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

Ganita Prakash Part-I, Grade 7, Textbook of Mathematics – Chapter 3 is called “A Peek Beyond the Point”. The “point” here is the decimal point. Till now you counted in ones, tens and hundreds. In this chapter you go the other way – you break one whole into smaller and smaller parts. You will see tenths, hundredths and thousandths, and learn how to write them using a decimal point. This is the decimals chapter of Class 7 maths, and the worksheet below covers every topic from it.

Here is what you will practise in this worksheet:

• Tenths, hundredths and thousandths
• Reading and writing decimal numbers (decimal place value)
• Comparing and putting decimals in order
• Changing fractions into decimals
• Unit conversion: mm–cm–m, gram–kilogram, and rupee–paise
• Adding and subtracting decimals

Keep these key facts ready before you begin:

• 1 whole = 10 tenths, 1 tenth = 10 hundredths, 1 hundredth = 10 thousandths
• 10 tenths = 1 whole, 100 hundredths = 1 whole
• 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m
• 1 kg = 1000 g, 1 g = 1000 mg
• 1 rupee = 100 paise

Tips that save marks. First, extra zeros on the right of a decimal do not change its value, so 0.2 = 0.20 = 0.200. But 0.2, 0.02 and 0.002 are all different – the place of the zero matters. Second, always line up the decimal points one below the other before you add or subtract.

The questions are set in four levels – Basic to warm up, then Standard, then Advanced, and finally the HOTS set to stretch your thinking. Work through them in order, and check your steps with the full answer key given at the end.

Class 7 Maths Worksheet – Chapter 3: A Peek Beyond the Point

Basic

1. Write the following fractions in decimal form:
   • 7/10
   • 36/100
   • 405/1000
   • 19/10
2. Write the following decimals as fractions with denominators 10, 100, or 1000:
   • 0.8
   • 0.45
   • 2.07
   • 5.125
3. State the place value of the underlined digit:
   • 4.72
   • 8.05
   • 12.346
   • 0.289
4. Write the following numbers in decimal form:
   • 6 ones and 4 tenths
   • 3 ones, 7 tenths and 5 hundredths
   • 2 tens, 5 ones and 8 hundredths
   • 145 tenths
5. Fill in the blanks:
   • 10 tenths = ______ unit
   • 100 hundredths = ______ unit
   • 10 hundredths = ______ tenth
   • 1 unit = ______ thousandths
6. Compare using <, > or =:
   • 0.6 ______ 0.60
   • 4.05 ______ 4.5
   • 2.109 ______ 2.19
   • 0.008 ______ 0.08
7. Find the sums:
   • 3.4 + 2.5
   • 7.08 + 1.21
   • 12 + 0.75

Standard

1. Arrange the following decimals in ascending order:
   • 4.5, 4.05, 4.505, 4.50, 4.005
2. Convert the following:
   • 47 mm into cm
   • 8.6 cm into mm
   • 325 cm into m
   • 2.45 m into cm
3. Convert the following:
   • 685 g into kg
   • 2.75 kg into g
   • 56 paise into rupees
   • ₹4.25 into paise
4. Find the differences:
   • 8.6 − 3.4
   • 15.00 − 7.28
   • 20.5 − 8.75
   • 6.236 − 0.487
5. Find the total length:
   • A ribbon is 3.75 m long and another ribbon is 2.6 m long. Find their combined length.
   • From the combined length, 1.25 m is cut off. How much ribbon remains?
6. Identify the pattern and write the next three terms:
   • 2.4, 2.7, 3.0, 3.3, …
   • 10.05, 10.15, 10.25, …
   • 8.5, 8.25, 8.00, …
7. Which decimal is closest to the given whole number?
   • Closest to 5: 4.78, 5.12, 5.45
   • Closest to 2: 1.89, 2.17, 2.35
   • Closest to 10: 9.92, 10.18, 10.05

Advance

1. A vegetable seller sells 2.75 kg of tomatoes, 1.5 kg of potatoes, 0.85 kg of onions and 0.4 kg of ginger.
   Find the total weight of vegetables sold.
2. A milkman delivers 4.75 L, 3.6 L and 5.25 L of milk on the first three days.
   If he delivers 18 L of milk in five days, how much milk does he deliver on the last two days?
3. A wire is 12.8 m long. It is cut into pieces of lengths 3.45 m, 2.75 m and 1.6 m.
   How much wire is left?
4. A packet of almonds weighs 0.750 kg, a packet of cashews weighs 0.625 kg, and a packet of raisins weighs 0.450 kg.
   Find:
   • The total weight of all packets
   • The difference between the heaviest and lightest packets
5. The length of a classroom is 8.75 m and its width is 6.5 m.
   How much longer is the classroom than it is wide?
6. Write the following decimal numbers in expanded form:
   • 35.407
   • 8.09
   • 0.506
7. A shop bill shows the following amounts: ₹125.50, ₹48.75, ₹99.25 and ₹16.50.
   Find:
   • The total bill amount
   • The change received if ₹300 is paid

