Measuring Time

Time allows us to describe when events happen and how long they last.

We use time measurements to:

• organize schedules
• measure the duration of activities
• plan journeys
• conduct scientific experiments
• record sporting performances
• follow recipes
• compare events

Common units of time include:

second (s)

minute (min)

hour

day

Important relationships are:

1 minute = 60 seconds

1 hour = 60 minutes

1 day = 24 hours

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Analog Clocks

An analog clock displays time using hands moving around a circular clock face.

Most analog clocks have:

• an hour hand
• a minute hand
• sometimes a second hand

The shorter hand usually shows the hour.

The longer hand usually shows the minutes.

A thin moving hand may show the seconds.

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Reading Minutes on an Analog Clock

A clock face contains:

60 minute divisions

There are 12 numbered positions.

Each numbered position represents:

5 minutes

Therefore:

1 = 5 minutes

2 = 10 minutes

3 = 15 minutes

4 = 20 minutes

5 = 25 minutes

6 = 30 minutes

7 = 35 minutes

8 = 40 minutes

9 = 45 minutes

10 = 50 minutes

11 = 55 minutes

12 = 00 minutes

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Quarter Past, Half Past, and Quarter To

Some times have common names.

3:15

can be called:

quarter past three

because 15 minutes is one quarter of an hour.

3:30

is:

half past three

because 30 minutes is half an hour.

3:45

can be called:

quarter to four

because 15 minutes remain before 4:00.

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Reading the Hour Hand Carefully

At:

4:30

the hour hand is not exactly on 4.

It has moved halfway between:

4 and 5

At:

4:45

the hour hand is even closer to 5.

This movement helps show that part of the current hour has already passed.

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Digital Clocks

A digital clock displays time using numbers.

For example:

08:35

means:

8 hours and 35 minutes

Digital time can be shown using either:

• the 12-hour clock
• the 24-hour clock

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The 12-Hour Clock

The 12-hour clock divides the day into two periods.

a.m. refers to times from midnight until before noon.

p.m. refers to times from noon until before midnight.

Examples:

7:30 a.m. — morning

11:45 a.m. — before noon

2:20 p.m. — afternoon

8:15 p.m. — evening

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Noon and Midnight

Two times can sometimes cause confusion.

12:00 noon = 12:00 p.m.

12:00 midnight = 12:00 a.m.

In situations where clarity is especially important, writing 12 noon or 12 midnight can avoid confusion.

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The 24-Hour Clock

The 24-hour clock numbers the hours from:

00 to 23

Examples:

07:30 = 7:30 a.m.

12:30 = 12:30 p.m.

15:45 = 3:45 p.m.

21:10 = 9:10 p.m.

23:55 = 11:55 p.m.

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Converting to 24-Hour Time

For most morning times, the hour stays the same.

8:25 a.m. → 08:25

For afternoon and evening times, add:

12 hours

to the hour.

Example:

4:30 p.m.

4 + 12 = 16

Therefore:

4:30 p.m. = 16:30

Another example:

9:15 p.m. = 21:15

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Converting from 24-Hour Time

For times after 12:59, subtract 12 from the hour.

Example:

18:40

18 − 12 = 6

Therefore:

18:40 = 6:40 p.m.

Example:

22:15

22 − 12 = 10

Therefore:

22:15 = 10:15 p.m.

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Measuring Elapsed Time

Elapsed time is the amount of time between the start and end of an event.

For example:

Start:

2:15 p.m.

End:

3:00 p.m.

Elapsed time:

45 minutes

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Using a Timeline

A timeline can make elapsed-time calculations easier.

Suppose a movie starts at:

1:45 p.m.

and ends at:

3:20 p.m.

Break the calculation into convenient steps.

1:45 → 2:00 = 15 min

2:00 → 3:00 = 60 min

3:00 → 3:20 = 20 min

Total:

15 + 60 + 20 = 95 minutes

Therefore:

Elapsed time = 1 hour 35 minutes

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Counting Up

Another useful strategy is to count up from the starting time.

Suppose:

Start = 8:35 a.m.

End = 11:10 a.m.

