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Year 3 Maths Time

Convert between analog & digital time

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Theory

Converting between analog and digital time is a Year 3 skill: matching a clock with hands to a digital time written as hours and minutes. You read the short hour hand for the hour and the long minute hand for the minutes, then write it as h:mm, like 6:20. This page shows how to change an analog clock into a digital time and how to set a clock from a digital time, including o'clock, quarter past, half past and quarter to. Curriculum: VC2M3M04 / AC9M3M04.

An analog clock shows the time with two hands on a round face. The short hand is the hour hand and the long hand is the minute hand.

A digital clock shows the time as numbers, like 6:20. The number before the colon is the hour. The two numbers after the colon are the minutes. The minutes always use two digits, so five past is written :05 and o'clock is written :00.

To convert means to change the same time from one form to the other. Each number on the clock face is 5 minutes, so you count by fives to turn the minute hand into digital minutes, and back again.

Analog clock showing half past eight matched to the digital time 8:30 A round analog clock with the short hour hand halfway between 8 and 9 and the long minute hand on the 6, next to a digital display reading 8:30. 1 2 3 4 5 6 7 8 9 10 11 12 reads 8:30
Half past eight on the clock is the digital time 8:30. The hour hand is halfway to 9 and the minute hand is on the 6.
Clock face showing the digital minutes at each numeral A round clock face with small grey numbers inside showing the digital minutes at each numeral: 5 at the 1, 10 at the 2, 15 at the 3, and so on up to 55, then 0 at the 12. 1 2 3 4 5 6 7 8 9 10 11 12 5 10 15 20 25 30 35 40 45 50 55 0
Each number is the digital minutes: the 4 means :20, the 6 means :30, the 9 means :45. Count by fives to convert.

These facts help you convert the hands into digital minutes.

\[ 1 \text{ number} = 5 \text{ minutes} \]
1 number =5 minutes
\[ \text{o'clock} = \text{:}00 \]
o'clock =:00
\[ \text{quarter past} = \text{:}15 \]
quarter past =:15
\[ \text{half past} = \text{:}30 \]
half past =:30
\[ \text{quarter to} = \text{:}45 \]
quarter to =:45
Minute hand points toDigital minutes
12:00
3:15
6:30
9:45
Past or to? A digital time always counts minutes past the hour. When someone says the minutes to the hour, take that away from 60. Ten to 10 is 60 − 10 = 50 minutes past 9, so the digital time is 9:50.
One numeral, two meanings. For the hour hand the 4 means 4 o'clock. For the minute hand the 4 means \(4 \times 5 = 20\) minutes, because the minute hand counts in fives.

Analog clock to digital time

  1. Read the hour. Find the short hand and see which number it has just passed. That is the hour, written before the colon.
  2. Read the minutes. Find the long hand. Count by fives to the number it points to, then count on any single marks.
  3. Write it as h:mm. Put the hour, a colon, then the minutes as two digits, like 3:38. Write :00 for o'clock.

Digital time to analog clock

  1. Point the hour hand. Put the short hand on the hour number, or just past it if there are minutes.
  2. Find the minute number. Divide the minutes by 5 to see which number the long hand points to. 40 minutes is 40 ÷ 5 = 8, so the minute hand points to the 8.
  3. Point the minute hand at that number.

Digital time to words

  1. 30 minutes or less: say the minutes past the hour. \(9\!:\!20\) is twenty past 9.
  2. More than 30 minutes: take the minutes away from 60 and say them to the next hour. \(9\!:\!40\) is \(60 - 40 = 20\) minutes to 10, or twenty to 10.
  3. After 12 comes 1. The hour after 12 is 1, so \(12\!:\!35\) is twenty-five to 1.
Example 1 — Analog to digital
Write the time on this clock as a digital time.
Analog clock showing twenty past six matched to the digital time 6:20 The short hour hand is a little past the 6 and the long minute hand points to the 4, next to a digital display reading 6:20. 1 2 3 4 5 6 7 8 9 10 11 12 reads 6:20
Solution
\(\text{hour hand}\)\(\to\)\(6\)
\(\text{minute hand} \to 4\)\(=\)\(20\text{ min}\)
minute hand at 4=20 minutes, so 6:20

The minute hand is on the 4, so count 5, 10, 15, 20. The digital time is 6:20.

