SPI Physics · Units, Measurement and Dimensions

Standard Units and Time

A standard unit is one agreed quantity used by everyone, so that the same thing gives the same measurement anywhere; time is measured in such units, from the second up to the millennium.

All Units, Measurement and Dimensions notes

Why this matters

Four questions in the bank, all EASY: why a standard unit is needed, how small lengths were measured in ancient India, which of four phrases is not a time interval, and the name for 1000 years. Each is one fact from the two tables on this page.

Concept 1 of 2: Why we need standard units

Measure a table with your handspan and a friend measures it with theirs: you get different numbers for the same table. Body measures change from person to person, so people agreed on fixed units that mean the same thing for everyone.

Definition

Measurement compares a quantity with a fixed amount called a unit: '2 metres' means two of the unit 'metre'.
A standard unit is the same everywhere. Its purpose is uniformity in measurement; trade and record keeping only benefit from it.
Old body measures were not standard, because hands, arms and feet differ in size.
The French made the metric system around 1790. Today the SI (International System of Units) is used worldwide; its unit of length is the metre.

Old unit	Measured with
Angul	The width of a finger
Mutthi	A closed fist
Handspan (balisht)	The stretch from thumb tip to little finger tip
Cubit	The length from the elbow to the tip of the fingers
Foot	The length of a person's foot
Pace	The length of one step

Ancient India measured small lengths in anguls and mutthis; the cubit was for longer lengths such as cloth.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Units, Measurement and Dimensions · Standard Units and Time

Standard unit is necessary for

Giving a use as the purpose

Buying, selling and keeping records all use standard units, but the reason a standard exists is uniformity: the same measurement for the same quantity everywhere.

Calling the yard an ancient Indian unit

The yard and the foot are British units and the metre is modern. Ancient India measured small lengths with the angul and the mutthi.

Drill 1 more on why we need standard units

Concept 2 of 2: Instants, intervals and units of time

'At sunrise' names a moment; 'for a minute' names a stretch of time. A clock reading is an instant, and the time between two readings is an interval. Units of time measure intervals.

Definition

An instant is a single moment: the time of sunrise, 9 o'clock, noon.
A time interval is the time between two instants: a second, a minute, a day, a year.
The SI unit of time is the second (s).

Unit	Equal to
Minute	60 seconds
Hour	60 minutes, or 3600 seconds
Day	24 hours, or 86400 seconds
Year	365 days (a leap year has 366)
Decade	10 years
Century	100 years
Millennium	1000 years Ten centuries make a millennium.

A trillion is a number (a million million), not a unit of time.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 2 · Units, Measurement and Dimensions · Standard Units and Time

Which of the following does not represent a time - interval?

Calling a moment an interval

The time of sunrise, or 'at 5 o'clock', is an instant. An interval always lasts for some time, like a minute or a day.

Mixing up century and millennium

A century is 100 years and a millennium is 1000 years. A decade is 10 years.

Taking a trillion for a span of time

A trillion is a number, a million million. It is not a unit of time, so it cannot name 1000 years.

Drill 1 more on instants, intervals and units of time

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Reference tables (2)

Why we need standard units6 rows

Old unit	Measured with
Angul	The width of a finger
Mutthi	A closed fist
Handspan (balisht)	The stretch from thumb tip to little finger tip
Cubit	The length from the elbow to the tip of the fingers
Foot	The length of a person's foot
Pace	The length of one step

Ancient India measured small lengths in anguls and mutthis; the cubit was for longer lengths such as cloth.

Instants, intervals and units of time7 rows

Unit	Equal to
Minute	60 seconds
Hour	60 minutes, or 3600 seconds
Day	24 hours, or 86400 seconds
Year	365 days (a leap year has 366)
Decade	10 years
Century	100 years
Millennium	1000 years Ten centuries make a millennium.

A trillion is a number (a million million), not a unit of time.

Watch out for (5)

Giving a use as the purpose
→ Why we need standard units
Calling the yard an ancient Indian unit
→ Why we need standard units
Calling a moment an interval
→ Instants, intervals and units of time
Mixing up century and millennium
→ Instants, intervals and units of time
Taking a trillion for a span of time
→ Instants, intervals and units of time

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