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Measurement of Time

NCERT Class 5 · Mathematics Based on NCERT Class 5 Mathematics textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter teaches students how to measure time accurately using hours, minutes, and seconds. It explains the relationship between these units and how to convert from one to another. The big idea is that time can be measured precisely, and seconds help us capture very short durations, like in a race. Students will learn to read clocks, calculate elapsed time, and convert between 12-hour and 24-hour formats.
Key Concepts (10)
Seconds
A unit of time used to measure very short durations. 1 minute = 60 seconds.
e.g. In a 200 m race, participants finish in 1 minute and a few seconds, so seconds help decide the winner.
Minutes
A unit of time equal to 60 seconds. Used to measure moderate durations.
e.g. Raghav studied for 50 minutes for each subject.
Hours
A unit of time equal to 60 minutes. Used to measure longer durations.
e.g. Raghu took 1 hour 5 minutes to reach his Nana ji's house.
12-hour format
A way of writing time using a.m. (before noon) and p.m. (after noon).
e.g. 05:30 a.m. means 5:30 in the morning; 02:30 p.m. means 2:30 in the afternoon.
24-hour format
A way of writing time from 00:00 to 23:59 hours, without a.m. or p.m.
e.g. 14:30 hours is the same as 02:30 p.m.
Elapsed time
The amount of time that passes from a start time to an end time.
e.g. From 01:15 p.m. to 01:42 p.m., the elapsed time is 27 minutes.
Conversion of hours to minutes
Multiply the number of hours by 60 to get minutes.
e.g. 2 hours = 2 × 60 = 120 minutes.
Conversion of minutes to hours
Divide the number of minutes by 60 to get hours. The remainder is the leftover minutes.
e.g. 180 minutes = 3 hours because 180 ÷ 60 = 3.
Conversion of minutes to seconds
Multiply the number of minutes by 60 to get seconds.
e.g. 5 minutes = 5 × 60 = 300 seconds.
Conversion of seconds to minutes
Divide the number of seconds by 60 to get minutes. The remainder is the leftover seconds.
e.g. 320 seconds = 5 minutes 20 seconds because 320 ÷ 60 = 5 remainder 20.
Formulas & Equations (6)
1 hour = 60 minutes
Reads as: One hour equals sixty minutes
Variables: hour (h), minute (min)
Use when: Converting hours to minutes or minutes to hours
⚠ Students often think 1 hour = 100 minutes, like in decimal systems.
1 minute = 60 seconds
Reads as: One minute equals sixty seconds
Variables: minute (min), second (sec)
Use when: Converting minutes to seconds or seconds to minutes
⚠ Students forget that 60 seconds make 1 minute, not 100.
Hours to minutes: multiply by 60
Reads as: To convert hours to minutes, multiply the number of hours by sixty
Variables: hours (h), minutes (min)
Use when: Converting a given time in hours to minutes
⚠ Students multiply by 100 instead of 60.
Minutes to hours: divide by 60
Reads as: To convert minutes to hours, divide the number of minutes by sixty
Variables: minutes (min), hours (h)
Use when: Converting a given time in minutes to hours and minutes
⚠ Students forget to write the remainder as minutes.
Minutes to seconds: multiply by 60
Reads as: To convert minutes to seconds, multiply the number of minutes by sixty
Variables: minutes (min), seconds (sec)
Use when: Converting minutes to seconds
⚠ Students multiply by 60 but forget to add extra seconds if any.
Seconds to minutes: divide by 60
Reads as: To convert seconds to minutes, divide the number of seconds by sixty
Variables: seconds (sec), minutes (min)
Use when: Converting seconds to minutes and seconds
⚠ Students write only the quotient and ignore the remainder.
How It Works
Calculating elapsed time
  1. Step 1: Identify the start time and end time.
  2. Step 2: Subtract the start time from the end time, handling hours and minutes separately.
  3. Step 3: If minutes in start time are greater than minutes in end time, borrow 1 hour (60 minutes) from the hours.
  4. Step 4: Write the answer in hours and minutes.
💡 Always check if you need to borrow 60 minutes from the hour when subtracting minutes.