Example 2 — To the minute
Write this clock as a digital time, to the minute.
Analog clock showing thirty-eight minutes past three matched to the digital time 3:38 The short hour hand is between 3 and 4, near the 4, and the long minute hand is between the 7 and 8, three little marks past the 7, next to a digital display reading 3:38. 1 2 3 4 5 6 7 8 9 10 11 12 reads 3:38
Solution
\(7\)\(\to\)\(35\text{ min}\)
\(35 + 3\)\(=\)\(38\text{ min}\)
35+3=38, so 3:38

The minute hand is 3 marks past the 7, so 35 + 3 = 38. The hour hand is just before the 4, so the hour is 3. The digital time is 3:38.

Example 3 — Digital to analog
A digital clock shows 9:50. Where do the hands point?
Digital time 9:50 matched to an analog clock showing ten to ten A digital display reading 9:50, next to a round analog clock with the short hour hand almost at the 10 and the long minute hand on the 10, which is 50 minutes past or ten minutes to ten. 9:50 shows 1 2 3 4 5 6 7 8 9 10 11 12
Solution
\(50 \div 5\)\(=\)\(10\)
\(\text{minute hand}\)\(\to\)\(10\)
50÷5=10

50 ÷ 5 = 10, so the minute hand points to the 10. The hour hand is almost at the 10. This is also ten to 10.

Example 4 — Words to digital
Zoe's bus leaves at quarter to eleven. Write this as a digital time.
Analog clock showing quarter to eleven matched to the digital time 10:45 The short hour hand is between 10 and 11, near the 11, and the long minute hand points to the 9, next to a digital display reading 10:45. 1 2 3 4 5 6 7 8 9 10 11 12 reads 10:45
Solution
\(\text{quarter to}\)\(=\)\(45\text{ min past}\)
\(45\text{ min past } 10\)\(=\)\(10\text{:}45\)
quarter to 11 = 10:45

Quarter to eleven is 15 minutes before 11, which is 45 minutes past 10. The digital time is 10:45.

Example 5 — Digital to words
Write \(11\!:\!40\) in words, using "to".
Solution
\(60 - 40\)\(=\)\(20\text{ min to go}\)
\(\text{next hour}\)\(=\)\(12\)
60 - 40 = 20, twenty to 12

40 minutes is more than 30, so count to the next hour: \(11\!:\!40\) is twenty to 12.

Example 6 — Past 12
The school concert starts at \(12\!:\!45\). Write this time in words.
Solution
\(60 - 45\)\(=\)\(15\text{ min to go}\)
\(\text{hour after }12\)\(=\)\(1\)
60 - 45 = 15, quarter to 1

45 minutes past 12 is 15 minutes before 1 o'clock, so \(12\!:\!45\) is quarter to 1.

Common pitfalls

Write minutes with two digits. Ten past 4 is 4:10, not 4:1. Five past 4 is 4:05, not 4:5.
Each number is 5 minutes, not 1. When the minute hand points to the 4, the digital minutes are 20, so it is written :20, not :04.
Keep the hour the short hand has just passed. At 8:30 the hour hand sits between 8 and 9, but the hour is still 8, so it is 8:30, not 9:30.
"To" times still count minutes past. Ten to 10 is written 9:50, not 10:50. Take the minutes away from 60 first.
"To" uses the next hour. \(4\!:\!50\) is ten to 5, not ten to 4. The hour hand is heading towards the 5.

Frequently asked questions

How do you change an analog clock into a digital time?

Read the short hour hand to get the hour, then read the long minute hand to get the minutes by counting the numbers in fives. Write the hour first, then a colon, then the two-digit minutes, like 6:20.

How do you write minutes in a digital time?

The minutes always take two digits after the colon. Five minutes past is written :05, ten past is :10, and o'clock is written :00.

What is quarter to eleven as a digital time?

Quarter to eleven is 15 minutes before 11 o'clock, which is 45 minutes past 10. As a digital time it is written 10:45.

How do you set an analog clock from a digital time?

Point the short hour hand at the hour number and the long minute hand at the minutes. Divide the minutes by 5 to find which number the minute hand points to, so 40 minutes points to the 8.

Why does 8:30 have the hour hand between two numbers?

At half past, the hour hand has moved halfway to the next hour, so at 8:30 it sits between the 8 and the 9. The hour is still 8 because the hand has not reached the 9 yet.

Is 9:50 the same as ten to ten?

Yes. 9:50 is 50 minutes past 9, and 60 minus 50 is 10, so it is also ten minutes to 10. Both names describe the same time.

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