8:35 → 9:00 = 25 min

9:00 → 11:00 = 2 h

11:00 → 11:10 = 10 min

Total:

2 hours 35 minutes

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Converting Hours and Minutes

Remember:

1 hour = 60 minutes

Therefore:

2 hours = 120 minutes

2.5 hours = 150 minutes

because:

2.5 × 60 = 150

However:

2 hours 30 minutes

can also be written as:

2.5 hours

because:

30/60 = 0.5

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Time Is Not Base 10

This is an important idea.

1 hour = 60 minutes

not 100 minutes.

Therefore:

1.5 hours

means:

1 hour + 0.5 hour

and:

0.5 × 60 = 30 minutes

So:

1.5 hours = 1 hour 30 minutes

It does not mean 1 hour 50 minutes.

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Fractions of an Hour

Common fractions of an hour are useful to recognize.

1/4 hour = 15 minutes

1/2 hour = 30 minutes

3/4 hour = 45 minutes

1/3 hour = 20 minutes

2/3 hour = 40 minutes

These relationships connect time with fractions and decimals.

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Elapsed Time Across Noon

Suppose an activity begins at:

11:40 a.m.

and finishes at:

1:25 p.m.

11:40 → 12:00 = 20 min

12:00 → 1:00 = 60 min

1:00 → 1:25 = 25 min

Total:

20 + 60 + 25 = 105 minutes

Therefore:

1 hour 45 minutes

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Elapsed Time Across Midnight

Suppose a flight leaves at:

22:45

and arrives at:

01:20 the next day

22:45 → 24:00 = 1 h 15 min

00:00 → 01:20 = 1 h 20 min

Total:

2 h 35 min

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Finding a Finishing Time

Sometimes we know the starting time and duration.

Suppose a lesson starts at:

9:25 a.m.

and lasts:

1 hour 40 minutes

Add 1 hour:

9:25 → 10:25

Add 40 minutes:

10:25 → 11:05

Finishing time:

11:05 a.m.

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Finding a Starting Time

Suppose an event finishes at:

4:30 p.m.

and lasts:

2 hours 15 minutes

Subtract 2 hours:

4:30 → 2:30

Subtract 15 minutes:

2:30 → 2:15

Starting time:

2:15 p.m.

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Time in Real Life

Time calculations are important for:

• school schedules
• transport
• cooking
• sports
• work
• appointments
• travel
• scientific experiments

A journey, for example, may require calculating departure time, travel duration, waiting time, and arrival time.

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What Is Temperature?

Temperature describes how hot or cold something is.

Temperature can be measured using instruments such as:

• liquid thermometers
• digital thermometers
• temperature probes
• weather instruments
• infrared thermometers

Two commonly encountered temperature scales are:

Celsius (°C)

and:

Fahrenheit (°F)

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The Celsius Scale

The Celsius scale is widely used in science and everyday temperature measurements around the world.

Some useful reference values are approximately:

0°C — freezing point of pure water under standard atmospheric pressure

20–25°C — typical comfortable indoor temperature range

37°C — approximately normal human body temperature

100°C — boiling point of pure water at standard atmospheric pressure

The freezing and boiling temperatures of water can change somewhat with conditions such as pressure.

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The Fahrenheit Scale

The Fahrenheit scale is another temperature scale, particularly familiar in the United States.

Useful reference values include:

32°F — freezing point of water under standard atmospheric pressure

68°F = 20°C

77°F = 25°C

98.6°F ≈ 37°C

212°F — boiling point of water at standard atmospheric pressure

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Celsius and Fahrenheit Are Different Scales

Celsius and Fahrenheit use different numerical values for the same temperature.

For example:

0°C = 32°F

and:

100°C = 212°F

The scales also use different-sized degree intervals.

A change of:

1°C

corresponds to a change of:

1.8°F

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Converting Celsius to Fahrenheit

The conversion equation is:

°F = (°C × 9/5) + 32

For example, convert:

20°C to °F

Calculate:

20 × 9/5 = 36

Then:

36 + 32 = 68

Therefore:

20°C = 68°F

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Another Celsius to Fahrenheit Example

Convert:

30°C to °F

30 × 9/5 = 54

54 + 32 = 86

Therefore:

30°C = 86°F

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Converting Fahrenheit to Celsius

The conversion equation is:

°C = (°F − 32) × 5/9

For example:

Convert:

77°F to °C

First:

77 − 32 = 45

Then:

45 × 5/9 = 25

Therefore:

77°F = 25°C

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Another Fahrenheit to Celsius Example

Convert:

50°F to °C

50 − 32 = 18

18 × 5/9 = 10

Therefore:

50°F = 10°C

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Useful Temperature Equivalents

An interesting point is:

-40°C = -40°F

This is the temperature at which the two scales have the same numerical value.

