What is a Number?
A number is a mathematical value used for counting, measuring, or labeling objects. Numbers can be whole, decimal, positive, or negative.
Examples of Numbers:
- Whole numbers: 5, 12, 0
- Negative numbers: -3, -10
- Decimal numbers: 4.5, 7.89
Numbers can be single-digit (like 7) or multi-digit (like 253).
What is a Digit?
A digit is a single symbol used to represent numbers. In the decimal system, there are 10 digits:
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Example:
- The number 57 consists of two digits: 5 and 7.
- The number 246 has three digits: 2, 4, and 6.
Key Differences Between Numbers and Digits
| Feature | Number | Digit |
|---|---|---|
| Definition | Represents a value | Single symbol (0-9) |
| Examples | 15, -2, 3.14 | 0, 1, 2, …, 9 |
| Composition | Can have multiple digits | Always a single character |
💡 Quick Tip:
- All digits are part of numbers, but not all numbers are single digits.
By understanding numbers and digits, you build a strong foundation in mathematics. Whether you’re counting, calculating, or coding, these basics are essential
Square Roots Explained: Definition, Examples & Practice Questions
What is a Square Root?
The square root of a number is a value that, when multiplied by itself, gives the original number. It is represented by the √ symbol (called the “radical sign”).
Square Root Examples:
- √9 = 3 (because 3 × 3 = 9)
- √25 = 5 (because 5 × 5 = 25)
Key Properties of Square Roots
✔ Inverse of Squaring – Finding a square root is the opposite of squaring a number.
✔ Two Solutions – Every positive number has two square roots (positive and negative). However, the principal (main) square root is always non-negative.
- Example: √16 = 4, but -4 × -4 = 16 as well.
✔ Perfect Squares – Numbers like 1, 4, 9, 16, etc., have exact whole-number square roots.
10 Square Root Practice Questions (MCQs with Answers)
Q1. What is √64?
- A) 6
- B) 7
- C) 8 ✅
- D) 9
Explanation: 8 × 8 = 64, so √64 = 8.
Q2. Which number is the square root of 121?
- A) 10
- B) 11 ✅
- C) 12
- D) 13
Explanation: 11 × 11 = 121.
Q3. What is √49?
- A) 6
- B) 7 ✅
- C) 8
- D) 9
Explanation: 7 × 7 = 49.
Q4. The square root of 1 is:
- A) 0
- B) 1 ✅
- C) 2
- D) 10
Explanation: 1 × 1 = 1.
Q5. Which of these is NOT a perfect square?
- A) 16
- B) 25
- C) 40 ✅
- D) 81
Explanation: 40 has no whole number that squares to it.
Q6. What is √0?
- A) 0 ✅
- B) 1
- C) Undefined
- D) None
Explanation: 0 × 0 = 0.
Q7. What is √(4/9)?
- A) 2/3 ✅
- B) 3/2
- C) 4/9
- D) 9/4
Explanation: √4 = 2 and √9 = 3 → 2/3.
Q8. Which number has a square root of 15?
- A) 120
- B) 150
- C) 225 ✅
- D) 300
Explanation: 15 × 15 = 225.
Q9. If √x = 12, what is x?
- A) 122
- B) 124
- C) 144 ✅
- D) 148
Explanation: Square both sides → x = 12² = 144.
Q10. The square root of 0.25 is:
- A) 0.2
- B) 0.25
- C) 0.5 ✅
- D) 2.5
Explanation: 0.5 × 0.5 = 0.25.
FAQs About Square Roots
1. Can negative numbers have square roots?
Yes, but their square roots are imaginary numbers (e.g., √-4 = 2i).
2. What’s the difference between √x and x²?
- √x gives the number that, when squared, equals x.
- x² means x multiplied by itself.
Mastering Decimals: Definitions, Conversions & Practice Problems
Understanding Decimal Numbers
What is a Decimal Number?
A decimal number is a number that contains a decimal point, separating the whole number part from the fractional part. Decimals allow us to represent numbers between whole numbers with precision.
Examples of decimal numbers:
- 3.5 (three and five tenths)
- 0.75 (seventy-five hundredths)
- 12.0 (twelve)
- 45.678 (forty-five and six hundred seventy-eight thousandths)
What is a Decimal Fraction?
A decimal fraction is a fraction where the denominator is a power of 10 (10, 100, 1000, etc.). These fractions can be easily expressed as decimal numbers.
Conversion examples:
- 0.3 = 3/10
- 0.25 = 25/100 = 1/4
- 0.007 = 7/1000
Decimal Operations Explained
1. Addition of Decimals
When adding decimals, always align the decimal points before performing the calculation.
Example:
3.50
+4.25
7.75
2. Subtraction of Decimals
Similar to addition, ensure decimal points are aligned when subtracting.
Example:
8.50
-2.25
6.25
3. Multiplication of Decimals
Multiply as whole numbers, then count total decimal places in factors to place the decimal in the product.
Example:
2.5 × 3 = 7.5
(1 decimal place × 0 decimal places = 1 decimal place in answer)
4. Division of Decimals
Eliminate decimals from the divisor by moving decimal points in both numbers.
Example:
7.2 ÷ 0.6 = 72 ÷ 6 = 12
Practice Questions with Solutions
Addition MCQs
- 3.5 + 4.25 = ?
✅ B) 7.75
Explanation: Align decimals → 3.50 + 4.25 = 7.75 - 12.6 + 3.45 = ?
✅ A) 15.95
Explanation: 12.60 + 3.45 = 15.95
Subtraction MCQs
- 8.5 − 2.25 = ?
✅ B) 6.25
Explanation: 8.50 – 2.25 = 6.25 - 10.5 − 3.2 = ?
✅ B) 7.3
Explanation: 10.5 – 3.2 = 7.3
Multiplication MCQs
- 2.5 × 3 = ?
✅ A) 7.5
Explanation: 25 × 3 = 75 → 1 decimal place = 7.5 - 1.2 × 1.5 = ?
✅ B) 1.8
Explanation: 12 × 15 = 180 → 2 decimal places = 1.80
Division MCQs
- 6 ÷ 2.0 = ?
✅ B) 3
Explanation: 6 ÷ 2 = 3 - 7.2 ÷ 0.6 = ?
✅ A) 12
Explanation: 72 ÷ 6 = 12
Conversion Between Fractions and Decimals
Fraction to Decimal Conversion
Divide the numerator by the denominator.
Examples:
- 1/2 = 1 ÷ 2 = 0.5
- 3/4 = 3 ÷ 4 = 0.75
- 2/5 = 2 ÷ 5 = 0.4
Decimal to Fraction Conversion
Write the decimal as a fraction with denominator 10, 100, etc., then simplify.
Examples:
- 0.6 = 6/10 = 3/5
- 0.25 = 25/100 = 1/4
- 0.125 = 125/1000 = 1/8
Square Roots of Decimals
Finding square roots of decimals follows the same principle as whole numbers.
Examples:
- √0.81 = 0.9 (since 0.9 × 0.9 = 0.81)
- √0.04 = 0.2 (since 0.2 × 0.2 = 0.04)
- √1.44 = 1.2 (since 1.2 × 1.2 = 1.44)
Frequently Asked Questions
Q: How do you round decimal numbers?
A: Identify the place value to round to, then look at the next digit. If it’s 5 or more, round up.
Q: What’s the difference between 0.5 and .5?
A: They represent the same value. The leading zero is often included for clarity.
Q: How do you compare decimals?
A: Compare digit by digit from left to right after aligning decimal points.
Q: Can all fractions be converted to exact decimals?
A: No, some fractions (like 1/3 = 0.333…) produce repeating decimals.
