GSEB Class 6 Maths Solutions Chapter 8 દશાંશ સંખ્યાઓ Exercise 8.4

Chapter 8 Decimal Numbers Ex 8.4

Question 1. Use decimals to express the following in rupees:
(a) 5 પૈસા
(b) 75 પૈસા
(c) 20 પૈસા
(d) 50 રૂપિયા 90 પૈસા
(e) 725 પૈસા
Answer:
(a) 5 પૈસા
We know that 100 paise equals 1 rupee.
\( \implies \) So, 1 paisa equals \( \frac{1}{100} \) of a rupee.
\( \implies \) Therefore, 5 paise will be \( 5 \times \frac{1}{100} \) rupees.
\( = \frac{5}{100} \) rupees
\( = 0.05 \) rupees

(b) 75 પૈસા
We know that 100 paise equals 1 rupee.
\( \implies \) So, 1 paisa equals \( \frac{1}{100} \) of a rupee.
\( \implies \) Therefore, 75 paise will be \( 75 \times \frac{1}{100} \) rupees.
\( = \frac{75}{100} \) rupees
\( = 0.75 \) rupees

(c) 20 પૈસા
We know that 100 paise equals 1 rupee.
\( \implies \) So, 1 paisa equals \( \frac{1}{100} \) of a rupee.
\( \implies \) Therefore, 20 paise will be \( 20 \times \frac{1}{100} \) rupees.
\( = \frac{20}{100} \) rupees
\( = 0.20 \) rupees

(d) 50 રૂપિયા 90 પૈસા
We know that 100 paise equals 1 rupee.
\( \implies \) So, 1 paisa equals \( \frac{1}{100} \) of a rupee.
\( \implies \) Therefore, 50 rupees 90 paise means 50 rupees plus 90 paise.
\( = 50 \) rupees \( + 90 \times \frac{1}{100} \) rupees
\( = 50 \) rupees \( + 0.90 \) rupees
\( = (50 + 0.90) \) rupees
\( = 50.90 \) rupees

(e) 725 પૈસા
We know that 100 paise equals 1 rupee.
\( \implies \) So, 1 paisa equals \( \frac{1}{100} \) of a rupee.
\( \implies \) Therefore, 725 paise will be \( \frac{725}{100} \) rupees.
\( = \frac{700 + 25}{100} \) rupees
\( = (\frac{700}{100} + \frac{25}{100}) \) rupees
\( = (7 + 0.25) \) rupees
\( = 7.25 \) rupees
In simple words: To convert paise into rupees, you just divide the number of paise by 100 because 100 paise makes 1 rupee. If you have both rupees and paise, convert only the paise part to rupees and then add it to the existing rupees.

Exam Tip: Remember that 1 Rupee = 100 Paise. Always divide the paise amount by 100 to convert it to rupees and add it to any existing rupee value. Use a decimal point to separate rupees and paise correctly.

Question 2. Use decimals to express the following in meters:
(a) 15 सेमी
(b) 6 સેમી
(c) 2 મીટર 45 સેમી
(d) 9 મીટર 7 સેમી
(e) 419 सेमी
Answer:
(a) 15 सेमी
We know that 100 centimeters equals 1 meter.
\( \implies \) So, 1 centimeter equals \( \frac{1}{100} \) of a meter.
\( \implies \) Therefore, 15 centimeters will be \( 15 \times \frac{1}{100} \) meters.
\( = \frac{15}{100} \) meters
\( = 0.15 \) meters

(b) 6 સેમી
We know that 100 centimeters equals 1 meter.
\( \implies \) So, 1 centimeter equals \( \frac{1}{100} \) of a meter.
\( \implies \) Therefore, 6 centimeters will be \( 6 \times \frac{1}{100} \) meters.
\( = \frac{6}{100} \) meters
\( = 0.06 \) meters

(c) 2 મીટર 45 સેમી
We know that 100 centimeters equals 1 meter.
\( \implies \) So, 1 centimeter equals \( \frac{1}{100} \) of a meter.
\( \implies \) Therefore, 2 meters 45 centimeters means 2 meters plus 45 centimeters.
\( = 2 \) meters \( + 45 \times \frac{1}{100} \) meters
\( = 2 \) meters \( + \frac{45}{100} \) meters
\( = (2 + 0.45) \) meters
\( = 2.45 \) meters

(d) 9 મીટર 7 સેમી
We know that 100 centimeters equals 1 meter.
\( \implies \) So, 1 centimeter equals \( \frac{1}{100} \) of a meter.
\( \implies \) Therefore, 9 meters 7 centimeters means 9 meters plus 7 centimeters.
\( = 9 \) meters \( + 7 \times \frac{1}{100} \) meters
\( = 9 \) meters \( + \frac{7}{100} \) meters
\( = (9 + 0.07) \) meters
\( = 9.07 \) meters

