GSEB Class 6 Maths Solutions Chapter 8 Decimals Exercise 8.4

Question 1. Express as rupees using decimals.
(a) 5 paise
(b) 75 paise
(c) 20 paise
(d) 50 rupees 90 paise
(e) 725 paise
Answer:
(a) 5 paise
We know that \( 1 \) paisa \( = \frac { 1 }{ 100 } \) Rs.
So, \( 5 \) paise \( = 5 \times \frac { 1 }{ 100 } = \frac { 5 }{ 100 } = 0.05 \) Rs.
(b) 75 paise
We know that \( 1 \) paisa \( = \frac { 1 }{ 100 } \) Rs.
So, \( 75 \) paise \( = 75 \times \frac { 1 }{ 100 } = \frac { 75 }{ 100 } = 0.75 \) Rs.
(c) 20 paise
We know that \( 1 \) paisa \( = \frac { 1 }{ 100 } \) Rs.
So, \( 20 \) paise \( = 20 \times \frac { 1 }{ 100 } = \frac { 20 }{ 100 } = 0.20 \) Rs.
(d) 50 rupees 90 paise
We know that \( 1 \) paisa \( = \frac { 1 }{ 100 } \) Rs.
So, \( 90 \) paise \( = 90 \times \frac { 1 }{ 100 } = 0.90 \) Rs.
Now, \( 50 \) rupees \( + 90 \) paise \( = 50 \) Rs. \( + 0.90 \) Rs. \( = (50 + 0.90) \) Rs. \( = 50.90 \) Rs.
(e) 725 paise
We know that \( 1 \) paisa \( = \frac { 1 }{ 100 } \) Rs.
So, \( 725 \) paise \( = 725 \times \frac { 1 }{ 100 } = \frac { 725 }{ 100 } = 7.25 \) Rs.
Alternatively, \( 725 \) paise \( = (7 + 0.25) \) Rs. \( = 7.25 \) Rs.
In simple words: To change paise into rupees, you divide the number of paise by 100, since 100 paise make 1 rupee. Just shift the decimal point two places to the left.

Exam Tip: Remember that 1 Rupee = 100 Paise. When converting smaller units (paise) to larger units (rupees), you always divide.

Question 2. Express as km using decimals.
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
(e) 419 cm
Answer:
(a) 15 cm
We know that \( 100 \) cm \( = 1 \) m.
This means \( 1 \) cm \( = \frac { 1 }{ 100 } \) m.
So, \( 15 \) cm \( = 15 \times \frac { 1 }{ 100 } \) m \( = \frac { 15 }{ 100 } \) m \( = 0.15 \) m.
To convert meters to kilometers, we know \( 1000 \) m \( = 1 \) km.
So, \( 0.15 \) m \( = \frac{0.15}{1000} \) km \( = 0.00015 \) km.
(b) 6 cm
We know that \( 1 \) cm \( = \frac { 1 }{ 100 } \) m.
So, \( 6 \) cm \( = 6 \times \frac { 1 }{ 100 } \) m \( = \frac { 6 }{ 100 } \) m \( = 0.06 \) m.
Then, \( 0.06 \) m \( = \frac{0.06}{1000} \) km \( = 0.00006 \) km.
(c) 2 m 45 cm
First, convert 45 cm to meters: \( 45 \) cm \( = 45 \times \frac { 1 }{ 100 } \) m \( = 0.45 \) m.
Now, combine with 2 m: \( 2 \) m \( + 0.45 \) m \( = (2 + 0.45) \) m \( = 2.45 \) m.
To convert meters to kilometers: \( 2.45 \) m \( = \frac{2.45}{1000} \) km \( = 0.00245 \) km.
(d) 9 m 7 cm
First, convert 7 cm to meters: \( 7 \) cm \( = 7 \times \frac { 1 }{ 100 } \) m \( = 0.07 \) m.
Now, combine with 9 m: \( 9 \) m \( + 0.07 \) m \( = (9 + 0.07) \) m \( = 9.07 \) m.
To convert meters to kilometers: \( 9.07 \) m \( = \frac{9.07}{1000} \) km \( = 0.00907 \) km.
(e) 419 cm
First, convert 419 cm to meters: \( 419 \) cm \( = 419 \times \frac { 1 }{ 100 } \) m \( = \frac { 419 }{ 100 } \) m.
We can write this as \( \left(\frac{400}{100}+\frac{19}{100}\right) \) m \( = \left(4+\frac{19}{100}\right) \) m \( = (4 + 0.19) \) m \( = 4.19 \) m.
To convert meters to kilometers: \( 4.19 \) m \( = \frac{4.19}{1000} \) km \( = 0.00419 \) km.
In simple words: To change centimeters to kilometers, first change centimeters to meters by dividing by 100, then change meters to kilometers by dividing by 1000. It's like taking two steps to reach the final unit.

