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Measurement - Measurement of Length

Grade 7ICSE

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

🔑Concepts

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Length is defined as the distance between any two points. The standard SI unit of length is the meter (mm).

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Multiples and sub-multiples of length are used for convenience: larger distances use kilometers (kmkm), while smaller lengths use centimeters (cmcm), millimeters (mmmm), or micrometers (μmμ m).

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The 'Least Count' of a measuring instrument is the smallest measurement that can be taken accurately. For a standard metric ruler, the least count is 0.1 cm0.1\ cm or 1 mm1\ mm.

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Parallax Error is the apparent shift in the position of an object when viewed from different angles. To avoid this, the eye must be placed vertically above the mark to be read.

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To measure the diameter of a spherical object (like a ball), it is placed between two rectangular wooden blocks on a ruler. The difference between the two readings on the ruler gives the diameter.

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To measure the length of a curved line, a thread is placed along the curve. The length of the straightened thread is then measured using a standard ruler.

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Astronomical distances are measured in Light Years. One light year is the distance traveled by light in vacuum in one year, approximately equal to 9.46×1012 km9.46 \times 10^{12}\ km.

📐Formulae

1 km=103 m=1000 m1\ km = 10^3\ m = 1000\ m

1 m=102 cm=100 cm1\ m = 10^2\ cm = 100\ cm

1 cm=10 mm=10−2 m1\ cm = 10\ mm = 10^{-2}\ m

1 mm=10−3 m1\ mm = 10^{-3}\ m

1 μm=10−6 m1\ \mu m = 10^{-6}\ m

1 A˚(Angstrom)=10−10 m1\ \text{Å} (Angstrom) = 10^{-10}\ m

Diameter=Reading2−Reading1\text{Diameter} = \text{Reading}_2 - \text{Reading}_1

💡Examples

Problem 1:

The length of a table is 1.25 m1.25\ m. Express this length in cmcm and mmmm.

Solution:

Length in cm=1.25×100=125 cmcm = 1.25 \times 100 = 125\ cm. Length in mm=1.25×1000=1250 mmmm = 1.25 \times 1000 = 1250\ mm.

Explanation:

To convert meters to centimeters, multiply by 10210^2. To convert meters to millimeters, multiply by 10310^3.

Problem 2:

A thread used to measure a curved line has its starting point at 2.3 cm2.3\ cm and ending point at 15.8 cm15.8\ cm on a ruler. Find the length of the curved line.

Solution:

L=15.8 cm−2.3 cm=13.5 cmL = 15.8\ cm - 2.3\ cm = 13.5\ cm

Explanation:

The length is the difference between the final mark and the initial mark on the ruler.

Problem 3:

A distance is given as 5×104 mm5 \times 10^4\ mm. Convert this into meters (mm).

Solution:

5×104 mm=500001000 m=50 m5 \times 10^4\ mm = \frac{50000}{1000}\ m = 50\ m

Explanation:

Since 1 m=1000 mm1\ m = 1000\ mm, we divide the value in mmmm by 10001000 to get the value in mm.