Converting 12-hour format to 24-hour format
  1. Step 1: For a.m. times (except 12 a.m.), keep the same hour and minutes, but write 'hours' instead of 'a.m.'.
  2. Step 2: For 12 a.m., write 00 hours.
  3. Step 3: For p.m. times (except 12 p.m.), add 12 to the hour. For 12 p.m., keep 12 hours.
💡 12:00 a.m. is 00:00 hours, and 12:00 p.m. is 12:00 hours. Do not add 12 to 12 p.m.
Converting 24-hour format to 12-hour format
  1. Step 1: If the hour is 00, write 12 a.m.
  2. Step 2: If the hour is between 01 and 11, write the same hour with a.m.
  3. Step 3: If the hour is 12, write 12 p.m.
  4. Step 4: If the hour is between 13 and 23, subtract 12 and write p.m.
💡 Hours from 13 to 23 become 1 to 11 p.m. after subtracting 12.
Finding start time or end time given elapsed time
  1. Step 1: If finding end time, add elapsed time to start time.
  2. Step 2: If finding start time, subtract elapsed time from end time.
  3. Step 3: Handle minutes exceeding 60 by converting to hours.
💡 When adding minutes, if total minutes exceed 60, convert 60 minutes to 1 hour and add to the hour.
Exam Traps — Don't Make These Mistakes
⚠ Confusing a.m. and p.m. in 12-hour format
✗ 02:30 p.m. as 02:30 hours in 24-hour format
→ 02:30 p.m. is after noon, so it should be 14:30 hours, not 02:30 hours.
✓ 02:30 p.m. = 14:30 hours
⚠ Forgetting to borrow when subtracting minutes
✗ From 03:10 p.m. to 04:05 p.m., elapsed time = 1 hour 5 minutes (by subtracting 10 from 5 directly)
→ You cannot subtract 10 from 5. You must borrow 1 hour (60 minutes) from 4 hours, making it 3 hours 65 minutes, then subtract.
✓ 04:05 p.m. = 03:65 p.m.; 03:65 - 03:10 = 0 hours 55 minutes.
⚠ Incorrect conversion of seconds to minutes
✗ 320 seconds = 5 minutes 20 seconds (correct), but they write 5.20 minutes
→ 5.20 minutes means 5 minutes and 0.20 of a minute (12 seconds), not 20 seconds. The decimal is not the same as minutes.
✓ 320 seconds = 5 minutes 20 seconds (write as 5 min 20 sec, not 5.20 min)
⚠ Mistaking 12 a.m. and 12 p.m.
✗ 12:00 a.m. is noon
→ 12:00 a.m. is midnight, not noon. 12:00 p.m. is noon.
✓ 12:00 a.m. = 00:00 hours (midnight); 12:00 p.m. = 12:00 hours (noon)
⚠ Adding elapsed time incorrectly across hours
✗ Start 06:15 p.m., add 1 hour 45 minutes, they write 07:60 p.m.
→ 60 minutes is 1 hour, so 07:60 p.m. should be 08:00 p.m.
✓ 06:15 p.m. + 1 hour 45 minutes = 07:60 p.m. = 08:00 p.m.
Compare & Contrast
Representation of time
12-hour format
24-hour format
12-hour format uses a.m. and p.m. and repeats 1-12 twice a day; 24-hour format uses 00-23 hours and does not use a.m./p.m.
Unit of time measurement
Minutes
Seconds
Minutes are used for moderate durations (e.g., 10 minutes to eat), while seconds are used for very short durations (e.g., blinking eyes takes a few seconds). 1 minute = 60 seconds.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks) on conversion, 1 LA (5 marks) on elapsed time word problems
Most asked: Conversion between 12-hour and 24-hour formats · Calculating elapsed time · Conversion of hours to minutes and minutes to seconds
Don't skip: Word problems involving start time, end time, and elapsed time (e.g., Jyoti went to play at 06:15 PM and came back after 1 hour 45 minutes. At what time did she reach home?)
One-Line Revision (read aloud before the exam)
  1. 1 hour = 60 minutes.
  2. 1 minute = 60 seconds.
  3. To convert hours to minutes, multiply by 60.
  4. To convert minutes to hours, divide by 60; the remainder is minutes.
  5. To convert minutes to seconds, multiply by 60.
  6. To convert seconds to minutes, divide by 60; the remainder is seconds.
  7. 12:00 a.m. is midnight (00:00 hours).
  8. 12:00 p.m. is noon (12:00 hours).
  9. For p.m. times (except 12 p.m.), add 12 to get 24-hour format.
  10. For a.m. times (except 12 a.m.), keep the same hour in 24-hour format.
  11. When subtracting minutes, if needed, borrow 60 minutes from the hour.
  12. Elapsed time = end time - start time.
  13. Seconds help measure very short durations like in a race.
  14. The double number line helps visualize conversions between hours and minutes.

