Another Peek Beyond the Point Class 7 Maths Worksheet with Answers Chapter 3

Ganita Prakash Part-II, Grade 7, Textbook of Mathematics – Chapter 4 is called “Another Peek Beyond the Point”. Think of it as Part 2 of decimals. Earlier you learnt to read, compare, add and subtract decimals. Now you go a step deeper – you learn to multiply and divide them. You just have to handle the decimal point with care as you already know these skills for whole numbers. This worksheet gives you plenty of practice on both operations.

Here is what you will work on:

• Multiplying a decimal by a whole number and by another decimal
• Dividing decimals using the long-division (place value) method
• Multiplying and dividing by 10, 100 and 1000
• Changing fractions into decimals
• Never-ending (recurring) decimals like 3.333…
• Word problems on money, length, weight and speed

Keep these rules ready before you begin:

• To multiply decimals: multiply the numbers as if there is no point. Then count the decimal places in both numbers and put the same total in the answer. Example – for 5.96 × 24.8, first do 596 × 248 = 147808. Places: 2 + 1 = 3. So the answer is 147.808.
• To multiply by 10, 100, 1000: shift the decimal point to the right by as many places as there are zeros.
• To divide by 10, 100, 1000: shift the decimal point to the left by that many places.
• When the divisor is a decimal: multiply both the divisor and the dividend by 10, 100… till the divisor becomes a whole number. Example – 4.68 ÷ 0.13 becomes 468 ÷ 13.
• Handy conversions: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 litre = 1000 ml.

The worksheet is set in four levels – Basic, then Standard, then Advanced, and lastly HOTS. A step-wise answer key is placed right after the last question so you can check yourself.

Class 7 Maths Worksheet – Chapter 4: Another Peek Beyond the Point

Basic

1. Convert the following fractions into decimals:
   • 43/100
   • 7/10
   • 256/1000
   • 125/100
2. Divide the following by 10, 100 or 1000:
   • 58 ÷ 10
   • 347 ÷ 100
   • 6 ÷ 100
   • 1234 ÷ 1000
3. Find the products:
   • 4.5 × 2
   • 3.6 × 5
   • 0.7 × 8
   • 1.25 × 4
4. Find the products:
   • 2.4 × 1.5
   • 0.6 × 0.4
   • 3.25 × 0.2
5. Fill in the blanks:
   • 2.35 × 10 = ______
   • 2.35 × 100 = ______
   • 2.35 × 1000 = ______
   • 56.2 ÷ 10 = ______
6. Find the quotients:
   • 8.4 ÷ 2
   • 7.5 ÷ 5
   • 3.6 ÷ 10
   • 45 ÷ 100
7. State whether the product is greater than, less than, or equal to both the numbers multiplied:
   • 3.5 × 2.4
   • 0.4 × 0.8
   • 0.6 × 5

Standard

1. Multiply:
   • 5.8 × 1.24
   • 4.23 × 3.7
   • 0.432 × 0.23
2. A pen costs ₹12.50. Find the cost of:
   • 4 pens
   • 9 pens
3. A car travels 14.5 km per litre of petrol. How far will it travel using 6.4 litres of petrol?
4. Find the quotients:
   • 24.86 ÷ 1.2
   • 2.46 ÷ 1.5
   • 2.46 ÷ 0.15
5. A 6.75 m ribbon is cut into 9 equal pieces. What is the length of each piece?
6. The perimeter of a regular octagon is 86.4 cm. Find the length of each side.
7. Given that 18 × 12 = 216, find:
   • 18 × 1.2
   • 1.8 × 1.2
   • 0.18 × 0.12
   • 18 ÷ 0.12

Advance

1. The price of 1 kg of apples is ₹84.50. Find the cost of 2.75 kg of apples.
2. A rectangular garden is 12.5 m long and 8.4 m wide. Find its area.
3. A shopkeeper buys notebooks for ₹23.60 each and sells them for ₹31.50 each.
   Find the profit made by selling 45 notebooks.
4. A water tanker contains 125.5 L of water. The water is filled equally into 25 buckets.
   How much water is filled in each bucket?
5. A cyclist travels 42.75 km in 2.5 hours at a uniform speed. Find the distance travelled in 1 hour.
6. The thickness of one ₹1 coin is 1.45 mm. Find the height, in centimetres, of a stack of 40 such coins.
7. A juice shop has 18.6 L of juice. It serves the juice equally in glasses containing 0.3 L each.
   How many glasses can be filled?

HOTS

1. Without calculating the exact product, decide in which cases the product is less than 1:
   • 7 × 0.6
   • 0.7 × 0.6
   • 0.7 × 6
   • 0.07 × 0.06
2. Given that 596 × 248 = 147808, write the value of:
   • 5.96 × 24.8
   • 59.6 × 2.48
   • 0.596 × 0.248
3. A student says, “Dividing a number always makes it smaller.” Is the statement correct?
   Explain using the following:
   • 24 ÷ 4
   • 24 ÷ 0.4
   • 24 ÷ 1
4. Determine whether each of the following years is a leap year using the Gregorian calendar rule:
   • 2024
   • 1900
   • 2000
   • 2100
   • 2400
5. In 100 years, how many calendar days are there under the rule:
   • Add one extra day every fourth year
   • Do not add the extra day in the 100th year
6. A machine produces 0.75 m of cloth every minute. How many minutes will it take to produce 48 m of cloth?
   If it runs for 2 hours, how much cloth will it produce?
7. A juice bottle contains 1.5 L. A school has 36 students, and each student receives 0.125 L of juice.
   How many bottles are needed?

