Cambridge Primary Checkpoint · Mathematics · Stage 6 · Geometry and Measure

Time: Decimals and Mixed Units

Change times such as 2.75 hours into hours and minutes and back again — with diagrams, worked examples, common mistakes and a 14-question practice quiz.

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Change a time given as a decimal (for example 2.75 hours) into mixed units (2 hours 45 minutes), and change mixed units back into a decimal. [6Gt.01]
You will use this with hours and minutes, minutes and seconds, days and hours, weeks and days, and years and months — and in word problems, timetables and calculator questions. [6Gt.01]

Time is the one measure where our usual decimal habits can trick us. In length, 2.5 m is 2 m 50 cm because there are 100 cm in a metre. In time, 2.5 hours is 2 hours 30 minutes, because there are only 60 minutes in an hour. This page shows you exactly how to change between the two forms, with diagrams, worked examples, the mistakes examiners see most, and a practice quiz.

1. Key words and facts

Word / phrase	Meaning / use
time interval	مدة زمنية — how long something lasts (a duration), not a time on a clock
mixed units	وحدات مختلطة — a time written with two units, e.g. 3 hours 20 minutes
decimal	عدد عشري — a number with a decimal point, e.g. 3.5
convert	يحوّل — change from one unit or form to another
hour (h)	ساعة — 60 minutes
minute (min)	دقيقة — 60 seconds
second (s)	ثانية — the smallest everyday unit of time
duration	المدة — another word for a time interval

Fact to remember	So 0.5 of the bigger unit is…
1 hour = 60 minutes	0.5 hour = 30 minutes
1 minute = 60 seconds	0.5 minute = 30 seconds
1 day = 24 hours	0.5 day = 12 hours
1 week = 7 days	0.5 week = 3.5 days
1 year = 12 months	0.5 year = 6 months

The number you multiply or divide by depends on the units. For hours and minutes it is 60; for days and hours it is 24; for years and months it is 12; for weeks and days it is 7. Always ask yourself: "How many of the small unit make ONE of the big unit?"

2. Why 0.1 hour is 6 minutes

A decimal is a part of ONE whole. When the whole is one hour, the whole is 60 minutes. So 0.1 of an hour is one tenth of 60 minutes = 60 ÷ 10 = 6 minutes. The double number line shows every tenth of an hour.

Each tenth of an hour is 6 minutes. Read straight down from the hours scale to the minutes scale.

Quarters and halves are the fractions you will meet most often. Learn them so well that you do not need to work them out:

A quarter of an hour is 15 minutes, half an hour is 30 minutes, three quarters of an hour is 45 minutes.

Decimal of an hour	Fraction	Minutes
0.1 h	1/10	6 min
0.2 h	1/5	12 min
0.25 h	1/4	15 min
0.3 h	3/10	18 min
0.4 h	2/5	24 min
0.5 h	1/2	30 min
0.6 h	3/5	36 min
0.75 h	3/4	45 min
0.8 h	4/5	48 min
0.9 h	9/10	54 min
0.05 h	1/20	3 min

3. Method: decimal → mixed units

The whole number part stays as the big unit. In 3.4 hours, the 3 means 3 whole hours.
Take the decimal part on its own (0.4).
Multiply the decimal part by the number of small units in one big unit: 0.4 × 60 = 24 minutes.
Write the answer in mixed units: 3 hours 24 minutes.
Check: is your number of minutes less than 60? (It must be.)

A bar model: two whole hours and 0.4 of the third hour.

Mental trick for × 60: multiply by 6, then by 10. For 0.7 hour: 0.7 × 6 = 4.2, and 4.2 × 10 = 42 minutes. Or use tenths: 0.7 is 7 tenths, and each tenth is 6 minutes, so 7 × 6 = 42 minutes.

Hundredths: 0.05 hour is 5 hundredths of 60 minutes = 3 minutes, so 0.15 hour = 9 minutes, 0.35 hour = 21 minutes, 0.85 hour = 51 minutes. (Check 0.85 hour: 0.8 h = 48 min and 0.05 h = 3 min, total 51 min.)

