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Number System - Numbers and Sequences

Grade 5Cambridge (IGCSE)

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Place Value: Understanding the value of each digit in numbers up to 1,000,0001,000,000. For example, in 672,341672,341, the digit 77 represents 70,00070,000.

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Rounding: Rules for rounding to the nearest 1010, 100100, 10001000, 10,00010,000, or 100,000100,000. If the deciding digit is 55 or greater, round up; otherwise, round down.

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Number Sequences: A list of numbers that follow a specific pattern or rule. Linear sequences usually involve adding or subtracting a fixed amount (the common difference).

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Negative Numbers: Numbers less than 00. They are used to represent values like temperature below freezing or debt. For example, −5<−2-5 < -2.

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Square Numbers: The result of multiplying an integer by itself. For example, 42=4×4=164^2 = 4 \times 4 = 16.

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Prime Numbers: Numbers greater than 11 that have exactly two factors: 11 and itself (e.g., 2,3,5,7,112, 3, 5, 7, 11).

📐Formulae

Square Number:n2=n×nSquare\ Number: n^2 = n \times n

Term−to−term Rule:Termn=Termn−1+dTerm-to-term\ Rule: Term_{n} = Term_{n-1} + d (where dd is the common difference)

Powers of 10:101=10,102=100,103=1000Powers\ of\ 10: 10^1 = 10, 10^2 = 100, 10^3 = 1000

💡Examples

Problem 1:

Find the next two terms in the sequence: 12,19,26,33,…12, 19, 26, 33, \dots

Solution:

The next terms are 4040 and 4747.

Explanation:

Identify the difference between consecutive terms: 19−12=719 - 12 = 7 and 26−19=726 - 19 = 7. The rule is to add 77. Therefore, 33+7=4033 + 7 = 40 and 40+7=4740 + 7 = 47.

Problem 2:

Round 456,782456,782 to the nearest 10,00010,000.

Solution:

460,000460,000

Explanation:

Look at the digit in the 10,00010,000 place, which is 55. Look at the digit to its right (the thousands place), which is 66. Since 66 is greater than or equal to 55, we round the 55 up to 66 and change all digits to the right to zero.

Problem 3:

Calculate the difference between a temperature of 8∘C8^{\circ}C and −5∘C-5^{\circ}C.

Solution:

13∘C13^{\circ}C

Explanation:

To find the difference, subtract the smaller number from the larger number: 8−(−5)=8+5=138 - (-5) = 8 + 5 = 13. Alternatively, on a number line, there are 88 steps from 88 to 00 and 55 steps from 00 to −5-5.

Problem 4:

Solve the following subtraction using the column method: 80,000−34,56780,000 - 34,567.

Solution:

80000−3456745433\begin{array}{r} 80000 \\ - 34567 \\ \hline 45433 \end{array}

Explanation:

Using the vertical column method, we regroup (borrow) from the ten-thousands place across the zeros to subtract each digit starting from the ones column.

Problem 5:

Identify the square numbers between 1010 and 3030.

Solution:

1616 and 2525

Explanation:

List the squares of integers: 32=93^2 = 9, 42=164^2 = 16, 52=255^2 = 25, 62=366^2 = 36. The numbers that fall between 1010 and 3030 are 1616 and 2525.