Decimal Fractions

Q1: Fill in the blanks:

i. 6 hundredths in decimal form is _______.

Step: \[ 6\text{ hundredths} = \frac{6}{100} = 0.06 \] Answer: 0.06

ii. \(\frac{6}{25}\) in decimal form is _______.

Step: \[ \frac{6}{25} = \frac{24}{100} = 0.24 \] Answer: 0.24

iii. 2 m 15 cm + 6 m 5 cm = _______ metres.

Step: Convert cm to metres: \[ 15\text{ cm} = 0.15\text{ m},\quad 5\text{ cm} = 0.05\text{ m} \] Add: \[ (2 + 0.15) + (6 + 0.05) = 2.15 + 6.05 = 8.20\text{ m} \] Answer: 8.20 metres

iv. 15P + 5P = ₹ ________.

Step: \[ 15P + 5P = 20P = \frac{20}{100} = ₹0.20 \] Answer: ₹0.20

v. 15 km + 75 m = _______.

Step: Convert 75 m to km: \[ 75\text{ m} = \frac{75}{1000} = 0.075\text{ km} \] Add: \[ 15 + 0.075 = 15.075\text{ km} \] Answer: 15.075 km

vi. (2 cm – 5 mm) = _______ cm.

Step: Convert 5 mm to cm: \[ 5\text{ mm} = \frac{5}{10} = 0.5\text{ cm} \] Subtract: \[ 2 – 0.5 = 1.5\text{ cm} \] Answer: 1.5 cm

Q2: Write (T) for true and (F) for false for each of the statements given below:

i. 3 m 5 cm = 3.5 m

Step: 5 cm = 0.05 m \[ 3 + 0.05 = 3.05 \ne 3.5 \] Answer: False (F)

ii. 16 km 30 m = 16.30 km

Step: 30 m = 0.030 km \[ 16 + 0.030 = 16.030 \ne 16.30 \] Answer: False (F)

iii. ₹8 + 6P = ₹(8.60)

Step: 6 paise = ₹0.06 \[ ₹8 + ₹0.06 = ₹8.06 \ne ₹8.60 \] Answer: False (F)

iv. 0.03 = 3 hundredths

Step: \[ \frac{3}{100} = 0.03 \] Answer: True (T)

v. 7 kg 80 g = 7.8 kg

Step: 80 g = 0.08 kg \[ 7 + 0.08 = 7.08 \ne 7.8 \] Answer: False (F)

vi. 0.1 + 0.01 + 0.001 = 0.111

Step:

  0.100  
+ 0.010  
+ 0.001  
 -------
  0.111

Answer: True (T)