RBSE Solutions Class 7 Maths Chapter 2 Fractions and Decimal Numbers Exercise 2.4

Question 1. Compare the following pairs of numbers and identify the greater one :
(i) 0.7 and 0.07
(ii) 2.03 and 2.30
(iii) 7 and 0.7
(iv) 1.35 and 1.49
(v) 3.507 and 3.570
(vi) 85.2 and 85.02
Answer:
(i) First, look at the whole numbers to the left of the decimal point. Both 0.7 and 0.07 have 0 there, so they are the same. Next, look at the first digit after the decimal point. For 0.7, it's 7. For 0.07, it's 0. Since 7 is bigger than 0, 0.7 is the greater number. Comparing digits place by place helps us find the larger decimal.
(ii) When comparing 2.03 and 2.30, both numbers have the same whole number part, which is 2. After the decimal point, we look at the first digit. In 2.03, it's 0. In 2.30, it's 3. Since 0 is less than 3, it means 2.03 is smaller than 2.30, or 2.30 is greater. This step-by-step comparison is key for identifying the larger decimal.
(iii) To compare 7 and 0.7, first look at their whole number parts. The number 7 has a whole part of 7. The number 0.7 has a whole part of 0. Since 7 is much larger than 0, the number 7 is clearly the greater number. A whole number will almost always be greater than a decimal less than one.
(iv) Let's compare 1.35 and 1.49. Both numbers have 1 as their whole number part. Now, look at the first digit after the decimal point. For 1.35, it's 3. For 1.49, it's 4. Since 3 is smaller than 4, we can say that 1.35 is less than 1.49. We only need to compare up to the first different digit to decide which is greater.
(v) To compare 3.507 and 3.570, first notice that both have 3 as the whole number. Next, the tenths digit is 5 for both. Then, look at the hundredths digit: for 3.507 it is 0, and for 3.570 it is 7. Since 0 is less than 7, 3.507 is less than 3.570. Comparing decimal numbers digit by digit is like comparing whole numbers, but starting from the leftmost digit after the decimal.
(vi) When comparing 85.2 and 85.02 (which is the same as 85.20 and 85.02), the whole number part, 85, is the same for both. Next, we look at the first digit after the decimal point. For 85.20, it is 2. For 85.02, it is 0. Since 2 is greater than 0, 85.20 is the larger number. Always compare digits from left to right, including the ones after the decimal point.
In simple words: To compare decimal numbers, first compare the whole number parts. If they are the same, compare the digits after the decimal point from left to right, one by one. The number with the first larger digit is the greater one.

🎯 Exam Tip: Always line up the decimal points when comparing numbers and add trailing zeros to make the number of decimal places equal for an easier comparison.

Question 2. Convert the following small units into bigger units :
(i) 7 Paise in rupees
(ii) 800 gm in kg
(iii) 75 metre to km
(iv) 3470 metre to km
(v) 7 kg 7 gm in kg
(vi) 47 km, 75 metre to km
Answer:
(i) To convert 7 Paise into rupees, we divide by 100, because there are 100 Paise in 1 Rupee. This gives us 0.07 rupees. Understanding common conversions helps in daily calculations.
\( 7 \text{ Paise} = \frac{7}{100} \text{ rupee} = 0.07 \text{ rupee} \)
(ii) To change 800 grams to kilograms, we divide 800 by 1000, because 1000 grams make 1 kilogram. This calculation gives us 0.800 kg. We use decimal points to show parts of a whole unit.
\( 800 \text{ gm} = \frac{800}{1000} \text{ kg} = 0.800 \text{ kg} \)
(iii) To convert 75 meters to kilometers, we divide 75 by 1000, since 1000 meters are in 1 kilometer. This results in 0.075 kilometers. This type of conversion helps us work with different scales of distance.
\( 75 \text{ m} = \frac{75}{1000} \text{ km} = 0.075 \text{ km} \)
(iv) To convert 3470 meters to kilometers, we divide 3470 by 1000, because there are 1000 meters in 1 kilometer. This calculation gives us 3.470 kilometers. Knowing these conversion factors simplifies measuring different lengths.
\( 3470 \text{ m} = \frac{3470}{1000} \text{ km} = 3.470 \text{ km} \)
(v) To express 7 kg 7 gm in kilograms, we first convert the 7 grams to kilograms by dividing by 1000, which is 0.007 kg. Then we add this to the 7 kg, resulting in 7.007 kg. This way, we can write mixed units as a single decimal unit.
\( 7 \text{ kg } 7 \text{ gm} = 7 \text{ kg} + \frac{7}{1000} \text{ kg} = 7 + 0.007 = 7.007 \text{ kg} \)
(vi) To convert 47 km 75 m into just kilometers, we change the 75 meters to kilometers by dividing by 1000, which gives 0.075 km. Then, we add this to the 47 km, making the total 47.075 km. This is a common method for combining units of length.
\( 47 \text{ km } 75 \text{ m} = 47 \text{ km} + \frac{75}{1000} \text{ km} = 47 + 0.075 = 47.075 \text{ km} \)
In simple words: To convert smaller units to larger units, divide by the conversion factor. For example, divide grams by 1000 to get kilograms, or Paise by 100 to get Rupees.

