RBSE Solutions Class 6 Maths Chapter 6 Decimal Numbers Exercise 6.2

 

Question 1. Write the decimal numbers for the place value of digits given in the table.

Answer: By looking at the place value table, we can write each number in decimal form. The position of each digit tells us its value, like how many tens or tenths there are.
(i) 230.057
(ii) 001.305 or 1.305
(iii) 253.505
(iv) 340.120 or 340.12
(v) 013.030 or 13.03
In simple words: We convert the numbers from the place value table into decimals. Each digit's place (like hundreds, tenths) shows its value in the decimal number.

🎯 Exam Tip: Remember that leading zeros (like in 001) are not usually written before the decimal point unless it's the only digit before the decimal, like 0.5. Trailing zeros after the last decimal digit (like in 340.120) can often be removed without changing the value.

 

Question 2. Write the following in decimal numbers.
(i) \( 23 + \frac{3}{10} + \frac{6}{1000} \)
(ii) \( \frac{7}{10} + \frac{3}{100} \)
(iii) \( 137 + \frac{6}{100} \)
(iv) \( 700 + 3 + \frac{5}{100} + \frac{3}{1000} \)
(v) \( \frac{3}{10} + \frac{7}{1000} \)
(vi) \( \frac{1}{10} + \frac{9}{100} \)
Answer: To write these expressions as decimal numbers, we add the whole numbers and then convert the fractions to their decimal equivalents before adding them up. Fractions with denominators of 10, 100, or 1000 can be easily written as decimals by placing the numerator in the correct decimal place.
(i) \( 23 + \frac{3}{10} + \frac{6}{1000} = 23 + 0.3 + 0.006 = 23.306 \)
(ii) \( \frac{7}{10} + \frac{3}{100} = 0.7 + 0.03 = 0.73 \)
(iii) \( 137 + \frac{6}{100} = 137 + 0.06 = 137.06 \)
(iv) \( 700 + 3 + \frac{5}{100} + \frac{3}{1000} = 700 + 3 + 0.05 + 0.003 = 703.053 \)
(v) \( \frac{3}{10} + \frac{7}{1000} = 0.3 + 0.007 = 0.307 \)
(vi) \( \frac{1}{10} + \frac{9}{100} = 0.1 + 0.09 = 0.19 \)
In simple words: We turn each fraction into a decimal by moving the decimal point based on the denominator (10, 100, 1000). Then, we add all these parts together to get the final decimal number.

🎯 Exam Tip: Be careful with place values when converting fractions to decimals; for example, \( \frac{6}{1000} \) is 0.006, not 0.6 or 0.06. Make sure to align the decimal points correctly when adding.

 

Question 3. Write the following decimal numbers in words.
(i) 1.20
(ii) 108.56
(iii) 10.756
(iv) 6.01
Answer: When writing decimal numbers in words, we say the whole number part first, then "point," and then each digit of the decimal part separately. This way, we clearly describe the value of each place.
(i) 1.20 or 1.2: One point two zero or One point two
(ii) 108.56: One hundred eight point five six
(iii) 10.756: Ten point seven five six
(iv) 6.01: Six point zero one
In simple words: For each number, say the whole number, then "point," and then say each digit after the point one by one.

🎯 Exam Tip: When writing decimal numbers in words, say "point" for the decimal separator. For the digits after the decimal, say each digit individually (e.g., 0.56 is "zero point five six," not "zero point fifty-six").