4. Method: mixed units → decimal

Keep the whole hours as the whole number part.
Write the minutes as a fraction of an hour: minutes/60. For 1 hour 12 minutes: 12/60.
Simplify the fraction and change it to a decimal: 12/60 = 1/5 = 0.2 (or work out 12 ÷ 60 = 0.2).
Join the parts: 1 hour 12 minutes = 1.2 hours.

Mixed units	Minutes as a fraction of an hour	Decimal
2 h 30 min	30/60 = 1/2	2.5 h
1 h 15 min	15/60 = 1/4	1.25 h
4 h 45 min	45/60 = 3/4	4.75 h
3 h 6 min	6/60 = 1/10	3.1 h
1 h 36 min	36/60 = 3/5	1.6 h
2 h 20 min	20/60 = 1/3	2.333… h

Notice the last row. 20 minutes is one third of an hour, and one third as a decimal goes on for ever (0.3333…). On a calculator, 2 hours 20 minutes appears as 2.333333. That is why times like 20 or 40 minutes are usually written as fractions (2⅓ hours) or kept in mixed units.

5. Other pairs of units

The same two methods work for any pair of time units. Only the multiplier changes.

Decimal	Working	Mixed units
3.5 minutes	0.5 × 60 s = 30 s	3 minutes 30 seconds
1.25 minutes	0.25 × 60 s = 15 s	1 minute 15 seconds
1.5 days	0.5 × 24 h = 12 h	1 day 12 hours
2.25 days	0.25 × 24 h = 6 h	2 days 6 hours
2.5 years	0.5 × 12 months = 6 months	2 years 6 months
1.75 years	0.75 × 12 months = 9 months	1 year 9 months
4.5 weeks	0.5 × 7 days = 3.5 days	4 weeks 3½ days

Sometimes you change everything into the small unit instead. 1.5 days = 1.5 × 24 = 36 hours. 2.5 minutes = 2.5 × 60 = 150 seconds. Going the other way, divide: 90 minutes = 90 ÷ 60 = 1.5 hours; 270 seconds = 270 ÷ 60 = 4.5 minutes.

القاعدة الذهبية

الساعة فيها 60 دقيقة مش 100! يعني 2.5 ساعة = ساعتين و30 دقيقة، مش ساعتين و50 دقيقة.
من عشري لمختلط: سيب الرقم الصحيح زي ما هو، واضرب الجزء العشري × 60. مثال: 1.4 ساعة → 0.4 × 60 = 24 ← ساعة و24 دقيقة.
من مختلط لعشري: اقسم الدقائق ÷ 60. مثال: 45 دقيقة = 45 ÷ 60 = 0.75 ساعة.

6. Worked examples

Worked example 1 (1 mark) Write 4.6 hours in hours and minutes.

Whole hours: 4.
Decimal part: 0.6 × 60 = 36 minutes (6 tenths × 6 minutes).
Answer: 4 hours 36 minutes.

Common mistake: writing 4 hours 6 minutes or 4 hours 60 minutes — copying the digits after the point instead of converting them.

Worked example 2 (1 mark) Write 2 hours 48 minutes as a decimal number of hours.

Minutes as a fraction of an hour: 48/60.
Simplify: 48/60 = 8/10 = 0.8 (divide top and bottom by 6).
Answer: 2.8 hours.

Common mistake: writing 2.48 hours. The digits 48 are minutes, not hundredths of an hour.

Worked example 3 (1 mark) Tick (✓) the longer time: 3.3 hours or 3 hours 25 minutes.

Change both into the same form. 3.3 hours = 3 hours + 0.3 × 60 minutes = 3 hours 18 minutes.
Compare: 3 hours 18 minutes is less than 3 hours 25 minutes.
Answer: 3 hours 25 minutes is longer (by 7 minutes).

Worked example 4 (2 marks) — calculator allowed A school day has 6 lessons. Each lesson lasts 0.75 hours. There is also a 0.5 hour break. How long is the school day? Give your answer in hours and minutes.

