Another Peek Beyond the Point — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Another Peek Beyond the Point" — 7 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Another Peek Beyond the Point" — 7 important questions with detailed answers for CB…
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Key Questions Covered:
- Define decimal numbers and explain place value for 45.678.
- Multiply: 2.5 × 3.4. Show all steps including decimal placement.
- Divide: 7.5 ÷ 2.5. Show the steps and verify the answer.
- Add: 12.35 + 8.47 and subtract: 15.6 - 7.25. Align decimal points clearly.
- Convert 0.625 to a fraction in simplest form.
- A length of 2.5 m is cut into 5 equal pieces. What is the length of each piece?
- + 1 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Define decimal numbers and explain place value for 45.678. | ✓ Solved |
| Multiply: 2.5 × 3.4. Show all steps including decimal pla… | ✓ Solved |
| Divide: 7.5 ÷ 2.5. Show the steps and verify the answer. | ✓ Solved |
| Add: 12.35 + 8.47 and subtract: 15.6 - 7.25. Align decima… | ✓ Solved |
| Convert 0.625 to a fraction in simplest form. | ✓ Solved |
| A length of 2.5 m is cut into 5 equal pieces. What is the… | ✓ Solved |
Showing 6 of 7 questions
Q1: Define decimal numbers and explain place value for 45.678.
Decimal Numbers:
Decimal numbers are numbers that contain a decimal point (.) separating the whole number part from the fractional part.
They are used to represent values between whole numbers with greater precision.
---
Place Value for 45.678:
Breakdown:
45.678 = 40 + 5 + 0.6 + 0.07 + 0.008
Place Value Chart:
| Digit | Place | Place Value | Value |
|-------|-------|-------------|-------|
| 4 | Tens | 10 | 40 |
| 5 | Ones/Units | 1 | 5 |
| . | Decimal Point | — | — |
| 6 | Tenths | 1/10 = 0...
Q2: Multiply: 2.5 × 3.4. Show all steps including decimal placement.
Multiply: 2.5 × 3.4
Method: Multiply as whole numbers, then place the decimal point
Step 1: Ignore the decimal points and multiply as whole numbers
25 × 34
Multiplying 25 × 34:
25
× 34
----
100 (25 × 4)
750 (25 × 30)
----
850
Step 2: Count the decimal places in the original numbers
2.5 has 1 decimal place
3.4 has 1 decimal place
Total decimal places = 1 + 1 = 2
Step 3: Place the decimal point
We need 2 decimal places in the answer.
From 850, moving decimal 2 places to th...
Q3: Divide: 7.5 ÷ 2.5. Show the steps and verify the answer.
Divide: 7.5 ÷ 2.5
Method: Convert to whole number division by multiplying both by 10
Step 1: Count decimal places
7.5 has 1 decimal place
2.5 has 1 decimal place
Maximum decimal places = 1
Step 2: Multiply both numbers by 10 (to eliminate decimals)
7.5 × 10 = 75
2.5 × 10 = 25
Now we have: 75 ÷ 25
Step 3: Perform whole number division
75 ÷ 25 = 3
Verification:
25 × 3 = 75 ✓
Step 4: Find the answer
Since we multiplied both numbers by the same value, the quotient remains the same.
7.5 ÷ 2.5 ...
Q4: Add: 12.35 + 8.47 and subtract: 15.6 - 7.25. Align decimal points clearly.
Problem 1: Add 12.35 + 8.47
Step 1: Align decimal points vertically
12.35
+ 8.47
-------
Step 2: Add from right to left
Hundredths place: 5 + 7 = 12 (write 2, carry 1)
Tenths place: 3 + 4 + 1 = 8
Ones place: 2 + 8 = 10 (write 0, carry 1)
Tens place: 1 + 1 = 2
Step 3: Write the answer
12.35
+ 8.47
-------
20.82
Answer: 12.35 + 8.47 = 20.82
---
Problem 2: Subtract 15.6 - 7.25
Step 1: Align decimal points (add zeros if needed)
15.60
- 7.25
--------
Step 2: Subtract from...
Q5: Convert 0.625 to a fraction in simplest form.
Convert 0.625 to a Fraction:
Step 1: Count the decimal places
0.625 has 3 decimal places
Step 2: Write as a fraction with denominator as a power of 10
Number of decimal places = 3
Denominator = 10³ = 1000
Fraction = 625/1000
Step 3: Simplify by finding GCD
Find GCD of 625 and 1000:
Factors of 625: 1, 5, 25, 125, 625
Factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Common factors: 1, 5, 25, 125
GCD = 125
Step 4: Divide both numerator and denominator by GCD
62...
Q6: A length of 2.5 m is cut into 5 equal pieces. What is the length of each piece?
Given:
Total length = 2.5 m
Number of equal pieces = 5
Step 1: Set up the division
Length of each piece = Total length ÷ Number of pieces
Length of each piece = 2.5 ÷ 5
Step 2: Convert to whole number division
Multiply both by 10:
2.5 × 10 = 25
5 × 10 = 50
Now: 25 ÷ 50 (or simplify as 2.5 ÷ 5)
Alternative: Direct division
25 ÷ 5 = 5 (in tenths)
So 2.5 ÷ 5 = 0.5
Step 3: Perform the division
2.5 ÷ 5 = 0.5 m
Step 4: Verify
0.5 × 5 = 2.5 ✓
Answer: Each piece has a length of 0.5 m (or 50 cm).
Showing 6 of 7 questions. Visit the full page for complete solutions.
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