MCQs — 10 Questions with Answers

Q1. How many seconds are there in 3 minutes?

  • A. 180 seconds ✓
  • B. 150 seconds
  • C. 200 seconds
  • D. 120 seconds

Answer: A — 3 minutes × 60 seconds per minute = 180 seconds.

Q2. Raghav took 1 hour 20 minutes to paint a picture. How many minutes is this?

  • A. 70 minutes
  • B. 80 minutes ✓
  • C. 90 minutes
  • D. 100 minutes

Answer: B — (1 × 60) + 20 = 60 + 20 = 80 minutes.

Q3. What is 05:30 p.m. in 24-hour format?

  • A. 05:30 hours
  • B. 17:30 hours ✓
  • C. 13:30 hours
  • D. 15:30 hours

Answer: B — Add 12 to afternoon times: 5:30 p.m. + 12 = 17:30 hours.

Q4. Raghu left his house at 08:00 and reached his Nana ji's house at 09:05. How long did the journey take?

  • A. 1 hour
  • B. 1 hour 5 minutes ✓
  • C. 5 minutes
  • D. 50 minutes

Answer: B — From 08:00 to 09:00 is 1 hour, plus 5 more minutes to 09:05 = 1 hour 5 minutes.

Q5. How many hours and minutes is 150 minutes?

  • A. 1 hour 30 minutes
  • B. 2 hours 30 minutes ✓
  • C. 3 hours
  • D. 2 hours 10 minutes

Answer: B — 150 ÷ 60 = 2 with remainder 30, so 2 hours 30 minutes.

Q6. Which activity would you measure in seconds?

  • A. Doing homework
  • B. Playing a cricket match
  • C. Snapping fingers ✓
  • D. Cooking lunch

Answer: C — Snapping fingers is a very quick action that happens in just a few seconds, so we use seconds to measure it precisely.

Q7. If Jyoti went to play at 06:15 p.m. and came back after 1 hour 45 minutes, what time did she reach home?

  • A. 07:00 p.m.
  • B. 07:45 p.m.
  • C. 08:00 p.m. ✓
  • D. 08:30 p.m.

Answer: C — 06:15 p.m. + 1 hour = 07:15 p.m.; then 07:15 p.m. + 45 minutes = 08:00 p.m.

Q8. Convert 220 minutes into hours and minutes.

  • A. 2 hours 40 minutes
  • B. 3 hours 40 minutes ✓
  • C. 2 hours 20 minutes
  • D. 4 hours

Answer: B — 220 ÷ 60 = 3 remainder 40;

Q9. Ragini finished her homework at 09:40 p.m. and it took 1 hour 10 minutes. When did she start?

  • A. 08:30 p.m. ✓
  • B. 08:20 p.m.
  • C. 08:50 p.m.
  • D. 07:30 p.m.

Answer: A — Work backward: 09:40 p.m. − 1 hour = 08:40 p.m.; then 08:40 p.m. − 10 minutes = 08:30 p.m.

Q10. Look at the clock image. The seconds hand is at 12 and the minute hand is at 2. How many seconds have passed?

  • A. 10 seconds ✓
  • B. 12 seconds
  • C. 2 seconds
  • D. 0 seconds

Answer: A — When the minute hand points to 2, that represents 10 minutes on the minute scale, but since we're asked about seconds and the seconds hand is at 12, we count: the minute hand at 2 means 10 minutes, so 0 seconds have passed in the current minute; if asking total, each number = 5 minutes, but for seconds: each number = 5 seconds, so minute hand at 2 = 10 seconds mark.

Flashcards

How many seconds are in 1 minute?

1 minute = 60 seconds.

If Raghav started yoga at 06:00 and finished at 07:20, how long did he practice?

From 06:00 to 07:20 is 1 hour and 20 minutes.

Convert 180 minutes into hours.

180 minutes ÷ 60 = 3 hours.

What is the 24-hour format for 02:30 p.m.?

02:30 p.m. = 14:30 hours (add 12 to afternoon times).

What is the 12-hour format for 20:45 hours?

20:45 hours = 08:45 p.m. (subtract 12 from times after 12:00).

How many minutes is 2 hours 45 minutes?

(2 × 60) + 45 = 120 + 45 = 165 minutes.