 

Question 4. Convert in fraction and write in simple form.
(i) 0.18
(ii) 0.25
(iii) 0.066
(iv) 0.40
Answer: To convert a decimal to a fraction, we write the decimal part over a power of 10 (10, 100, 1000, etc.) that matches the number of decimal places. Then, we simplify the fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor.
(i) \( 0.18 = \frac{18}{100} = \frac{18 \div 2}{100 \div 2} = \frac{9}{50} \)
(ii) \( 0.25 = \frac{25}{100} = \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \)
(iii) \( 0.066 = \frac{66}{1000} = \frac{66 \div 2}{1000 \div 2} = \frac{33}{500} \)
(iv) \( 0.40 = \frac{40}{100} = \frac{40 \div 20}{100 \div 20} = \frac{2}{5} \)
In simple words: To change a decimal to a fraction, put the decimal part over 100 (if two digits) or 1000 (if three digits), then make the fraction as small as possible by dividing the top and bottom by the same number.

🎯 Exam Tip: Always simplify the fraction to its lowest terms. For example, \( \frac{25}{100} \) is not fully simplified; it must be reduced to \( \frac{1}{4} \).

 

Question 5. Which number is greater? Write the reason as well.
(i) 0.4 or 0.04
(ii) 3 or 0.7
(iii) 0.999 or 0.19
(iv) 5.64 or 5.603
Answer: To find the greater number, we compare digits from left to right, starting with the whole number part and then moving to the decimal places. We add zeros at the end of decimal numbers to make them have the same number of decimal places, which helps in comparison.
(i) 0.4 or 0.04
Comparing 0.40 and 0.04. The digit in the tenths place (first digit after decimal) is 4 in 0.40 and 0 in 0.04. Since 4 > 0, 0.4 is greater than 0.04.
(ii) 3 or 0.7
Comparing the whole number parts: 3 has a whole number part of 3, while 0.7 has a whole number part of 0. Since 3 > 0, 3 is greater than 0.7.
(iii) 0.999 or 0.19
Comparing 0.999 and 0.190. In the tenths place, 0.999 has 9, and 0.190 has 1. Since 9 > 1, 0.999 is greater than 0.19.
(iv) 5.64 or 5.603
Comparing 5.640 and 5.603. The whole number parts are both 5. The tenths parts are both 6. In the hundredths place, 5.640 has 4, and 5.603 has 0. Since 4 > 0, 5.64 is greater than 5.603.
In simple words: To compare decimal numbers, first look at the whole numbers. If they are the same, look at the first digit after the decimal, then the second, and so on. The number with the bigger digit in the first different place is the greater one.

🎯 Exam Tip: Always start comparing from the leftmost digit (the largest place value). If digits are the same, move to the next digit to the right. Padding with zeros after the last decimal digit can help visualize the comparison, e.g., compare 0.40 with 0.04.

 

Question 6. Use decimal and convert into rupees.
(i) 5 paise
(ii) 75 paise
(iii) 80 paise
(iv) 50 paise
Answer: We know that 100 paise make 1 Rupee (Rs). To convert paise into rupees, we divide the amount in paise by 100. This is because paise are smaller units, and rupees are larger. Dividing by 100 moves the decimal point two places to the left.
(i) 5 paise \( = \text{Rs } \frac{1}{100} \times 5 = \text{Rs } \frac{5}{100} = \text{Rs } 0.05 \)
(ii) 75 paise \( = \text{Rs } \frac{1}{100} \times 75 = \text{Rs } \frac{75}{100} = \text{Rs } 0.75 \)
(iii) 80 paise \( = \text{Rs } \frac{1}{100} \times 80 = \text{Rs } \frac{80}{100} = \text{Rs } 0.80 \) or Rs 0.8
(iv) 50 paise \( = \text{Rs } \frac{1}{100} \times 50 = \text{Rs } \frac{50}{100} = \text{Rs } 0.50 \) or Rs 0.5
In simple words: To change paise into rupees, divide the number of paise by 100. This is like moving the decimal point two places to the left.

🎯 Exam Tip: Remember the basic conversion: 1 Rupee = 100 paise. When converting a smaller unit to a larger unit, you always divide. Ensure you write 'Rs' before the decimal amount.

