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Std 5 Mathematics · Chapter 9

9. Decimal Fractions

Solutions to Problem Sets 36 to 42 — writing, reading and converting decimals, and adding and subtracting decimal fractions. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part Two.

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Key Ideas

Decimal fraction: a fraction with denominator 10, 100, 1000 … 710 = 0.7, 14100 = 0.14, 3100 = 0.03 (0 in the tenths place).
Places after the point: first place = tenths (110), second place = hundredths (1100). 6.57 is read “six point five seven”.
Units: 100 paise = ₹ 1, 100 cm = 1 m, 10 mm = 1 cm. So 1 paisa = ₹ 0.01, 1 cm = 0.01 m, 1 mm = 0.1 cm.
Common values: half = 0.5, quarter = 0.25, three quarters = 0.75.
Adding / subtracting: write the decimal points one below the other, fill empty places with 0, and work from the right as with whole numbers.

Problem Set 36

QWrite the following mixed fractions in decimal form and read them aloud.
  1. 3 910 = 3.9 — read as “three point nine”
  2. 1 410 = 1.4 — read as “one point four”
  3. 5 310 = 5.3 — read as “five point three”
  4. 810 = 0.8 — read as “zero point eight”
  5. 710 = 0.7 — read as “zero point seven”

Problem Set 37

QWrite the following mixed fractions in decimal form and read them aloud.
  1. 9 110 = 9.1 — read as “nine point one”
  2. 9 1100 = 9.01 — read as “nine point zero one”
  3. 4 53100 = 4.53 — read as “four point five three”
  4. 78100 = 0.78 — read as “zero point seven eight”
  5. 5100 = 0.05 — read as “zero point zero five”
  6. 510 = 0.5 — read as “zero point five”
  7. 210 = 0.2 — read as “zero point two”
  8. 20100 = 0.20 — read as “zero point two zero”

Compare (1) and (2): 9 110 = 9.1 but 9 1100 = 9.01. With hundredths, an empty tenths place must be filled with 0. Also, 0.20 = 0.2, since 20 hundredths = 2 tenths.

Problem Set 38

QRead the decimal fraction and write down the place value of each digit.

(1) 6.13 — read as “six point one three”

  • 6 — Units — 6
  • 1 — Tenths — 1 × 110 = 0.1
  • 3 — Hundredths — 3 × 1100 = 0.03

(2) 48.84 — read as “forty-eight point eight four”

  • 4 — Tens — 40
  • 8 — Units — 8
  • 8 — Tenths — 8 × 110 = 0.8
  • 4 — Hundredths — 4 × 1100 = 0.04

(3) 72.05 — read as “seventy-two point zero five”

  • 7 — Tens — 70
  • 2 — Units — 2
  • 0 — Tenths — 0 × 110 = 0
  • 5 — Hundredths — 5 × 1100 = 0.05

(4) 3.4 — read as “three point four”

  • 3 — Units — 3
  • 4 — Tenths — 4 × 110 = 0.4

(5) 0.59 — read as “zero point five nine”

  • 0 — Units — 0
  • 5 — Tenths — 5 × 110 = 0.5
  • 9 — Hundredths — 9 × 1100 = 0.09

Problem Set 39

1Write how many rupees and how many paise.
  1. ₹ 58.43 = 58 rupees 43 paise
  2. ₹ 9.30 = 9 rupees 30 paise
  3. ₹ 2.30 = 2 rupees 30 paise
  4. ₹ 2.3 = 2 rupees 30 paise (2.3 = 2.30)

₹ 2.3 is not 2 rupees 3 paise. 0.3 rupee = 3 tenths = 30 hundredths = 30 paise. 3 paise would be written ₹ 2.03.

2Write how many rupees in decimal form.
  1. 6 rupees 25 paise = ₹ 6.25
  2. 15 rupees 70 paise = ₹ 15.70
  3. 8 rupees 5 paise = ₹ 8.05
  4. 22 rupees 4 paise = ₹ 22.04
  5. 720 paise = 700 paise + 20 paise = 7 rupees 20 paise = ₹ 7.20
3Write how many metres and how many centimetres.
  1. 58.75 m = 58 m 75 cm
  2. 9.30 m = 9 m 30 cm
  3. 0.30 m = 0 m 30 cm, that is, 30 cm
  4. 0.3 m = 0 m 30 cm, that is, 30 cm
  5. 1.62 m = 1 m 62 cm
  6. 91.4 m = 91 m 40 cm
  7. 7.02 m = 7 m 2 cm
  8. 0.09 m = 0 m 9 cm, that is, 9 cm
4Write how many metres in decimal form.
  1. 1 m 50 cm = 1.50 m (or 1.5 m)
  2. 50 m 40 cm = 50.40 m (or 50.4 m)
  3. 50 m 4 cm = 50.04 m
  4. 734 cm = 7 m 34 cm = 7.34 m
  5. 10 cm = 0.10 m (or 0.1 m)
  6. 2 cm = 0.02 m
5Write how many centimetres and how many millimetres.
  1. 6.9 cm = 6 cm 9 mm
  2. 20.4 cm = 20 cm 4 mm
  3. 0.8 cm = 0 cm 8 mm, that is, 8 mm
  4. 0.5 cm = 0 cm 5 mm, that is, 5 mm

1 cm = 10 mm, so the first decimal place of a length in centimetres gives the millimetres.

