GSEB Class 7 Maths Solutions Chapter 2 Fractions and Decimals Exercise 2.5

Question 1. Which is greater?
(i) 0.5 or 0.05
(ii) 0.7 or 0.5
(iii) 1 or 0.7
(iv) 1.37 or 1.49
(v) 2.03 or 2.30
(vi) 0.8 or 0.88
Answer:
(i) When we compare the digits at the tenths place, we find that \( 5 > 0 \). Therefore, \( 0.5 > 0.05 \).
(ii) When we compare the digits at the tenths place, we get \( 7 > 5 \). Therefore, \( 0.7 > 0.5 \).
(iii) When we compare the digits at the ones place, we observe that \( 1 > 0 \). Therefore, \( 1 > 0.7 \).
(iv) Since the digits at the ones place are identical, we compare the digits at the tenths place. We notice that \( 3 < 4 \). Therefore, \( 1.37 < 1.49 \) or \( 1.49 > 1.37 \).
(v) Since the digits at the ones place are identical, we compare the digits at the tenths place. We notice that \( 0 < 3 \). Therefore, \( 2.03 < 2.30 \) or \( 2.30 > 2.03 \).
(vi) We can also write 0.8 as 0.80. Now, the digits at the tenths place are identical. When we compare the digits at the hundredths place, we get \( 0 < 8 \). Therefore, \( 0.80 < 0.88 \) or \( 0.88 > 0.8 \).
In simple words: To find out which number is bigger, you look at the digits from left to right. Start with the ones place, then the tenths, then the hundredths. The number with the larger digit at the first different place is the greater one. Sometimes, you might need to add a zero to the end of a number to make them have the same number of decimal places for easier comparison.

Exam Tip: To compare decimals, always align the decimal points and add trailing zeros to make the number of decimal places equal. Then compare the numbers from left to right, digit by digit.

Question 2. Express as rupees using decimals:
(i) 7 paise
(ii) 7 rupees 1 paise
(iii) 77 rupees 77 paise
(iv) 50 paise
(v) 235 paise
Answer:
We understand that:
\( 100 \text{ paise} = \text{Rs } 1 \)
\( \implies 1 \text{ paise} = \text{Rs } \frac { 1 }{ 100 } \)
(i) \( 7 \text{ paise} = 7 \times \text{Rs } \frac { 1 }{ 100 } = \text{Rs } 0.07 \)
(ii) \( 7 \text{ rupees } 7 \text{ paise} = \text{Rs } 7 + \text{Rs } 0.07 = \text{Rs } 7.07 \)
(iii) \( 77 \text{ rupees } 77 \text{ paise} = \text{Rs } 77 + 77 \text{ paise} \)
\( = \text{Rs } 77 + \text{Rs } 77 \times \frac { 1 }{ 100 } \)
\( = \text{Rs } 77 + \text{Rs } 0.77 = \text{Rs } 77.77 \)
(iv) \( 50 \text{ paise} = 50 \times \frac { 1 }{ 100 } \text{ Rs } = \text{Rs } 0.50 \)
(v) \( 235 \text{ paise} = 200 \text{ paise} + 35 \text{ paise} \)
\( = \text{Rs } 2 + \text{Rs } 35 \times \frac { 1 }{ 100 } \) (since \( 200 \text{ paise} = \text{Rs } 2 \))
\( = \text{Rs } 2 + \text{Rs } 0.35 = \text{Rs } 2.35 \)
In simple words: To change paise into rupees, just divide the number of paise by 100. Remember that 100 paise equals 1 rupee. If you have both rupees and paise, add the converted paise (as a decimal) to the rupees.

Exam Tip: Always remember the conversion factor: 1 Rupee = 100 Paise. When expressing paise as decimals of rupees, ensure you place the decimal point correctly after two digits from the right.