Answer Key

Basic – Answers

1. • 43/100 = 0.43
   • 7/10 = 0.7
   • 256/1000 = 0.256
   • 125/100 = 1.25
2. • 58 ÷ 10 = 5.8
   • 347 ÷ 100 = 3.47
   • 6 ÷ 100 = 0.06
   • 1234 ÷ 1000 = 1.234

   Hint: Move the decimal point left by the number of zeroes in the divisor.

3. • 4.5 × 2 = 9
   • 3.6 × 5 = 18
   • 0.7 × 8 = 5.6
   • 1.25 × 4 = 5
4. • 2.4 × 1.5 = 3.6
   • 0.6 × 0.4 = 0.24
   • 3.25 × 0.2 = 0.65
5. • 2.35 × 10 = 23.5
   • 2.35 × 100 = 235
   • 2.35 × 1000 = 2350
   • 56.2 ÷ 10 = 5.62
6. • 8.4 ÷ 2 = 4.2
   • 7.5 ÷ 5 = 1.5
   • 3.6 ÷ 10 = 0.36
   • 45 ÷ 100 = 0.45
7. • 3.5 × 2.4: Product is greater than both numbers.
   • 0.4 × 0.8: Product is less than both numbers.
   • 0.6 × 5: Product is greater than 0.6 but less than 5.

Standard – Answers

1. • 5.8 × 1.24 = 7.192
   • 4.23 × 3.7 = 15.651
   • 0.432 × 0.23 = 0.09936
2. • Cost of 4 pens = 12.50 × 4 = ₹50
   • Cost of 9 pens = 12.50 × 9 = ₹112.50
3. 14.5 × 6.4 = 92.8 km
4. • 24.86 ÷ 1.2 = 20.7166… (approx. 20.72)
   • 2.46 ÷ 1.5 = 1.64
   • 2.46 ÷ 0.15 = 16.4
5. 6.75 ÷ 9 = 0.75 m
6. 86.4 ÷ 8 = 10.8 cm
7. • 18 × 1.2 = 21.6
   • 1.8 × 1.2 = 2.16
   • 0.18 × 0.12 = 0.0216
   • 18 ÷ 0.12 = 150

Advance – Answers

1. 84.50 × 2.75 = ₹232.375
   Cost = ₹232.38 approximately
2. Area = 12.5 × 8.4 = 105 sq m
3. Profit on one notebook = ₹31.50 − ₹23.60 = ₹7.90
   Total profit = ₹7.90 × 45 = ₹355.50
4. 125.5 ÷ 25 = 5.02 L
5. 42.75 ÷ 2.5 = 17.1 km
6. Total height = 1.45 × 40 = 58 mm
   58 mm = 5.8 cm
7. 18.6 ÷ 0.3 = 62 glasses

HOTS – Answers

1. The products less than 1 are:
   • 0.7 × 0.6
   • 0.07 × 0.06

   Hint: The product of two positive decimals less than 1 is less than 1.

2. • 5.96 × 24.8 = 147.808
   • 59.6 × 2.48 = 147.808
   • 0.596 × 0.248 = 0.147808

   Hint: Count the total decimal places in the two factors.

3. No, the statement is incorrect.
   • 24 ÷ 4 = 6: quotient is smaller than the dividend.
   • 24 ÷ 0.4 = 60: quotient is greater than the dividend.
   • 24 ÷ 1 = 24: quotient equals the dividend.
4. • 2024: Leap year
   • 1900: Not a leap year
   • 2000: Leap year
   • 2100: Not a leap year
   • 2400: Leap year

   Hint: A century year must be divisible by 400 to be a leap year.

5. • Extra day every fourth year: 100 × 365 + 25 = 36,525 days
   • No extra day in the 100th year: 100 × 365 + 24 = 36,524 days
6. Time required = 48 ÷ 0.75 = 64 minutes
   Cloth produced in 2 hours = 0.75 × 120 = 90 m
7. Total juice needed = 36 × 0.125 = 4.5 L
   Bottles needed = 4.5 ÷ 1.5 = 3 bottles

Other Class 7 Maths worksheet

Ganita Prakash Part-I, Grade 7

• Large Numbers Around Us Class 7 Maths Worksheet
• Arithmetic Expressions Class 7 Maths Worksheet
• A Peek Beyond the Point Class 7 Maths Worksheet
• Number Play Class 7 Maths Worksheet
• Working with Fractions Class 7 Maths Worksheet

Ganita Prakash Part-II, Grade 7

• Operations with Integers Class 7 Maths Worksheet
• Another Peek Beyond the Point Class 7 Maths Worksheet
• Finding the Unknown Class 7 Maths Worksheet

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