GSEB Class 6 Maths Solutions Chapter 8 દશાંશ સંખ્યાઓ Exercise 8.5

 

Question 1. Find the sum of each of the following:
(a) \( 0.007 + 8.5 + 30.08 \)
(b) \( 18 + 0.632 + 13.8 \)
(c) \( 27.076 + 0.55 + 0.004 \)
(d) \( 25.65 + 9.005 + 3.7 \)
(e) \( 0.75 + 10.425 + 2 \)
(f) \( 280.69 + 25.2 + 38 \)
Answer:
(a) To find the sum of \( 0.007 \), \( 8.5 \), and \( 30.08 \), we arrange them in a place value table and then add them up.

The total comes out to be \( 38.587 \). So, \( 0.007 + 8.5 + 30.08 = 38.587 \).
(b) To find the sum of \( 18 \), \( 0.632 \), and \( 13.8 \), we arrange them in a place value table and then add them up.
The total comes out to be \( 29.432 \). So, \( 15 + 0.632 + 13.8 = 29.432 \).
(c) To find the sum of \( 27.076 \), \( 0.55 \), and \( 0.004 \), we arrange them in a place value table and then add them up.
The total comes out to be \( 27.630 \). So, \( 27.076 + 0.55 + 0.004 = 27.63 \).
(d) To find the sum of \( 25.65 \), \( 9.005 \), and \( 3.7 \), we arrange them in a place value table and then add them up.
The total comes out to be \( 38.355 \). So, \( 25.65 + 9.005 + 3.7 = 38.355 \).
(e) To find the sum of \( 0.75 \), \( 10.425 \), and \( 2 \), we arrange them in a place value table and then add them up.
The total comes out to be \( 13.175 \). So, \( 0.75 + 10.425 + 2 = 13.175 \).
(f) To find the sum of \( 280.69 \), \( 25.2 \), and \( 38 \), we arrange them in a place value table and then add them up.
The total comes out to be \( 343.890 \). So, \( 280.69 + 25.2 + 38 = 343.89 \).
In simple words: To add numbers with decimals, make sure the decimal points line up in a straight column. Then, add the numbers normally, starting from the rightmost digits, and put the decimal point in the answer in the same place.

Exam Tip: When adding decimals, always align the decimal points vertically. Adding zeros to the end of numbers after the decimal point (e.g., changing 8.5 to 8.500) can make alignment easier and prevent errors.

 

Question 2. Rashid bought a math textbook for Rs \( 35.75 \) and a science textbook for Rs \( 32.60 \). Find the total amount spent by Rashid.
Answer:
Cost of math textbook \( = \) Rs \( 35.75 \)
Cost of science textbook \( = + \) Rs \( 32.60 \)
Total amount spent \( = \) Rs \( 68.35 \)
Rashid spent a total of Rs \( 68.35 \) on both books.
In simple words: Rashid paid Rs 35.75 for his math book and Rs 32.60 for his science book. To find out how much money he spent altogether, you simply add those two amounts.

Exam Tip: For problems involving money, clearly label each amount and its purpose. Always align the decimal points when adding or subtracting monetary values to ensure accuracy.

 

Question 3. Radhika's mother gave her Rs \( 10.50 \) and her father gave her Rs \( 15.80 \). Find the total amount given to Radhika by her parents.
Answer:
Amount given by mother \( = \) Rs \( 10.50 \)
Amount given by father \( = + \) Rs \( 15.80 \)
Total amount given by parents \( = \) Rs \( 26.30 \)
Radhika received a total of Rs \( 26.30 \) from her parents.
In simple words: Radhika's mom gave her Rs 10.50, and her dad gave her Rs 15.80. To find the total amount, you need to combine the money from both parents.

Exam Tip: When dealing with combined amounts from different sources, ensure all values are correctly added. Present your answer clearly with the final total and unit (Rs).

 

Question 4. Nasreen bought 3 meters 20 cm of cloth for her shirt and 2 meters 5 cm of cloth for her pants. Find the total length of cloth she bought.
Answer:
Note: We need to convert centimeters to meters.
\( 100 \) centimeters \( = 1 \) meter
So, \( 1 \) centimeter \( = \frac{1}{100} \) meter
Cloth bought for shirt \( = 3 \) meters \( 20 \) cm
\( = 3 \) meters \( + 20 \) cm
\( = 3 \) meters \( + 20 \times \frac{1}{100} \) meters
\( = 3 \) meters \( + \frac{20}{100} \) meters
\( = 3.20 \) meters
Cloth bought for pants \( = 2 \) meters \( 5 \) cm
\( = 2 \) meters \( + 5 \) cm
\( = 2 \) meters \( + 5 \times \frac{1}{100} \) meters
\( = 2 \) meters \( + \frac{5}{100} \) meters
\( = 2.05 \) meters
Total cloth bought:
Cloth for shirt \( = 3.20 \) meters
Cloth for pants \( = + 2.05 \) meters
Total cloth purchased \( = 5.25 \) meters
Nasreen bought a total of \( 5.25 \) meters of cloth.
In simple words: Nasreen bought cloth for a shirt (3 meters 20 cm) and pants (2 meters 5 cm). To find the total, you must change centimeters into meters first. Then, add the total meters of cloth.