Question 3.
(i) Express 5 cm in m and kilometre
(ii) Express 35 mm in cm, m and km
Answer:
We understand that \( 1 \text{ cm} = 10 \text{ mm} \), \( 100 \text{ cm} = 1 \text{ m} \), \( 1000 \text{ m} = 1 \text{ km} \).
(i) \( 5 \text{ cm} = \frac { 5 }{ 100 } \text{ m} = 0.05 \text{ m} \)
Since \( 1 \text{ km} = 1000 \text{ m} = 1000 \times 100 \text{ cm} = 100000 \text{ cm} \)
\( 5 \text{ cm} = \frac { 5 }{ 100000 } \text{ km} = 0.00005 \text{ km} \)
(ii) \( 35 \text{ mm} = \frac { 35 }{ 10 } \text{ cm} = 3.5 \text{ cm} \)
\( 35 \text{ mm} = \frac { 35 }{ 1000 } \text{ m} = 0.035 \text{ m} \)
\( 35 \text{ mm} = \frac { 35 }{ 1000000 } \text{ km} = 0.000035 \text{ km} \) (since \( 1 \text{ km} = 1000 \text{ m} = 1000 \times 1000 \text{ mm} = 1000000 \text{ mm} \))
In simple words: To convert smaller units to larger units, you divide by the conversion factor. For example, to change centimeters to meters, divide by 100. To change millimeters to centimeters, divide by 10. For kilometers, you divide by a much larger number.

Exam Tip: Memorize the key conversion factors (e.g., 1 m = 100 cm, 1 km = 1000 m, 1 cm = 10 mm). When converting from a smaller unit to a larger unit, you divide; when converting from a larger unit to a smaller unit, you multiply.

Question 4. Express in kg:
(i) 200 g
(ii) 3470 g
(iii) 4 kg 8 g
Answer:
We understand that \( 1000 \text{ g} = 1 \text{ kg} \).
(i) \( 200 \text{ g} = \frac { 200 }{ 1000 } \text{ kg} \)
\( = \frac { 2 }{ 10 } \text{ kg} \)
\( = 0.2 \text{ kg} \)
(ii) \( 3470 \text{ g} = \frac { 3470 }{ 1000 } \text{ kg} \)
\( = 3.470 \text{ kg} \)
(iii) \( 4 \text{ kg } 8 \text{ g} = 4 \text{ kg} + \frac { 8 }{ 1000 } \text{ kg} \)
\( = 4 \text{ kg} + 0.008 \text{ kg} = 4.008 \text{ kg} \)
In simple words: To change grams into kilograms, you must divide the number of grams by 1000, since 1 kilogram has 1000 grams. If you already have some kilograms, just add the converted grams to them.

Exam Tip: Remember that 1 kg = 1000 g. When converting grams to kilograms, divide by 1000. Pay close attention to the placement of the decimal point when dealing with fractions of a kilogram.

Question 5. Write the following decimal numbers in the expanded form:
(i) 20.03
(ii) 2.03
(iii) 200.03
(iv) 2.034
Answer:
(i) \( 20.03 = 2 \times 10 + 0 \times 1 + 0 \times \frac { 1 }{ 10 } + 3 \times \frac { 1 }{ 100 } \)
\( = 2 \times 10 + \frac { 3 }{ 100 } \)
(ii) \( 2.03 = 2 \times 1 + 0 \times \frac { 1 }{ 10 } + 3 \times \frac { 1 }{ 100 } \)
\( = 2 \times 1 + \frac { 3 }{ 100 } \)
(iii) \( 200.03 = 2 \times 100 + 0 \times 10 + 0 \times 1 + 0 \times \frac { 1 }{ 10 } + 3 \times \frac { 1 }{ 100 } \)
\( = 2 \times 100 + \frac { 3 }{ 100 } \)
(iv) \( 2.034 = 2 \times 1 + 0 \times \frac { 1 }{ 10 } + 3 \times \frac { 1 }{ 100 } + 4 \times \frac { 1 }{ 1000 } \)
\( = 2 \times 1 + \frac { 3 }{ 100 } + \frac { 4 }{ 1000 } \)
In simple words: Expanded form means showing the value of each digit separately. For decimals, digits to the left of the decimal point are multiplied by powers of ten (1, 10, 100, etc.), and digits to the right are multiplied by fractions (1/10, 1/100, 1/1000, etc.).

Exam Tip: To write a decimal in expanded form, identify the place value of each digit (ones, tens, tenths, hundredths, etc.) and represent it as a sum of its multiplied value. Remember that the decimal point separates whole numbers from fractional parts.