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Estimating Temperature Conversions

Sometimes an approximate conversion is sufficient.

For Celsius to Fahrenheit, a rough mental estimate is:

double the Celsius value and add about 30

For example:

20°C

Estimate:

20 × 2 + 30 = 70°F

Exact:

68°F

This approximation is useful for quick mental estimates over common everyday temperatures, but it should not replace the exact formula when precision matters.

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Measuring Temperature Accurately

Correct measurement requires more than simply reading a number.

When measuring temperature:

• choose an appropriate thermometer or sensor
• identify the scale being used
• identify the smallest scale division
• place the sensor correctly
• allow the reading to stabilize
• read the value carefully
• record the unit
• repeat measurements when appropriate

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Reading a Thermometer Scale

Suppose a thermometer has numbered marks at:

20°C

and:

30°C

with 10 equal intervals between them.

The difference is:

30 − 20 = 10°C

There are:

10 intervals

Therefore, each interval represents:

1°C

If the liquid level is 6 intervals above 20°C:

20 + 6 = 26°C

Temperature:

26°C

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Resolution

The resolution of a measuring instrument is the smallest change that it can display or distinguish.

For example:

Thermometer A has markings every:

1°C

Thermometer B displays:

0.1°C

Thermometer B has finer resolution.

This does not automatically guarantee that it is more accurate, but it allows smaller changes to be displayed.

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Accuracy and Precision

Accuracy describes how close a measurement is to the accepted or true value.

Precision describes how closely repeated measurements agree with one another.

For example, repeated measurements might be:

24.1°C

24.1°C

24.2°C

These are quite close together, indicating good precision.

Whether they are accurate depends on how close they are to the actual temperature.

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Recording Temperature

A measurement should include:

number + unit

Correct:

23.5°C

Incomplete:

23.5

Without the unit, the reader cannot know whether the measurement is Celsius, Fahrenheit, or another temperature scale.

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Temperature Change

Suppose the temperature increases from:

12°C to 27°C

Temperature change:

27 − 12 = 15°C

Therefore:

increase = 15°C

If temperature falls from:

18°C to 5°C

change:

5 − 18 = -13°C

This represents a:

13°C decrease

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Temperatures Below Zero

Temperatures can be negative.

For example:

−5°C

means five degrees below zero Celsius.

Suppose the temperature rises from:

−5°C to 3°C

Calculate the change:

3 − (−5) = 8°C

Therefore:

temperature increased by 8°C

A number line can help visualize this.

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Real-World Example: Weather

Suppose the morning temperature is:

18°C

and the afternoon temperature is:

27°C

Increase:

27 − 18 = 9°C

If the evening temperature falls to:

22°C

Decrease from the afternoon:

27 − 22 = 5°C

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Real-World Example: Cooking

Time and temperature often work together in cooking.

Suppose instructions say:

Bake at 180°C for 35 minutes.

If the food enters the oven at:

5:45 p.m.

the estimated finishing time is:

6:20 p.m.

The instructions involve two different measurements:

temperature = 180°C

time = 35 min

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Real-World Example: Science Experiment

Suppose students measure water temperature every:

2 minutes

for:

10 minutes

They might record:

These data can be used to study how temperature changes over time.

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Temperature-Time Graphs

A temperature-time graph usually places:

time on the horizontal axis

and:

temperature on the vertical axis

A rising line indicates increasing temperature.

A falling line indicates decreasing temperature.

A horizontal line indicates that the measured temperature remains constant over that interval.

Graphs make trends easier to identify.

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Real-World Example: Travel

A train leaves at:

08:35

and arrives at:

11:10

Elapsed time:

08:35 → 09:00 = 25 min

09:00 → 11:00 = 2 h

11:00 → 11:10 = 10 min

Total:

2 h 35 min

If the outside temperature changes from:

14°C at departure

to:

22°C at arrival

temperature increase:

22 − 14 = 8°C

One situation can involve both time and temperature calculations.

