# Second – Definition with Examples

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## What Is a Second (s or sec)?

Second (s or sec) is a unit of time measurement according to the International system of units. So, one second of time is the quantum of time that elapses between 9,192,631,770 cycles of radiation that is produced between two levels of the Cesium-133 atom. The same can be tricky to understand at first, but it is the most accurate depiction of the time that passes between two seconds.

## Definition of Seconds

In the context of mathematics, the term “second” may hold several different meanings. According to the International System of Units (SI), seconds are the base unit of time. It is the smallest measure of time, followed by minutes, hours, days, and weeks.

Based on the International System of Units, the time definition of a second is unique but has changed over time. Since 2019, the definition of seconds has been based on the properties specific to the Cesium-133 atom. It is believed to be a more accurate way to keep track of time.

## Symbol and Abbreviations of a Second

How to write seconds using symbols and abbreviations ? Well, you begin by stating the number of seconds and follow it by writing the second symbol, which is “s” or “sec.”

## How Is a Second Expressed?

Besides the Cesium-133 atom, there are other ways to express seconds as well. For example, we can say that a second is equal to the time required for an electromagnetic field to propagate a distance of 299,792,458 meters in a vacuum.

Another way to express seconds is to state it as equal to $\frac{1}{86400}$ part of a mean solar day. However, this definition of a second may be limited in accuracy and may not truly represent the meaning of seconds.

## Are there units of time smaller than seconds?

The usual abbreviations for the second that we follow are “s” or “sec.” However, there are yet other smaller units for measurement of time. For example, take a look at the following units, which are smaller than seconds.

• $1\times10^-{3}$ seconds is equal to one millisecond.
• $1\times10^-{6}$ seconds is equal to one microsecond.
• $1\times10^-{9}$ seconds is equal to one nanosecond.
• $1\times10^-{12}$ seconds is equal to one picosecond.

If we want to picture how long a second is, then going by the definition above, during each of these time spans, the electromagnetic field propagates through a vacuum over distances varying between 300 km, 300 m, 300 millimeters, and 300 micrometers in each of the above cases.

## Uses for Seconds

There are many instances when we use seconds as a base for measurement. As the base unit for the measurement of time, it can help us record events that occur in daily life. Take a look at the example of the following events:

• Checking a patient’s heart rate by counting the number of beats per minute.
• Assessing the speed of a car by counting the miles or kilometers for which it runs for hours.
• The time that it takes for a dish to cook properly is minutes or seconds.

While these events take their time to occur and are easily measured in hours, minutes, and seconds, there are yet other events that occur quite rapidly. The movement of sound waves or bursts of gamma rays are examples of events that take place in a very short span of time and can be measured in units of seconds.

The second is also used as a common base unit for very long durations of time. A good example of such long spans of time is geologic time units like millennium or mega-annum.

## Fun Facts!

• The second is also an ordinal number that is used after the first natural number. Take, for example, the grading system. So, the second grade will come after the first. The second position will come after the first, and so on.
• Seconds are also a part of measuring the degrees of longitude and latitude. The latter is used to denote a specific position on Planet Earth.

## Conclusion

At SplashLearn, it is always fun to get to learn about various mathematical concepts. The fun quizzes and examples are a great way to get introduced to various topics. So, get ready to hop aboard and learn the meaning of seconds and how you can work your way around them in the world of mathematics.

## Solved Examples

1. How will we convert 3 minutes and 15 seconds into pure seconds?

Solution: 3 minutes and 15 seconds are equal to 195 seconds.

We know that 1 minute $= 60$ seconds. Hence, 3 minutes $= 3 \times 60$ seconds $= 180$ seconds

So 3 minutes and 15 seconds $= 180$ seconds $+ 15$ seconds $= 195$ seconds

2. How can we convert 70 seconds into minutes?

Solution: 70 seconds are equal to 1.166 minutes

We know that 1 minute $= 60$ seconds

70 seconds $= \frac{70}{60}$ minutes

$= 1.166$ minutes

3. Can we convert 45 seconds to a minute?

Solution: To convert 45 seconds into minutes, we divide 45 by 60

$= \frac{45}{60}$

$= \frac{3}{4}$ minutes

$= 0.75$ minutes

Thus, 45 seconds $= 0.75$ minutes

4. Convert 7680 seconds into hours.

Solution: We can start by converting seconds into minutes and then into hours.

7680 seconds $= (7680 \div 60)$ minutes (1 second $= \frac{1}{60}$ minute)

$= 128$ minutes

$= (128 \div 60)$ hours (1 minute $= \frac{1}{60}$ hour)

$= 2$ hours 8 minutes

5. If it takes Mr. Ashton 2 hours and 30 minutes to get from station A to station B, at what time must he take a train to reach station B if he must get there by 6 p.m.?

Solution: Mr. Ashton must take his train from station A at 3:30 a.m.

If Mr. Ashton wants to reach station B at 6 p.m., and it takes 2 hours and 30 minutes to get to the station, he will need to leave at 3:30 p.m.

$3:30 + 2:30 = 6$

Thus, he must leave the station at 3:30 p.m.

## Practice Problems

1

### Out of the given units of time, identify the most reasonable unit to measure the time that it would take to make one sandwich.

Seconds
Minutes
Hours
Minutes + Hours
CorrectIncorrect
Minutes are the most reasonable unit of time that it would take to make one sandwich.
2

### How many seconds are there in 11 minutes?

100 seconds
110 seconds
600 seconds
660 seconds
CorrectIncorrect
We know that 1 minute $= 60$ seconds
11 minutes $= 11 \times 60$ seconds
11 minutes $= 660$ seconds
3

### How much are 4800 seconds in hours?

1 hour 20 minutes
1 hour
2 hours
1 hour 40 minutes.
CorrectIncorrect
Correct answer is: 1 hour 20 minutes
We start by converting seconds into minutes.
4800 seconds $= \frac{4800}{60}$ minutes $= 80$ minutes
We know that 1 hour $= 60$ minutes.
80 minutes $= 60$ minutes $+ 20$ minutes $= 1$ hour $+ 20$ minutes
Thus, 4800 seconds $= 1$ hour 20 minutes.
4

### Convert 36000 seconds into hours.

8 hours
20 hours
10 hours
15 hours
CorrectIncorrect
We start by converting seconds into minutes.
36,000 seconds $= \frac{36000}{60}$ minutes
600 minutes
We know that 1 hour $= 60$ minutes.
600 minutes $= \frac{600}{60}$ hours
10 hours
5

### Convert 4 hours 16 minutes into seconds.

15,360 seconds
15,000 seconds
14,000 seconds
10,000 seconds
CorrectIncorrect
We know that 1 hour $= 60$ minutes and 1 minute $= 60$ seconds
Converting 16 minutes to seconds, we get $16 \times 60 = 960$ seconds
Converting 4 hours into seconds, we get $4 \times 60 \times 60 = 14,400$ seconds
Thus, we get a total of 15,360 seconds.