Exam Tip: Always ensure all units are consistent before performing calculations. Convert all measurements to a single unit (e.g., meters) to avoid errors in addition or subtraction.

 

Question 5. Naresh walked 2 km 35 meters in the morning and 1 km 7 meters in the evening. How much distance did Naresh walk in total?
Answer:
Note: We need to convert meters to kilometers.
\( 1000 \) meters \( = 1 \) km
So, \( 1 \) meter \( = \frac{1}{1000} \) km
Distance walked in the morning \( = 2 \) km \( 35 \) meters
\( = 2 \) km \( + 35 \) meters
\( = 2 \) km \( + \frac{35}{1000} \) km
\( = 2 \) km \( + 0.035 \) km
\( = 2.035 \) km
Distance walked in the evening \( = 1 \) km \( 7 \) meters
\( = 1 \) km \( + 7 \) meters
\( = 1 \) km \( + \frac{7}{1000} \) km
\( = 1 \) km \( + 0.007 \) km
\( = 1.007 \) km
Total distance walked:
Distance walked in the morning \( = 2.035 \) km
Distance walked in the evening \( = + 1.007 \) km
Total distance walked \( = 3.042 \) km
Naresh walked a total distance of \( 3.042 \) km.
In simple words: Naresh walked some distance in the morning and some in the evening. To find his total walking distance, first change all meters into kilometers, then add the two kilometer distances together.

Exam Tip: When converting smaller units to larger units (like meters to kilometers), remember to divide by the conversion factor. This ensures accurate decimal representation for addition.

 

Question 6. Sunita traveled 15 km 268 meters by bus, 7 km 7 meters by car, and 500 meters by walking to reach her school. How far is her school from her home?
Answer:
Note: We need to convert meters to kilometers.
\( 1000 \) meters \( = 1 \) km
So, \( 1 \) meter \( = \frac{1}{1000} \) km
Distance Sunita traveled by bus \( = 15 \) km \( 268 \) meters
\( = 15 \) km \( + 268 \) meters
\( = 15 \) km \( + \frac{268}{1000} \) km
\( = 15 \) km \( + 0.268 \) km
\( = 15.268 \) km
Distance Sunita traveled by car \( = 7 \) km \( 7 \) meters
\( = 7 \) km \( + 7 \) meters
\( = 7 \) km \( + \frac{7}{1000} \) km
\( = 7 \) km \( + 0.007 \) km
\( = 7.007 \) km
Distance Sunita traveled by walking \( = 500 \) meters
\( = 500 \times \frac{1}{1000} \) km
\( = \frac{500}{1000} \) km
\( = 0.500 \) km
Total distance Sunita traveled:
By bus \( = 15.268 \) km
By car \( = + 7.007 \) km
By walking \( = + 0.500 \) km
Total distance \( = 22.775 \) km
Sunita's school is \( 22.775 \) km away from her home.
In simple words: Sunita traveled to school using three ways: bus, car, and walking. First, change all distances into kilometers. Then, add up all the kilometer distances to find the total distance from her home to school.

Exam Tip: When adding multiple distances, ensure each segment is converted to the same unit before summing them. This problem involves mixed units (km and meters), so uniform conversion is key for accuracy.

 

Question 7. Ravi bought 5 kg 400 grams of rice, 2 kg 20 grams of sugar, and 10 kg 850 grams of flour. Find the total weight of the items Ravi bought.
Answer:
Note: We need to convert grams to kilograms.
\( 1000 \) grams \( = 1 \) kg
So, \( 1 \) gram \( = \frac{1}{1000} \) kg
Ravi's purchase of rice \( = 5 \) kg \( 400 \) grams
\( = 5 \) kg \( + 400 \) grams
\( = 5 \) kg \( + \frac{400}{1000} \) kg
\( = 5 \) kg \( + 0.400 \) kg
\( = 5.400 \) kg
Ravi's purchase of sugar \( = 2 \) kg \( 20 \) grams
\( = 2 \) kg \( + 20 \) grams
\( = 2 \) kg \( + \frac{20}{1000} \) kg
\( = 2 \) kg \( + 0.020 \) kg
\( = 2.020 \) kg
Ravi's purchase of flour \( = 10 \) kg \( 850 \) grams
\( = 10 \) kg \( + 850 \) grams
\( = 10 \) kg \( + \frac{850}{1000} \) kg
\( = 10 \) kg \( + 0.850 \) kg
\( = 10.850 \) kg
Ravi's total purchase:
Rice \( = 5.400 \) kg
Sugar \( = + 2.020 \) kg
Flour \( = + 10.850 \) kg
Total weight purchased \( = 18.270 \) kg
Ravi bought a total weight of \( 18.270 \) kg.
In simple words: Ravi bought rice, sugar, and flour. Each item has a weight given in kilograms and grams. First, change all gram amounts into kilograms. Then, add up the kilograms for all items to find the total weight Ravi purchased.

Exam Tip: When dealing with weights, remember that \( 1 \) kilogram equals \( 1000 \) grams. Converting all quantities to kilograms before addition simplifies the calculation and reduces the chance of errors.