Question 6. Write the place value of 2 in the following decimal numbers:
(i) 2.56
(ii) 21.37
(iii) 10.25
(iv) 9.42
(v) 63.352
Answer:
(i) In 2.56, the digit 2 is at the ones place. Therefore, its place value is \( 2 \times 1 \), which is 2.
(ii) In 21.37, the digit 2 is at the tens place. Therefore, its place value is \( 2 \times 10 \), which is 20.
(iii) In 10.25, the digit 2 is at the tenths place. Therefore, its place value is \( 2 \times \frac { 1 }{ 10 } \), which is \( \frac { 2 }{ 10 } \).
(iv) In 9.42, the digit 2 is at the hundredths place. Therefore, its place value is \( 2 \times \frac { 1 }{ 100 } \), which is \( \frac { 2 }{ 100 } \).
(v) In 63.352, the digit 2 is at the thousandths place. Therefore, its place value is \( 2 \times \frac { 1 }{ 1000 } \), which is \( \frac { 2 }{ 1000 } \).
In simple words: The place value of a digit tells you how much it's worth based on where it sits in the number. For whole numbers, it's ones, tens, hundreds. For decimals, it's tenths, hundredths, thousandths.

Exam Tip: Understand that the position of a digit determines its value. Digits to the left of the decimal point represent whole numbers (units, tens, hundreds), while digits to the right represent fractional parts (tenths, hundredths, thousandths).

Question 7. Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?
Answer:

Distance from A to B = 7.5 km
Distance from B to C = 12.7 km
Thus, the distance from A to C through B is:
\( = (7.5 + 12.7) \text{ km} \)
\( = 20.2 \text{ km} \)
Therefore, the total distance travelled by Dinesh = 20.2 km.
Next, the distance from A to D = 9.3 km
And the distance from D to C = 11.8 km
Thus, the distance from A to C through D is:
\( = (9.3 + 11.8) \text{ km} \)
\( = 21.1 \text{ km} \)
Therefore, the total distance travelled by Ayub = 21.1 km.
Since \( (21.1 - 20.2) \text{ km} = 0.9 \text{ km} \) or 900 m.
Ayub travelled a greater distance by 900 m.
In simple words: First, calculate the total distance Dinesh travelled by adding the two segments of his journey. Then, do the same for Ayub's journey. Compare the two total distances to see who travelled more and subtract to find the exact difference.

Exam Tip: When solving problems involving distances, draw a simple diagram to visualize the paths taken. Carefully add up all segments for each person's journey before comparing the totals to determine who travelled more and by how much.

Question 8. Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
Answer:
Shyama purchased 5 kg 300 g apples and 3 kg 250 g mangoes.
The total fruits purchased by Shyama are:
\( = 5 \text{ kg } 300 \text{ g} + 3 \text{ kg } 250 \text{ g} \)
\( = 8 \text{ kg } 550 \text{ g} \)
Sarala purchased 4 kg 800 g oranges and 4 kg 150 g bananas.
The total fruits purchased by Sarala are:
\( = 4 \text{ kg } 800 \text{ g} + 4 \text{ kg } 150 \text{ g} = 8 \text{ kg } 950 \text{ g} \)
Since \( 8 \text{ kg } 950 \text{ g} - 8 \text{ kg } 550 \text{ g} = 0 \text{ kg } 400 \text{ g} \)
or \( \frac { 400 }{ 1000 } \text{ kg} = 0.4 \text{ kg} \).
Therefore, Sarala purchased more fruits by 0.4 kg.
In simple words: To find out who bought more fruits, you need to add up the total weight of fruits for each person. Convert all weights to a single unit (like kilograms) before adding them. Then, compare the two totals and subtract to find the difference.

Exam Tip: Always convert all quantities to a single, consistent unit (e.g., kilograms or grams) before performing addition or subtraction. This prevents errors in calculation when comparing different items.

Question 9. How much less is 28 km than 42.6 km?
Answer:
To find out how much less 28 km is than 42.6 km, we perform subtraction:
\( 42.6 \text{ km} - 28 \text{ km} = 14.6 \text{ km} \)
Therefore, 28 km is 14.6 km less than 42.6 km.
In simple words: To figure out the difference between two numbers and see how much smaller one is, you simply subtract the smaller number from the larger number.

Exam Tip: When asked "how much less" or "what is the difference," always subtract the smaller value from the larger value. Ensure your units are consistent throughout the calculation.