☰ Contents · Mathematics

Decimal fractions

Lessons 56–57 · 2 lessons · B.Q. Khaydarov. Mathematics Grade 5, Parts 1–2. Revised and expanded third edition. Tashkent, 2020
56

Decimal fractions

Textbook: Part 2, lesson 56, pp. 76–79
GoalThe idea of a decimal fraction; reading and writing decimals; converting between decimals and common fractions.
New words
decimal fraction · o‘nli kasrdecimal comma · vergultenths place · o‘ndan birlar xonasihundredths place · yuzdan birlar xonasi
Explanation

Fractions whose denominator is 10, 100, 1000 and so on are called decimal fractions. They are written without the denominator: first the whole part, then the decimal point, then the numerator of the fractional part. For example, 7 3/10 = 7.3 and 5 7/100 = 5.07. The number of zeros in the denominator must equal the number of digits after the point, so a zero is put in front of the numerator if needed: 4 7/1000 = 4.007. For a proper fraction the whole part is 0: 35/100 = 0.35. The first place after the point is tenths, the second is hundredths and the third is thousandths. In Uzbek, 8.52 is read as «8 whole 52 hundredths».

Worked examples
3 m 25 cm = 3 m + 25/100 m = 3 25/100 m = 3.25 m. 6 kg 40 g = 6 40/1000 kg = 6.040 kg = 6.04 kg.
0.09 = 9/100, 12.5 = 12 5/10, 2.003 = 2 3/1000. The zero matters: 0.09 and 0.9 are not equal.
Class activity

“Ruler decimals”: measure 4 objects (pencil, eraser, etc.) in cm and mm, then write each length in centimetres as a decimal (for example, 13 cm 6 mm = 13.6 cm).

Practice
1
Write 2 m 7 cm in metres as a decimal.
2
Write 9/100 as a decimal.
3
Express 4.015 kg in kg and g.
4
Why are 0.5 and 0.05 not equal?