HOTS

1. Use the digits 1, 2, 4, 5 and 8 exactly once to form a decimal number as close as possible to 25.
   Write the number and explain your choice.
2. Using the digits 0, 1, 4, 6 and 8 exactly once, form:
   • The smallest decimal number between 100 and 1000
   • The greatest decimal number less than 100
3. A bus timetable states that a bus will arrive 4.5 hours after 12 noon.
   At what time will the bus arrive? Explain why it is not 4:05 p.m.
4. In cricket, “5.4 overs” means 5 overs and 4 balls, not 5.4 mathematical overs.
   How many balls have been bowled in 5.4 overs?
5. A medicine dose is written as 0.05 mg. A person reads it incorrectly as 0.5 mg.
   How many times greater is the incorrect dose?
6. Without calculating the exact sums, decide which is greater:
   • 6.499 + 3.501 or 10
   • 8.25 + 1.74 or 10
   • 12.05 − 2.06 or 10
7. Rohan says, “A decimal number with more digits after the decimal point is always greater.”
   Is he correct? Give two examples to justify your answer.

Answer Key

Basic – Answers

1. • 7/10 = 0.7
   • 36/100 = 0.36
   • 405/1000 = 0.405
   • 19/10 = 1.9
2. • 0.8 = 8/10
   • 0.45 = 45/100
   • 2.07 = 2 + 7/100
   • 5.125 = 5 + 125/1000
3. • In 4.72, 7 is in the tenths place.
   • In 8.05, 5 is in the hundredths place.
   • In 12.346, 3 is in the tenths place.
   • In 0.289, 9 is in the thousandths place.
4. • 6 ones and 4 tenths = 6.4
   • 3 ones, 7 tenths and 5 hundredths = 3.75
   • 2 tens, 5 ones and 8 hundredths = 25.08
   • 145 tenths = 14.5
5. • 10 tenths = 1 unit
   • 100 hundredths = 1 unit
   • 10 hundredths = 1 tenth
   • 1 unit = 1000 thousandths
6. • 0.6 = 0.60
   • 4.05 < 4.5
   • 2.109 < 2.19
   • 0.008 < 0.08
7. • 3.4 + 2.5 = 5.9
   • 7.08 + 1.21 = 8.29
   • 12 + 0.75 = 12.75

Standard – Answers

1. 4.005 < 4.05 < 4.5 = 4.50 < 4.505
   • Hint: Add zeroes where needed: 4.500, 4.050 and 4.005.
2. • 47 mm = 4.7 cm
   • 8.6 cm = 86 mm
   • 325 cm = 3.25 m
   • 2.45 m = 245 cm
3. • 685 g = 0.685 kg
   • 2.75 kg = 2750 g
   • 56 paise = ₹0.56
   • ₹4.25 = 425 paise
4. • 8.6 − 3.4 = 5.2
   • 15.00 − 7.28 = 7.72
   • 20.5 − 8.75 = 11.75
   • 6.236 − 0.487 = 5.749
5. Combined length = 6.35 m
   Ribbon remaining = 5.10 m
6. • 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.2
   • 10.05, 10.15, 10.25, 10.35, 10.45, 10.55
   • 8.5, 8.25, 8.00, 7.75, 7.50, 7.25
7. • Closest to 5: 5.12
   • Closest to 2: 1.89
   • Closest to 10: 10.05

Advance – Answers

1. 2.75 + 1.5 + 0.85 + 0.4 = 5.50 kg
2. First three days = 13.60 L
   Last two days = 18 − 13.60 = 4.40 L
3. Wire left = 12.8 − 3.45 − 2.75 − 1.6 = 5.00 m
4. Total weight = 1.825 kg
   Difference = 0.750 − 0.450 = 0.300 kg
5. 8.75 − 6.5 = 2.25 m
6. • 35.407 = 3 tens + 5 ones + 4 tenths + 7 thousandths
   • 8.09 = 8 ones + 9 hundredths
   • 0.506 = 5 tenths + 6 thousandths
7. Total bill = ₹290.00
   Change = ₹10.00
   • Hint: 125.50 + 48.75 + 99.25 + 16.50 = 290.00.

HOTS – Answers

1. 25.148
   • Hint: Make 25 before the decimal point. To keep the extra decimal part smallest, use 148 after the point.
2. • Smallest decimal number between 100 and 1000 = 104.68
   • Greatest decimal number less than 100 = 86.410
3. 4:30 p.m.
   • Hint: 0.5 hour means half an hour, which is 30 minutes.
4. 34 balls
   • Hint: 5 overs = 30 balls, and 4 more balls makes 34 balls.
5. The incorrect dose is 10 times greater.
   • Hint: 0.5 ÷ 0.05 = 10.
6. • 6.499 + 3.501 = 10
   • 8.25 + 1.74 = 9.99, so it is less than 10
   • 12.05 − 2.06 = 9.99, so it is less than 10
7. No, Rohan is incorrect.
   • Example 1: 2.5 > 2.05
   • Example 2: 7.9 > 7.899

   Hint: Compare digits according to their place values, not merely the number of digits.

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

Back to all Class 7 Maths Worksheets