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Real-World Example: Sports

Suppose a race starts at:

10:15 a.m.

and finishes at:

11:42 a.m.

Elapsed time:

10:15 → 11:15 = 1 h

11:15 → 11:42 = 27 min

Total:

1 h 27 min

Time measurements are central to many sports because performance may depend on differences of minutes, seconds, or even fractions of a second.

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Worked Example 1: Reading Time

The minute hand points to 8.

Minutes:

8 × 5 = 40 minutes

The hour hand is between 3 and 4.

Time:

3:40

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Worked Example 2: 12-Hour to 24-Hour Time

Convert:

6:25 p.m.

Add 12 to the hour:

6 + 12 = 18

Answer:

18:25

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Worked Example 3: 24-Hour to 12-Hour Time

Convert:

21:45

Subtract 12:

21 − 12 = 9

Answer:

9:45 p.m.

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Worked Example 4: Elapsed Time

Start:

7:50 a.m.

End:

10:25 a.m.

7:50 → 8:00 = 10 min

8:00 → 10:00 = 2 h

10:00 → 10:25 = 25 min

Total:

2 h 35 min

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Worked Example 5: Find the Finishing Time

Start:

13:40

Duration:

2 h 35 min

Add 2 hours:

15:40

Add 35 minutes:

16:15

Answer:

16:15

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Worked Example 6: Celsius to Fahrenheit

Convert:

25°C

Use:

°F = (°C × 9/5) + 32

°F = (25 × 9/5) + 32

= 45 + 32

= 77°F

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Worked Example 7: Fahrenheit to Celsius

Convert:

68°F

Use:

°C = (°F − 32) × 5/9

°C = (68 − 32) × 5/9

= 36 × 5/9

= 20°C

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Worked Example 8: Temperature Difference

Morning:

−3°C

Afternoon:

8°C

Change:

8 − (−3)

= 11°C

The temperature increased by:

11°C

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Worked Example 9: Time and Temperature

An experiment begins at:

14:25

with a temperature of:

21°C

It lasts:

1 hour 50 minutes

and finishes at:

36°C

Finishing time:

14:25 + 1 h = 15:25

15:25 + 50 min = 16:15

Temperature change:

36 − 21 = 15°C

Therefore:

Finishing time = 16:15

Temperature increase = 15°C

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Worked Example 10: Multi-Step Schedule

A journey begins at:

09:35

Travel time:

1 h 45 min

Break:

25 min

Second journey:

55 min

First arrival:

09:35 + 1:45 = 11:20

After break:

11:20 + 0:25 = 11:45

Final arrival:

11:45 + 0:55 = 12:40

Answer:

12:40

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Estimating Time

Estimation helps check time calculations.

Suppose a journey begins around:

9:00

and lasts approximately:

3 hours

The finishing time should be around:

12:00

If an exact calculation gives:

6:00 p.m.

the answer should be checked.

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Estimating Temperature

Approximate reference temperatures can also help identify unreasonable measurements.

For example:

Room temperature is often around:

20–25°C

If a classroom thermometer reads:

250°C

the reading is clearly unreasonable for a normal classroom environment.

Reasonableness is an important part of measurement.

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Choosing an Appropriate Measuring Instrument

Different situations require different instruments.

For example:

Class duration: clock

100 m sprint: stopwatch or electronic timer

Cooking time: kitchen timer

Room temperature: thermometer

Laboratory experiment: temperature probe or laboratory thermometer

The instrument should have appropriate resolution and range for the task.

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Common Mistakes

Mistake 1: Treating time as base 10

1.5 hours = 1 h 30 min

not 1 h 50 min.

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Mistake 2: Confusing the hour and minute hands

The shorter hand usually represents hours.

The longer hand usually represents minutes.

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Mistake 3: Forgetting a.m. or p.m.

7:00 a.m.

and:

7:00 p.m.

are 12 hours apart.

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Mistake 4: Incorrect 24-hour conversions

7:30 p.m. = 19:30

not 17:30.

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Mistake 5: Simply subtracting clock digits

Elapsed-time calculations must respect:

60 minutes = 1 hour

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Mistake 6: Forgetting the temperature unit

Write:

24°C

not simply:

24

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Mistake 7: Assuming Celsius and Fahrenheit use the same numbers

For example:

20°C = 68°F

not 20°F.

