Convert the following times from hours and minutes to hours, giving your answers as mixed numbers and decimals, correct to 2 decimal places. (a) 1 hour 40 minutes (b) 3 hours 10 minutes (c) 1 hour 6 minutes (d) 2 hours 18 minutes (e) 3 hours 5 minutes (f) 6 hours 2 minutes (g) i hour 7 minutes (h) 2 hours 23 minutes
The Correct Answer and Explanation is:
To convert times given in hours and minutes into a mixed number and a decimal, we follow these steps:
- Convert the minutes into a fraction of an hour. Since there are 60 minutes in an hour, we divide the number of minutes by 60.
- Convert this fraction into a decimal. This can be done by performing the division of minutes by 60.
Conversion Steps:
- For mixed numbers:
- Keep the hours as a whole number.
- Convert the minutes into a fraction of an hour (e.g., 40 minutes is ( \frac{40}{60} )).
- Simplify the fraction if possible, and then express the answer as a mixed number (e.g., 1 hour ( \frac{2}{3} ) hour).
- For decimals:
- Divide the minutes by 60 and then add this result to the whole number of hours.
Examples:
(a) 1 hour 40 minutes
- Convert minutes to fraction: ( \frac{40}{60} = \frac{2}{3} ) hour.
- Mixed number: 1 ( \frac{2}{3} ) hours.
- Decimal: ( \frac{40}{60} = 0.67 ), so the decimal is ( 1 + 0.67 = 1.67 ) hours.
(b) 3 hours 10 minutes
- Convert minutes to fraction: ( \frac{10}{60} = \frac{1}{6} ) hour.
- Mixed number: 3 ( \frac{1}{6} ) hours.
- Decimal: ( \frac{10}{60} = 0.17 ), so the decimal is ( 3 + 0.17 = 3.17 ) hours.
(c) 1 hour 6 minutes
- Convert minutes to fraction: ( \frac{6}{60} = \frac{1}{10} ) hour.
- Mixed number: 1 ( \frac{1}{10} ) hours.
- Decimal: ( \frac{6}{60} = 0.10 ), so the decimal is ( 1 + 0.10 = 1.10 ) hours.
(d) 2 hours 18 minutes
- Convert minutes to fraction: ( \frac{18}{60} = \frac{3}{10} ) hour.
- Mixed number: 2 ( \frac{3}{10} ) hours.
- Decimal: ( \frac{18}{60} = 0.30 ), so the decimal is ( 2 + 0.30 = 2.30 ) hours.
(e) 3 hours 5 minutes
- Convert minutes to fraction: ( \frac{5}{60} = \frac{1}{12} ) hour.
- Mixed number: 3 ( \frac{1}{12} ) hours.
- Decimal: ( \frac{5}{60} = 0.08 ), so the decimal is ( 3 + 0.08 = 3.08 ) hours.
(f) 6 hours 2 minutes
- Convert minutes to fraction: ( \frac{2}{60} = \frac{1}{30} ) hour.
- Mixed number: 6 ( \frac{1}{30} ) hours.
- Decimal: ( \frac{2}{60} = 0.03 ), so the decimal is ( 6 + 0.03 = 6.03 ) hours.
(g) 1 hour 7 minutes
- Convert minutes to fraction: ( \frac{7}{60} ) hour.
- Mixed number: 1 ( \frac{7}{60} ) hours.
- Decimal: ( \frac{7}{60} = 0.12 ), so the decimal is ( 1 + 0.12 = 1.12 ) hours.
(h) 2 hours 23 minutes
- Convert minutes to fraction: ( \frac{23}{60} ) hour.
- Mixed number: 2 ( \frac{23}{60} ) hours.
- Decimal: ( \frac{23}{60} = 0.38 ), so the decimal is ( 2 + 0.38 = 2.38 ) hours.
Final Answers:
- (a) 1 hour 40 minutes = 1 ( \frac{2}{3} ) hours = 1.67 hours
- (b) 3 hours 10 minutes = 3 ( \frac{1}{6} ) hours = 3.17 hours
- (c) 1 hour 6 minutes = 1 ( \frac{1}{10} ) hours = 1.10 hours
- (d) 2 hours 18 minutes = 2 ( \frac{3}{10} ) hours = 2.30 hours
- (e) 3 hours 5 minutes = 3 ( \frac{1}{12} ) hours = 3.08 hours
- (f) 6 hours 2 minutes = 6 ( \frac{1}{30} ) hours = 6.03 hours
- (g) 1 hour 7 minutes = 1 ( \frac{7}{60} ) hours = 1.12 hours
- (h) 2 hours 23 minutes = 2 ( \frac{23}{60} ) hours = 2.38 hours
These conversions provide a way to express time in different formats, which is useful for calculations, planning, or scheduling.