 

Question 7. Use decimal and convert into kilometers.
(i) 70 km 5 m
(ii) 88 m
(iii) 800 m
Answer: We know that 1000 meters (m) make 1 kilometer (km). To convert meters into kilometers, we divide the number of meters by 1000. This division helps us express smaller units of length (meters) in terms of larger units (kilometers) using decimals. Dividing by 1000 means shifting the decimal point three places to the left.
(i) 70 km 5 m \( = 70 \text{ km} + 5 \text{ m} \)
\( = 70 \text{ km} + \frac{5}{1000} \text{ km} \)
\( = 70 \text{ km} + 0.005 \text{ km} \)
\( = 70.005 \text{ km} \)
(ii) 88 m \( = \frac{88}{1000} \text{ km} = 0.088 \text{ km} \)
(iii) 800 m \( = \frac{800}{1000} \text{ km} = 0.800 \text{ km} \) or 0.8 km
In simple words: To change meters to kilometers, divide the meters by 1000. This is like moving the decimal point three places to the left.

🎯 Exam Tip: Always remember that 1 km = 1000 m. When converting meters to kilometers, place the decimal point three places to the left. For example, 5 m is 0.005 km, not 0.5 km or 0.05 km.

 

Question 8. Solve the following :
(i) 0.007 + 8.6 + 0.008
(ii) 280.69 + 26.8 + 8.80
(iii) 0.76 + 10.425 + 2
(iv) 32.62 + 36.60
(v) 8.28 - 5.25
(vi) 2.29 - 0.95
Answer: To solve decimal addition and subtraction problems, it is important to align the decimal points vertically. Adding zeros to the end of decimal numbers can help ensure all numbers have the same number of decimal places, making the calculation easier and more accurate. This helps avoid mistakes in place value.
(i) \( 0.007 + 8.6 + 0.008 \)
Aligning by decimal point:
    0.007
    8.600
+ 0.008
    8.615
So, \( 0.007 + 8.6 + 0.008 = 8.615 \)

(ii) \( 280.69 + 26.8 + 8.80 \)
Aligning by decimal point:
  280.69
    26.80
+   8.80
  316.29
So, \( 280.69 + 26.8 + 8.80 = 316.29 \)

(iii) \( 0.76 + 10.425 + 2 \)
Aligning by decimal point:
    0.760
  10.425
+   2.000
  13.185
So, \( 0.76 + 10.425 + 2 = 13.185 \)

(iv) \( 32.62 + 36.60 \)
Aligning by decimal point:
  32.62
+ 36.60
  69.22
So, \( 32.62 + 36.60 = 69.22 \)

(v) \( 8.28 - 5.25 \)
Aligning by decimal point:
  8.28
- 5.25
  3.03
So, \( 8.28 - 5.25 = 3.03 \)

(vi) \( 2.29 - 0.95 \)
Aligning by decimal point:
  2.29
- 0.95
  1.34
So, \( 2.29 - 0.95 = 1.34 \)
In simple words: For adding or subtracting decimals, always line up the decimal points. You can add zeros at the end of numbers to make them all the same length after the decimal, then just add or subtract like regular numbers.

🎯 Exam Tip: When performing decimal calculations, lining up the decimal points is crucial. If you add or subtract numbers with different numbers of decimal places, fill in with trailing zeros to avoid misaligning place values.

 

Question 9. Ravi bought 15 kg 400 gm rice, 2 kg 20 gm sugar, and 100 kg 860 gm flour. How much total weight did Ravi buy?
Answer: To find the total weight of all items Ravi bought, we need to add the weights of the rice, sugar, and flour. It's helpful to convert all weights into kilograms (kg) and grams (gm) or completely into kilograms using decimals before adding. This ensures all units are consistent for calculation.
Weight of rice = 15 kg 400 gm = 15.400 kg
Weight of sugar = 2 kg 20 gm = 2.020 kg
Weight of flour = 100 kg 860 gm = 100.860 kg

Adding all weights (in kg):
  15.400
    2.020
+ 100.860
  118.280

So, Ravi bought a total of 118.280 kg, which is 118 kg 280 gm.
In simple words: Ravi bought rice, sugar, and flour. To find the total weight, we add up the weight of each item. We write each weight in kilograms with decimals, then sum them up.