6Write how many centimetres in decimal form.
  1. 7 cm 1 mm = 7.1 cm
  2. 16 mm = 1 cm 6 mm = 1.6 cm
  3. 144 mm = 14 cm 4 mm = 14.4 cm
  4. 8 mm = 0.8 cm

Problem Set 40

QWrite the following fractions as decimal fractions.
  1. Two and a half = 2 12 = 2.5
  2. Two and a quarter = 2 14 = 2.25
  3. Two and three quarters = 2 34 = 2.75
  4. Ten and a half = 10 12 = 10.5
  5. Fourteen and three quarters = 14 34 = 14.75
  6. Sixteen and a quarter = 16 14 = 16.25
  7. Twenty-eight and a half = 28 12 = 28.5

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Problem Set 41

1Convert the following into decimal fractions and add them.

(1) ‘One and a half metre’ and ‘two and a half metres’

1.5 m + 2.5 m

1.5+ 2.5 4.0

Total = 4 m (4.0 m)

(2) ‘Four and three quarter rupees’ and ‘seven and a quarter rupees’

₹ 4.75 + ₹ 7.25

4.75+ 7.25 12.00

Total = ₹ 12 (₹ 12.00)

(3) ‘Six and a half metres’ and ‘three and three quarter metres’

6.5 m + 3.75 m = 6.50 m + 3.75 m

6.50+ 3.75 10.25

Total = 10.25 m

2Add: (1) 23.4 + 87.9 (2) 35.74 + 816.6 (3) 6.95 + 74.88 (4) 41.03 + 9.98
(1) 23.4+ 87.9 111.3
(2) 35.74+ 816.60 852.34
(3) 6.95+ 74.88 81.83
(4) 41.03+ 9.98 51.01
  1. 23.4 + 87.9 = 111.3
  2. 35.74 + 816.6 = 852.34
  3. 6.95 + 74.88 = 81.83
  4. 41.03 + 9.98 = 51.01

In (2), 816.6 is written as 816.60 so that both numbers have two decimal places.

3(1) 51.4 cm + 68.5 cm (2) 94.7 m + 1738.45 m (3) ₹ 5158.75 + ₹ 841.25
(1) 51.4+ 68.5 119.9
(2) 94.70+ 1738.45 1833.15
(3) 5158.75+ 841.25 6000.00
  1. 51.4 cm + 68.5 cm = 119.9 cm
  2. 94.7 m + 1738.45 m = 1833.15 m
  3. ₹ 5158.75 + ₹ 841.25 = ₹ 6000.00

Problem Set 42

1Subtract the following.
(1) 25.74− 13.42 12.32
(2) 206.35− 168.22 38.13
(3) 63.4− 31.8 31.6
(4) 63.43− 31.80 31.63
(5) 63.40− 31.83 31.57
(6) 8.23− 5.45 2.78
(7) 18.23− 9.45 8.78
(8) 78.03− 41.65 36.38
  1. 25.74 − 13.42 = 12.32
  2. 206.35 − 168.22 = 38.13
  3. 63.4 − 31.8 = 31.6
  4. 63.43 − 31.8 = 31.63
  5. 63.4 − 31.83 = 31.57
  6. 8.23 − 5.45 = 2.78
  7. 18.23 − 9.45 = 8.78
  8. 78.03 − 41.65 = 36.38

Compare (3), (4) and (5): always match the decimal places first. In (4), 31.8 becomes 31.80; in (5), 63.4 becomes 63.40.

2Vrinda was 1.48 m tall. After a year, her height became 1.53 m. How many centimetres did her height increase in a year?
1.53− 1.48 0.05

Increase = 1.53 m − 1.48 m = 0.05 m. Since 1 m = 100 cm, 0.05 m = 5 cm.

Her height increased by 5 cm in a year.

Something More: Decimal Units of Measurement

AComplete the table of decimal units for distance, mass and volume.
QuantityKilo (1000)Hecto (100)Deca (10)Basic unitDeci (1/10)Centi (1/100)Milli (1/1000)
Distancekilometrehectometredecametremetredecimetrecentimetremillimetre
Masskilogram = 1000 ghectogram = 100 gdecagram = 10 ggramdecigramcentigrammilligram
Volumekilolitre = 1000 Lhectolitre = 100 Ldecalitre = 10 Llitredecilitrecentilitremillilitre

The textbook table gives only the distance row. The mass and volume rows follow the same pattern (in bold): each unit is 10 times the one on its right. The units used most often are kilometre, metre, centimetre, kilogram, gram, litre and millilitre.

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