🎯 Exam Tip: Remember the common conversion factors: 1 Rupee = 100 Paise, 1 kg = 1000 gm, 1 km = 1000 m. Always clearly show your division when converting units.

Question 3. Write the expanded form of the following numbers:
(i) 25.03
(ii) 2.503
(iii) 205.3
(iv) 2.053
Answer:
(i) The number 25.03 can be written in expanded form by breaking it down by place value. Here, 2 is in the tens place, 5 in the ones place, 0 in the tenths place, and 3 in the hundredths place. So, it's two tens, five ones, zero tenths, and three hundredths. This shows how each digit contributes to the number's total value.
\( 25.03 = 2 \times 10 + 5 \times 1 + 0 \times \frac{1}{10} + 3 \times \frac{1}{100} \)
(ii) For 2.503, the expanded form shows 2 in the ones place, 5 in the tenths place, 0 in the hundredths place, and 3 in the thousandths place. Each decimal place represents a fraction of a whole, like one-tenth or one-thousandth. This helps to visualize the value of each digit in a decimal number.
\( 2.503 = 2 \times 1 + 5 \times \frac{1}{10} + 0 \times \frac{1}{100} + 3 \times \frac{1}{1000} \)
(iii) The number 205.3 in expanded form shows 2 in the hundreds place, 0 in the tens place, 5 in the ones place, and 3 in the tenths place. Even a zero digit holds its place value, indicating absence in that position. This helps understand the structure of numbers with both whole and fractional parts.
\( 205.3 = 2 \times 100 + 0 \times 10 + 5 \times 1 + 3 \times \frac{1}{10} \)
(iv) For 2.053, the expanded form means 2 is in the ones place, 0 in the tenths place, 5 in the hundredths place, and 3 in the thousandths place. The decimal point separates the whole number part from the fractional part. This breakdown makes it clear what each number stands for.
\( 2.053 = 2 \times 1 + 0 \times \frac{1}{10} + 5 \times \frac{1}{100} + 3 \times \frac{1}{1000} \)
In simple words: Expanded form means showing the value of each digit based on its place, like tens, ones, tenths, and hundredths.

🎯 Exam Tip: Remember that each place to the right of the decimal point represents a fraction (tenths, hundredths, thousandths), while places to the left are whole numbers (ones, tens, hundreds).

Question 4. Find the place value of 3 in following numbers:
(i) 34.82
(ii) 643.45
(iii) 547.03
(iv) 24.203
Answer:
The place value of a digit tells us how much it is worth based on its position in the number. For instance, a 3 in the tens place means 30, while a 3 in the hundredths place means 3 out of 100. Understanding place value is fundamental for all number operations. This helps us know the exact contribution of each digit to the total value of the number.