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Mistake 8: Using the Celsius–Fahrenheit formula in the wrong order

For Fahrenheit to Celsius:

subtract 32 first, then multiply by 5/9.

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Mistake 9: Ignoring negative temperatures

For example:

From −4°C to 6°C is an increase of:

10°C

not 2°C.

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A Reliable Elapsed-Time Strategy

Step 1: Identify the starting time.

Step 2: Identify the ending time.

Step 3: Count forward to a convenient hour.

Step 4: Count the whole hours.

Step 5: Count the remaining minutes.

Step 6: Add the intervals.

Step 7: Check that the answer fits between the starting and ending times.

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A Reliable Temperature Strategy

Step 1: Identify the temperature scale.

Step 2: Read the instrument carefully.

Step 3: Determine the smallest scale division.

Step 4: Record the value and unit.

Step 5: Repeat measurements when appropriate.

Step 6: If comparing temperatures, calculate the difference.

Step 7: If converting scales, use the correct equation.

Step 8: Check whether the result is reasonable.

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Did You Know?

Time and temperature are both measurements, but their scales behave differently.

Metric length conversions are largely based on powers of 10.

Time commonly uses relationships such as:

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

Temperature scales use their own reference points and interval sizes.

This is why converting time or temperature requires different strategies from converting metres, grams, or litres.

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Key Terms

• Time: Measurement describing when events occur or how long they last.
• Analog clock: Clock displaying time using hands on a clock face.
• Digital clock: Clock displaying time using numbers.
• Hour hand: Hand indicating the hour on an analog clock.
• Minute hand: Hand indicating minutes.
• Second hand: Hand indicating seconds.
• a.m.: Times from midnight until before noon.
• p.m.: Times from noon until before midnight.
• 24-hour clock: System numbering the hours of a day from 00 to 23.
• Elapsed time: Amount of time between two events.
• Duration: Length of time an event lasts.
• Temperature: Measurement describing how hot or cold something is.
• Celsius (°C): Temperature scale commonly used internationally and in science.
• Fahrenheit (°F): Another temperature scale, commonly used in the United States.
• Thermometer: Instrument used to measure temperature.
• Temperature probe: Sensor used to measure temperature, often electronically.
• Resolution: Smallest change an instrument can display or distinguish.
• Accuracy: Closeness of a measurement to an accepted or true value.
• Precision: Closeness of repeated measurements to one another.

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Key Equations and Relationships

Time

1 minute = 60 seconds

1 hour = 60 minutes

1 day = 24 hours

1/4 hour = 15 minutes

1/2 hour = 30 minutes

3/4 hour = 45 minutes

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Celsius to Fahrenheit

°F = (°C × 9/5) + 32

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Fahrenheit to Celsius

°C = (°F − 32) × 5/9

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Temperature change

Temperature Change = Final Temperature − Initial Temperature

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Key Takeaways

• Time can be represented using analog or digital clocks.
• Analog clocks use hour and minute hands to show time.
• Each numbered position on a standard clock represents 5 minutes.
• The 12-hour clock uses a.m. and p.m.
• The 24-hour clock numbers hours from 00 to 23.
• Elapsed time is the duration between two events.
• Counting forward on a timeline is a reliable method for calculating elapsed time.
• Time is not a base-10 measurement system: 60 minutes = 1 hour.
• Fractions and decimals of an hour can be converted into minutes.
• Temperature describes how hot or cold something is.
• Celsius and Fahrenheit are different temperature scales.
• Water freezes at approximately 0°C or 32°F under standard atmospheric pressure.
• Water boils at approximately 100°C or 212°F under standard atmospheric pressure.
• Celsius and Fahrenheit temperatures can be converted using mathematical equations.
• Temperature measurements should always include a unit.
• Instrument resolution should be considered when recording measurements.
• Negative temperatures must be handled carefully when calculating temperature changes.
• Time and temperature are frequently used together in cooking, travel, sports, weather observations, and scientific experiments.
• Estimation helps identify unreasonable measurements and calculations.
• Accurate measurement involves choosing an appropriate instrument, reading it carefully, recording the correct units, and interpreting the result in context.