Exam Tip: Remember the conversion factors: \( 1 \) m = \( 100 \) cm and \( 1 \) km = \( 1000 \) m. Break down complex conversions into smaller, easier steps.

Question 3. Express as cm using decimals.
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm
Answer:
(a) 5 mm
We know that \( 1 \) mm \( = \frac { 1 }{ 10 } \) cm.
So, \( 5 \) mm \( = 5 \times \frac { 1 }{ 10 } \) cm \( = \frac { 5 }{ 10 } \) cm \( = 0.5 \) cm.
(b) 60 mm
We know that \( 1 \) mm \( = \frac { 1 }{ 10 } \) cm.
So, \( 60 \) mm \( = 60 \times \frac { 1 }{ 10 } \) cm \( = \frac { 60 }{ 10 } \) cm \( = 6.0 \) cm.
(c) 164 mm
We know that \( 1 \) mm \( = \frac { 1 }{ 10 } \) cm.
So, \( 164 \) mm \( = 164 \times \frac { 1 }{ 10 } \) cm \( = \frac { 164 }{ 10 } \) cm.
This can be written as \( \left(\frac{100+60+4}{10}\right) \) cm \( = \left(\frac{100}{10}+\frac{60}{10}+\frac{4}{10}\right) \) cm.
\( = \left(10+6+\frac{4}{10}\right) \) cm \( = 16.4 \) cm.
(d) 9 cm 8 mm
First, convert 8 mm to centimeters: \( 8 \) mm \( = 8 \times \frac { 1 }{ 10 } \) cm \( = 0.8 \) cm.
Now, combine with 9 cm: \( 9 \) cm \( + 0.8 \) cm \( = (9 + 0.8) \) cm \( = 9.8 \) cm.
(e) 93 mm
We know that \( 1 \) mm \( = \frac { 1 }{ 10 } \) cm.
So, \( 93 \) mm \( = 93 \times \frac { 1 }{ 10 } \) cm \( = \frac { 93 }{ 10 } \) cm.
This can be written as \( \left(\frac{90}{10}+\frac{3}{10}\right) \) cm \( = (9 + 0.3) \) cm \( = 9.3 \) cm.
In simple words: To convert millimeters to centimeters, you just divide by 10. This moves the decimal point one place to the left, because 10 millimeters make up 1 centimeter.

Exam Tip: Remember the basic conversion: 1 cm = 10 mm. When moving from a smaller unit (mm) to a larger unit (cm), always divide.