🎯 Exam Tip: Pay close attention to whether the digit is to the left (whole number) or right (decimal fraction) of the decimal point when determining its place value.

Question 5. Paras's father purchased 7 kg 250 gm green Chilli, 15 kg 750 gm tomatoes and 950 gm green coriander leaves from the vegetable market. How much vegetable did he bring.
Answer: To find the total weight of vegetables, we add the weight of each item. First, combine the kilograms: 7 kg + 15 kg = 22 kg. Then, combine the grams: 250 gm + 750 gm + 950 gm = 1950 gm. Convert 1950 gm to kilograms by dividing by 1000, which is 1.950 kg. Now, add all kilograms together: 22 kg + 1.950 kg = 23.950 kg. So, Paras's father brought a total of 23.950 kg of vegetables. Converting grams to kilograms is important for accurate calculations.
Total vegetables \( = 23 \text{ kg } 950 \text{ gm} \)
\( = \left(23 + \frac{950}{1000}\right) \text{ kg} \)
\( = 23 + 0.950 \text{ kg} \)
\( = 23.950 \text{ kg} \)
In simple words: Add all the kilograms together and all the grams together. Then change the total grams to kilograms and add that to the total kilograms to get the final answer.

🎯 Exam Tip: When adding mixed units, always convert them to a single unit (e.g., all kilograms or all grams) before performing the addition to avoid errors.

Question 6. Bhawna got Rs. 37.25 in her bank account towards interest and Anita got Rs. 25.50 in her bank account towards interest. Who got more interest amount and how much?
Answer: Bhawna received Rs. 37.25 in interest, while Anita received Rs. 25.50. To find who got more and by how much, we subtract Anita's interest from Bhawna's. Rs. 37.25 - Rs. 25.50 = Rs. 11.75. This means Bhawna received Rs. 11.75 more interest than Anita. Finding the difference helps us compare amounts easily.
Interest received by Bhavna = Rs. 37.25
Interest received by Anita = Rs. 25.50
Difference = Rs. 37.25 - Rs. 25.50 = Rs. 11.75
Hence, Bhavna gets Rs. 11.75 more.
In simple words: Subtract the smaller interest amount from the larger one to find out who got more and by how much.

🎯 Exam Tip: Always align decimal points correctly when subtracting amounts involving money to ensure accuracy.

Question 7. How much less is 42.7 km from 48 km?
Answer: To find out how much less 42.7 km is from 48 km, we need to subtract 42.7 from 48. We can write 48 as 48.0 to make the subtraction easier. So, 48.0 km - 42.7 km = 5.3 km. This calculation tells us the exact difference in distance. Subtracting decimals requires careful alignment of the decimal points.
\( 48.0 \text{ km} \)
\( - 42.7 \text{ km} \)
\( ----- \)
\( 5.3 \text{ km} \)
In simple words: Subtract the smaller distance from the larger distance to find the difference.

🎯 Exam Tip: When subtracting decimals from whole numbers, remember to write the whole number with a decimal point and enough zeros to match the number of decimal places in the other number.

Question 8. What value should be added to the sum of 24.57 and 36.3 to get 70?
Answer: First, we need to find the sum of 24.57 and 36.3. Adding these two numbers gives 60.87. We want to find a number, let's call it 'x', that when added to 60.87 will equal 70. So, we set up the equation: 60.87 + x = 70. To find x, we subtract 60.87 from 70. This calculation results in 9.13. Therefore, 9.13 should be added to the sum to get 70. Setting up an equation helps in solving such problems systematically.
Let the value to be added be \( x \).
So, \( (24.57 + 36.3) + x = 70 \)
\( 60.87 + x = 70 \)
\( x = 70 - 60.87 \)
\( x = 9.13 \)
Thus, 9.13 should be added.
In simple words: First, add the given numbers. Then, subtract this sum from 70 to find the missing number.

🎯 Exam Tip: Always perform the addition first to find the total sum, then use subtraction to find the unknown value needed to reach the target number.