(e) 419 सेमी
We know that 100 centimeters equals 1 meter.
\( \implies \) So, 1 centimeter equals \( \frac{1}{100} \) of a meter.
\( \implies \) Therefore, 419 centimeters will be \( 419 \times \frac{1}{100} \) meters.
\( = \frac{419}{100} \) meters
\( = (\frac{400+19}{100}) \) meters
\( = (\frac{400}{100} + \frac{19}{100}) \) meters
\( = (4 + 0.19) \) meters
\( = 4.19 \) meters
In simple words: To change centimeters into meters, you just divide by 100. If you have both meters and centimeters, convert the centimeter part to meters first and then add it to the meters already there.

Exam Tip: Always remember that 1 meter = 100 centimeters. To convert cm to m, divide by 100. When both units are given, convert the smaller unit (cm) to the larger unit (m) and then combine them.

Question 3. Use decimals to express the following in centimeters:
(a) 5 મિમી
(b) 60 मिमी
(c) 164 मिमी
(d) 9 સેમી 8 મિમી
(e) 93 મિમી
Answer:
(a) 5 મિમી
We know that 10 millimeters equals 1 centimeter.
\( \implies \) So, 1 millimeter equals \( \frac{1}{10} \) of a centimeter.
\( \implies \) Therefore, 5 millimeters will be \( 5 \times \frac{1}{10} \) centimeters.
\( = \frac{5}{10} \) centimeters
\( = 0.5 \) centimeters

(b) 60 મિમી
We know that 10 millimeters equals 1 centimeter.
\( \implies \) So, 1 millimeter equals \( \frac{1}{10} \) of a centimeter.
\( \implies \) Therefore, 60 millimeters will be \( 60 \times \frac{1}{10} \) centimeters.
\( = \frac{60}{10} \) centimeters
\( = 6 \) centimeters

(c) 164 मिमी
We know that 10 millimeters equals 1 centimeter.
\( \implies \) So, 1 millimeter equals \( \frac{1}{10} \) of a centimeter.
\( \implies \) Therefore, 164 millimeters will be \( 164 \times \frac{1}{10} \) centimeters.
\( = \frac{164}{10} \) centimeters
\( = (\frac{100+60+4}{10}) \) centimeters
\( = (\frac{100}{10} + \frac{60}{10} + \frac{4}{10}) \) centimeters
\( = 10 + 6 + 0.4 \) centimeters
\( = 16.4 \) centimeters

(d) 9 સેમી 8 મિમી
We know that 10 millimeters equals 1 centimeter.
\( \implies \) So, 1 millimeter equals \( \frac{1}{10} \) of a centimeter.
\( \implies \) Therefore, 9 centimeters 8 millimeters means 9 centimeters plus 8 millimeters.
\( = 9 \) centimeters \( + 8 \times \frac{1}{10} \) centimeters
\( = 9 \) centimeters \( + \frac{8}{10} \) centimeters
\( = 9 \) centimeters \( + 0.8 \) centimeters
\( = 9.8 \) centimeters

(e) 93 मिमी
We know that 10 millimeters equals 1 centimeter.
\( \implies \) So, 1 millimeter equals \( \frac{1}{10} \) of a centimeter.
\( \implies \) Therefore, 93 millimeters will be \( 93 \times \frac{1}{10} \) centimeters.
\( = \frac{93}{10} \) centimeters
\( = (\frac{90}{10} + \frac{3}{10}) \) centimeters
\( = (9 + 0.3) \) centimeters
\( = 9.3 \) centimeters
In simple words: To convert millimeters to centimeters, divide the number of millimeters by 10. If you have both centimeters and millimeters, convert the millimeters to centimeters and then add them together.

Exam Tip: The key conversion to remember is 1 cm = 10 mm. When expressing mm in cm, divide by 10. Always double-check your decimal placement for accuracy.

Question 4. Use decimals to express the following in kilometers:
(a) 8 મીટર
(b) 88 મીટર
(c) 8888 મીટર
(d) 70 કિમી 5 મીટર
Answer:
(a) 8 મીટર
We know that 1000 meters equals 1 kilometer.
\( \implies \) So, 1 meter equals \( \frac{1}{1000} \) of a kilometer.
\( \implies \) Therefore, 8 meters will be \( 8 \times \frac{1}{1000} \) kilometers.
\( = \frac{8}{1000} \) kilometers
\( = 0.008 \) kilometers

(b) 88 મીટર
We know that 1000 meters equals 1 kilometer.
\( \implies \) So, 1 meter equals \( \frac{1}{1000} \) of a kilometer.
\( \implies \) Therefore, 88 meters will be \( 88 \times \frac{1}{1000} \) kilometers.
\( = \frac{88}{1000} \) kilometers
\( = 0.088 \) kilometers

