the length of one side is 2 cm2\ cm. Calculate its density and determine if it will sink in water (density of water =1.0 g/cm3= 1.0\ g/cm^3).

Solution:

  1. Calculate volume: V=s3=2 cm×2 cm×2 cm=8 cm3V = s^3 = 2\ cm \times 2\ cm \times 2\ cm = 8\ cm^3
  2. Calculate density: ρ=mV=160 g8 cm3=20 g/cm3\rho = \frac{m}{V} = \frac{160\ g}{8\ cm^3} = 20\ g/cm^3

Explanation:

Since the density of the metal cube (20 g/cm320\ g/cm^3) is much higher than the density of water (1.0 g/cm31.0\ g/cm^3), the cube will sink.

Problem 2:

Express the speed of light, which is approximately 300,000,000 m/s300,000,000\ m/s, in scientific notation.

Solution:

300,000,000=3×108 m/s300,000,000 = 3 \times 10^8\ m/s

Explanation:

To convert to scientific notation, we move the decimal point 8 places to the left to get a number between 1 and 10, which becomes the coefficient, and the power of 10 reflects the number of places moved.

Problem 3:

A student measures the mass of a sample as 45.2 g45.2\ g, but the actual mass is 48.0 g48.0\ g. Calculate the absolute error using vertical subtraction.

Solution:

48.0−45.22.8\begin{array}{r} 48.0 \\ - 45.2 \\ \hline 2.8 \end{array} The error is 2.8 g2.8\ g.

Explanation:

The absolute error is the difference between the actual value and the measured value.