Lessons: 6 × 0.75 = 4.5 hours.
Add the break: 4.5 + 0.5 = 5 hours.
Check with minutes: 0.75 h = 45 min, 6 × 45 = 270 min = 4 h 30 min; plus 30 min = 5 h 0 min. ✓
Answer: 5 hours 0 minutes (5 hours).

Marks: 1 mark for a correct method (6 × 0.75 + 0.5 or 6 × 45 + 30), 1 mark for the correct answer.

Worked example 5 (2 marks) A train leaves Cairo at 08:50. The journey takes 2.7 hours. At what time does the train arrive?

Convert the duration: 2.7 hours = 2 hours + 0.7 × 60 minutes = 2 hours 42 minutes.
Add 2 hours: 08:50 → 10:50.
Add 42 minutes: 10:50 + 10 min = 11:00, then + 32 min = 11:32.
Answer: 11:32.

Common mistake: adding 2.7 to 8.50 to get 11.20 — you cannot add decimal hours to a clock time. Convert first.

Worked example 6 (2 marks) Mariam runs for 1 hour 24 minutes on Monday and 0.9 hours on Tuesday. How much longer did she run on Monday? Give your answer in minutes.

Monday: 1 hour 24 minutes = 60 + 24 = 84 minutes.
Tuesday: 0.9 hours = 0.9 × 60 = 54 minutes.
Difference: 84 − 54 = 30 minutes.
Answer: 30 minutes.

Common mistakes

Treating time as if it were base 10: 1.5 hours is NOT 1 hour 50 minutes, and 1 hour 30 minutes is NOT 1.30 hours.
Converting the whole number as well: in 3.2 hours, only the 0.2 changes to minutes (12 min). The 3 hours stay.
Getting more than 59 minutes in the answer (e.g. 2 hours 75 minutes). 75 minutes = 1 hour 15 minutes, so the answer is 3 hours 15 minutes.
Using 60 for every unit: days use 24, years use 12, weeks use 7.
Adding a decimal duration straight to a clock time. Change the duration to hours and minutes first.
Forgetting units in the answer, or giving minutes when the question asks for hours (read the answer line).

How Checkpoint asks this

Fill in the boxes: "3.25 hours = □ hours □ minutes". Write a number in each box.
Tick or ring: which of these is the same as 1 hour 45 minutes? Watch for the trap answer 1.45 hours.
Compare or order times written in different forms. Change them all into minutes first — it is the safest way.
Word problems on Paper 2 (calculator) where the calculator shows a decimal such as 4.75. You must change it to 4 hours 45 minutes yourself.
"Explain" questions: a character makes the 1.5 = 1 h 50 min mistake and you say why it is wrong. Use the fact 1 hour = 60 minutes in your sentence.
Show your working on 2-mark questions: a correct method can earn 1 mark even if you slip with the arithmetic.

خلي بالك في الامتحان

لو الآلة الحاسبة طلّعت 3.5 ساعة، اكتبها 3 ساعات و30 دقيقة — متكتبش 3 ساعات و5 دقايق.
عشان تقارن بين وقتين، حوّل الاتنين لدقايق الأول.

Practice

Remember

1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours, 1 week = 7 days, 1 year = 12 months.
Decimal → mixed units: keep the whole number, multiply the decimal part by 60 (or 24, 12, 7).
Mixed units → decimal: divide the minutes by 60 (e.g. 45 ÷ 60 = 0.75).
Learn: 0.1 h = 6 min, 0.25 h = 15 min, 0.5 h = 30 min, 0.75 h = 45 min.
1.5 hours is 1 hour 30 minutes — never 1 hour 50 minutes.
Convert a decimal duration to hours and minutes before adding it to a clock time.

All pages in this course

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Checkpoint 6 Maths: The Test and How to Prepare

Number: integers and calculation

Number: place value, decimals, fractions, percentages and ratio

Geometry and measure

Statistics and probability

Practice tests