(c) 8888 મીટર
We know that 1000 meters equals 1 kilometer.
\( \implies \) So, 1 meter equals \( \frac{1}{1000} \) of a kilometer.
\( \implies \) Therefore, 8888 meters will be \( 8888 \times \frac{1}{1000} \) kilometers.
\( = \frac{8888}{1000} \) kilometers
\( = (\frac{8000+888}{1000}) \) kilometers
\( = (\frac{8000}{1000} + \frac{888}{1000}) \) kilometers
\( = (8 + 0.888) \) kilometers
\( = 8.888 \) kilometers

(d) 70 કિમી 5 મીટર
We know that 1000 meters equals 1 kilometer.
\( \implies \) So, 1 meter equals \( \frac{1}{1000} \) of a kilometer.
\( \implies \) Therefore, 70 kilometers 5 meters means 70 kilometers plus 5 meters.
\( = 70 \) kilometers \( + 5 \times \frac{1}{1000} \) kilometers
\( = 70 \) kilometers \( + \frac{5}{1000} \) kilometers
\( = 70 \) kilometers \( + 0.005 \) kilometers
\( = 70.005 \) kilometers
In simple words: To convert meters to kilometers, you divide by 1000. If both kilometers and meters are given, change only the meters part into kilometers and then add it to the given kilometers.

Exam Tip: Remember that 1 km = 1000 m. When converting meters to kilometers, move the decimal point three places to the left. If you have a combined measurement, make sure to convert only the meter part to kilometers before adding.

Question 5. Use decimals to express the following in kilograms:
(a) 2 ग्राम
(b) 100 ग्राम
(c) 3750 ग्राम
(d) 5 કિગ્રા 8 ગ્રામ
(e) 26 કિગ્રા 50 ગ્રામ
Answer:
(a) 2 ગ્રામ
We know that 1000 grams equals 1 kilogram.
\( \implies \) So, 1 gram equals \( \frac{1}{1000} \) of a kilogram.
\( \implies \) Therefore, 2 grams will be \( 2 \times \frac{1}{1000} \) kilograms.
\( = \frac{2}{1000} \) kilograms
\( = 0.002 \) kilograms

(b) 100 ગ્રામ
We know that 1000 grams equals 1 kilogram.
\( \implies \) So, 1 gram equals \( \frac{1}{1000} \) of a kilogram.
\( \implies \) Therefore, 100 grams will be \( 100 \times \frac{1}{1000} \) kilograms.
\( = \frac{100}{1000} \) kilograms
\( = \frac{1}{10} \) kilograms
\( = 0.1 \) kilograms

(c) 3750 ગ્રામ
We know that 1000 grams equals 1 kilogram.
\( \implies \) So, 1 gram equals \( \frac{1}{1000} \) of a kilogram.
\( \implies \) Therefore, 3750 grams will be \( 3750 \times \frac{1}{1000} \) kilograms.
\( = \frac{3750}{1000} \) kilograms
\( = (\frac{3000+750}{1000}) \) kilograms
\( = (\frac{3000}{1000} + \frac{750}{1000}) \) kilograms
\( = (3 + 0.750) \) kilograms
\( = 3.750 \) kilograms

(d) 5 કિગ્રા 8 ગ્રામ
We know that 1000 grams equals 1 kilogram.
\( \implies \) So, 1 gram equals \( \frac{1}{1000} \) of a kilogram.
\( \implies \) Therefore, 5 kilograms 8 grams means 5 kilograms plus 8 grams.
\( = 5 \) kilograms \( + 8 \times \frac{1}{1000} \) kilograms
\( = 5 \) kilograms \( + \frac{8}{1000} \) kilograms
\( = 5 \) kilograms \( + 0.008 \) kilograms
\( = 5.008 \) kilograms

(e) 26 કિગ્રા 50 ગ્રામ
We know that 1000 grams equals 1 kilogram.
\( \implies \) So, 1 gram equals \( \frac{1}{1000} \) of a kilogram.
\( \implies \) Therefore, 26 kilograms 50 grams means 26 kilograms plus 50 grams.
\( = 26 \) kilograms \( + 50 \times \frac{1}{1000} \) kilograms
\( = 26 \) kilograms \( + \frac{50}{1000} \) kilograms
\( = 26 \) kilograms \( + 0.050 \) kilograms
\( = 26.050 \) kilograms
In simple words: To change grams into kilograms, you simply divide the number of grams by 1000. If you have both kilograms and grams, first convert the grams to kilograms, and then add it to the existing kilograms.

Exam Tip: Remember that 1 kg = 1000 g. When converting grams to kilograms, divide by 1000. Pay close attention to the decimal point placement, ensuring it is three places to the left for accurate conversion.