A degree is a big step: about 111 km of latitude. To give a place more exactly, we split each degree into smaller parts, the same way an hour is split into minutes. You will use what you know about fractions and decimals.
Key idea
One degree has 60 minutes (written ′), and one minute has 60 seconds (″). So 40° 30′ means 40 and 30/60 degrees, which is 40.5°.
Why it works
Babylonian astronomers counted in sixties more than 3,000 years ago, and we still split circles and hours their way. Because 60 can be divided evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, many fractions of a degree come out as whole minutes: a quarter degree is 15′, a third is 20′.
Worked example: Minutes to a decimal
Write 51° 30′ N as a decimal.
- 30′ is 30/60 of a degree.
- 30 ÷ 60 = 0.5.
- So 51° 30′ = 51.5°.
Answer: 51.5° N (London is near here).
Worked example: A decimal to minutes
Write 33.75° S in degrees and minutes.
- Keep the whole degrees: 33°.
- Multiply the decimal part by 60: 0.75 × 60 = 45.
- So it is 33° 45′.
Answer: 33° 45′ S
Worked example: GPS signs
A phone shows a place at -22.9, -43.2. What does that mean?
- GPS apps often write south latitudes and west longitudes as negative numbers.
- The first number is the latitude: -22.9 means 22.9° S.
- The second is the longitude: -43.2 means 43.2° W.
Answer: 22.9° S, 43.2° W (Rio de Janeiro).
| Minutes | Fraction of a degree | Decimal |
|---|---|---|
| 6′ | 6/60 = 1/10 | 0.1° |
| 15′ | 15/60 = 1/4 | 0.25° |
| 30′ | 30/60 = 1/2 | 0.5° |
| 45′ | 45/60 = 3/4 | 0.75° |
Common mistake
Reading 40° 30′ as 40.30°. Minutes are sixtieths, not hundredths: 30′ is half a degree, so 40° 30′ = 40.5°. Check: the decimal part can never reach 1, and a decimal part of .30 would be only 18′. Also check the sign on GPS numbers: a minus sign means S or W.