🎯 Exam Tip: When dealing with combined units like kg and gm, convert everything to a single unit (usually the larger one, like kg) using decimals before adding. Remember that 1 kg = 1000 gm, so 400 gm is 0.400 kg.

 

Question 10. Lily goes for an evening walk. She walked 2 km 100 m on Monday, 3 km 500 m on Tuesday and 2 km 700 m on Wednesday. How much total distance did she walk?
Answer: To find the total distance Lily walked, we need to add the distances she covered each day. It's easiest to convert each distance into kilometers using decimals first, and then sum them up. This ensures consistent units for accurate addition.
Distance walked on Monday = 2 km 100 m = 2.100 km
Distance walked on Tuesday = 3 km 500 m = 3.500 km
Distance walked on Wednesday = 2 km 700 m = 2.700 km

Adding all three distances:
  2.100
  3.500
+ 2.700
  8.300

Thus, Lily walked a total of 8.300 km or 8 km 300 m in three days.
In simple words: Lily walked different distances each day. To find the total distance, we add up all the distances. We change meters to kilometers with decimals, then add them.

🎯 Exam Tip: In word problems involving mixed units (km and m), always convert them to a single unit, preferably the decimal form of the larger unit (km), before performing calculations. This reduces errors in addition.

 

Question 11. Teena has 20 m 50 cm long cloth. She cut 4 m 25 cm cloth out of it. How much cloth is left with Teena now?
Answer: To find out how much cloth is left, we need to subtract the length of the cut cloth from the total length of the cloth Teena had. It is best to convert both lengths to meters using decimals first, so the subtraction is straightforward. This way, all measurements are in the same unit.
Total cloth Teena has = 20 m 50 cm = 20.50 m
Length of cloth cut out = 4 m 25 cm = 4.25 m

Subtracting the cut length from the total length:
  20.50
-  4.25
  16.25

Thus, Teena has 16.25 m or 16 m 25 cm cloth left with her.
In simple words: Teena had a long piece of cloth and cut a part of it. To know how much is left, we subtract the cut part from the total cloth. We write lengths in meters with decimals, then subtract.

🎯 Exam Tip: When subtracting measurements with mixed units (m and cm), always convert them to a single decimal unit (e.g., meters) before subtracting. Remember that 100 cm = 1 m, so 50 cm is 0.50 m.

 

Question 12. Ravi had a total of 12 kg of vegetables. He bought 4 kg 150 gm tomatoes and 5 kg 750 gm onions. How much did the potatoes weigh?
Answer: To find the weight of the potatoes, we first need to find the total weight of the tomatoes and onions. Then, we subtract this combined weight from the total weight of vegetables Ravi had. Converting all weights to kilograms in decimal form simplifies the addition and subtraction.
Weight of tomatoes = 4 kg 150 gm = 4.150 kg
Weight of onions = 5 kg 750 gm = 5.750 kg

Total weight of tomatoes and onions:
  4.150
+ 5.750
  9.900 kg

Total weight of vegetables = 12 kg = 12.000 kg
Weight of potatoes = Total weight - (Weight of tomatoes + Weight of onions)
Weight of potatoes = \( 12.000 \text{ kg} - 9.900 \text{ kg} \)
  12.000
-  9.900
    2.100 kg

Thus, the weight of potatoes is 2.100 kg or 2 kg 100 gm.
In simple words: First, add the weight of tomatoes and onions. Then, subtract that total from the full weight of all vegetables to find the weight of the potatoes.

🎯 Exam Tip: For problems involving total quantities and known parts, always find the sum of the known parts first. Then, subtract this sum from the total to find the unknown part. Ensure all units are consistent (e.g., kilograms) before performing calculations.