Question 4. Express as km using decimals.
(a) 8 m
(b) 88 m
(c) 8888 m
(d) 70 km 5 m
Answer:
(a) 8 m
We know that \( 1000 \) m \( = 1 \) km.
So, \( 1 \) m \( = \frac { 1 }{ 1000 } \) km.
Therefore, \( 8 \) m \( = 8 \times \frac { 1 }{ 1000 } \) km \( = \frac { 8 }{ 1000 } \) km \( = 0.008 \) km.
(b) 88 m
We know that \( 1000 \) m \( = 1 \) km.
So, \( 1 \) m \( = \frac { 1 }{ 1000 } \) km.
Therefore, \( 88 \) m \( = 88 \times \frac { 1 }{ 1000 } \) km \( = \frac { 88 }{ 1000 } \) km \( = 0.088 \) km.
(c) 8888 m
We know that \( 1 \) m \( = \frac { 1 }{ 1000 } \) km.
Therefore, \( 8888 \) m \( = 8888 \times \frac { 1 }{ 1000 } \) km \( = \frac { 8888 }{ 1000 } \) km.
This can be expressed as \( \left(\frac{8000+888}{1000}\right) \) km \( = \left(\frac{8000}{1000}+\frac{888}{1000}\right) \) km.
\( = [8 + 0.888] \) km \( = 8.888 \) km.
(d) 70 km 5 m
We know that \( 1 \) m \( = \frac { 1 }{ 1000 } \) km.
First, convert 5 m to kilometers: \( 5 \) m \( = 5 \times \frac { 1 }{ 1000 } \) km \( = \frac { 5 }{ 1000 } \) km \( = 0.005 \) km.
Now, combine with 70 km: \( 70 \) km \( + 0.005 \) km \( = [70 + 0.005] \) km \( = 70.005 \) km.
In simple words: To change meters into kilometers, you need to divide by 1000. This is because 1000 meters are equal to 1 kilometer. Just move the decimal point three places to the left.

Exam Tip: Keep in mind that 1 km = 1000 m. When converting from a smaller unit (m) to a larger unit (km), always use division.

Question 5. Express as kg using decimals.
(a) 2 g
(b) 100 g
(c) 3750 g
(d) 5 kg 8 g
(e) 26 kg 50 g
Answer:
(a) 2 g
We know that \( 1000 \) g \( = 1 \) kg.
So, \( 1 \) g \( = \frac { 1 }{ 1000 } \) kg.
Therefore, \( 2 \) g \( = 2 \times \frac { 1 }{ 1000 } \) kg \( = \frac { 2 }{ 1000 } \) kg \( = 0.002 \) kg.
(b) 100 g
We know that \( 1 \) g \( = \frac { 1 }{ 1000 } \) kg.
Therefore, \( 100 \) g \( = 100 \times \frac { 1 }{ 1000 } \) kg \( = \frac { 100 }{ 1000 } \) kg \( = 0.1 \) kg.
(c) 3750 g
We know that \( 1 \) g \( = \frac { 1 }{ 1000 } \) kg.
Therefore, \( 3750 \) g \( = 3750 \times \frac { 1 }{ 1000 } \) kg \( = \frac { 3750 }{ 1000 } \) kg.
This can be written as \( \left(\frac{3000+750}{1000}\right) \) kg \( = \left(\frac{3000}{1000}+\frac{750}{1000}\right) \) kg.
\( = (3 + 0.750) \) kg \( = 3.750 \) kg.
(d) 5 kg 8 g
We know that \( 1 \) g \( = \frac { 1 }{ 1000 } \) kg.
First, convert 8 g to kilograms: \( 8 \) g \( = 8 \times \frac { 1 }{ 1000 } \) kg \( = \frac { 8 }{ 1000 } \) kg \( = 0.008 \) kg.
Now, combine with 5 kg: \( 5 \) kg \( + 0.008 \) kg \( = (5 + 0.008) \) kg \( = 5.008 \) kg.
(e) 26 kg 50 g
We know that \( 1 \) g \( = \frac { 1 }{ 1000 } \) kg.
First, convert 50 g to kilograms: \( 50 \) g \( = 50 \times \frac { 1 }{ 1000 } \) kg \( = \frac { 50 }{ 1000 } \) kg \( = 0.050 \) kg.
Now, combine with 26 kg: \( 26 \) kg \( + 0.050 \) kg \( = (26 + 0.050) \) kg \( = 26.050 \) kg.
In simple words: To change grams into kilograms, you must divide the number of grams by 1000. This is because 1000 grams equal 1 kilogram, so you move the decimal point three places to the left.

Exam Tip: Remember that 1 kg = 1000 g. When converting smaller units (g) to larger units (kg), use division to find the decimal equivalent.