Jyoti went to play at 06:15 p.m. and came back after 1 hour 45 minutes. What time did she return?

06:15 p.m. + 1 hour 45 minutes = 08:00 p.m.

Convert 320 seconds into minutes and seconds.

320 ÷ 60 = 5 minutes and 20 seconds (since 5 × 60 = 300, and 320 − 300 = 20).

When is seconds used instead of minutes to measure time?

Seconds are used for short time durations like races, quick activities, or precise measurements.

If lunch break starts at 12:30 p.m. and lasts 35 minutes, when does it end?

12:30 p.m. + 35 minutes = 01:05 p.m.

Important Board Questions

How many seconds are in 5 minutes? [1 mark]

Use the rule: 1 minute = 60 seconds. Multiply 5 by 60.

Fill in the blanks: (i) 1 hour 10 minutes = _____ minutes (ii) 75 minutes = _____ hour _____ minutes [2 marks]

For (i): Convert 1 hour to 60 minutes, then add 10. For (ii): Divide 75 by 60 to find the hour; the remainder is minutes.

Raghav studies 4 subjects, spending 50 minutes on each. Find the total time taken in hours and minutes. Explain your strategy. [3 marks]

Step 1: Find total minutes = 4 × 50 = 200 minutes. Step 2: Convert 200 minutes to hours and minutes by dividing by 60 (200 ÷ 60 = 3 remainder 20).

A group of children left for a picnic at 08:30 a.m. They returned after 4 hours and 10 minutes. (i) At what time did they return? (ii) Convert this return time to 24-hour format. (iii) How many minutes was the picnic duration? Show all steps. [5 marks]

Step 1: Add 4 hours 10 minutes to 08:30 a.m. (Add hours first: 08:30 + 4 hours = 12:30; then add 10 minutes = 12:40 p.m.). Step 2: Convert 12:40 p.m. to 24-hour format (add 12: 12 + 12 = 24, so it becomes 00:40, but noon times stay as 12:40 hours). Step 3: Convert 4 hours 10 minutes to minutes = (4 × 60) + 10 = 240 + 10 = 250 minutes.

True or False: 12:30 a.m. and 12:30 p.m. are the same time. Give a reason. [2 marks]

12:30 a.m. is after midnight (very early morning, around 12:30 in the night). 12:30 p.m. is after noon (afternoon). They are 12 hours apart.

Assertion-Reason Questions for Measurement of Time

Q1. Assertion (A):

In a race, seconds are more useful than minutes to show which runner is fastest.

Reason (R):

Seconds help us measure very small time differences that minutes cannot show clearly.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true. Seconds give us precision to see small differences—for example, one runner finishes in 1:55 and another in 1:57. The reason correctly explains why the assertion is true.

Q2. Assertion (A):

1 hour equals 60 minutes.

Reason (R):

We use this conversion to change hours into minutes and minutes into hours.

Answer: B — Both A and R are true, but R is NOT the correct explanation of A — Both the assertion and reason are true and correct, but the reason is not the explanation for why 1 hour = 60 minutes. The reason just tells us how to use this fact.

Q3. Assertion (A):

The time 02:30 p.m. in 24-hour format is 14:30 hours.

Reason (R):

Afternoon times require us to add 12 to the hour number in 24-hour format.

Answer: A — Both A and R are true, and R is the correct explanation of A — The assertion is true (2 + 12 = 14, so 14:30), and the reason correctly explains why. This is the exact rule for converting p.m. times to 24-hour format.

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Case-Based Questions (CBQ) for Measurement of Time

Case Study:

Akira and her friends went to the park at 05:00 p.m. They played for 1 hour 45 minutes and then went to an ice cream shop. At the ice cream shop, it took Akira 15 minutes to eat her ice cream. After that, she took 20 minutes to walk back home. What time did Akira reach home?

Q1. At what time did Akira reach the ice cream shop?

  • A. 06:45 p.m. ✓
  • B. 07:00 p.m.
  • C. 06:15 p.m.
  • D. 07:15 p.m.

Answer: A

Q2. How long did Akira spend eating ice cream and walking home combined?

  • A. 20 minutes
  • B. 25 minutes
  • C. 35 minutes ✓
  • D. 40 minutes

Answer: C

Q3. What time did Akira reach home?

  • A. 07:20 p.m.
  • B. 07:30 p.m.
  • C. 07:40 p.m. ✓
  • D. 08:00 p.m.

Answer: C

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