Question
Write the number two million two thousand and two in figures.
▶️Answer/Explanation
$2002002$
- Two million → This is 2,000,000
- Two thousand → This is 2,000
- Two → This is 2
write them as a single number
$2,002,002$
Question
The temperature at midnight is $-4^{\circ}C$.
The temperature at noon is $25^{\circ}C$
Work out the difference between these two temperatures.
▶️Answer/Explanation
$29$
Midnight temperature: \(-4^\circ C\)
Noon temperature: \( 25^\circ C \)
The difference between the two temperatures is the distance between them on the number line.
$
25 – (-4) = 25 + 4 = 29^\circ C
$
Question
Find the greatest odd number that is a factor of $140$ and a factor of $210$.
▶️Answer/Explanation
$35$
Prime factorization of 140:
$
140 = 2^2 \times 5 \times 7
$
Prime factorization of 210
$
210 = 2 \times 3 \times 5 \times 7
$
The odd common factors powers of 2.
Common odd factors: 5 and 7.
The greatest odd factor is:
$35$
Question
Work out the highest common factor (HCF) of 36 and 90.
▶️Answer/Explanation
To find the highest common factor (HCF) of 36 and 90, we can use the method of prime factorization.
Prime factorize both numbers.
36 can be expressed as\( 2^2\times 3^2.\)
90 can be expressed as \(2\times 3^2\times 5.\)
Identify the common prime factors and their lowest powers.
The common prime factors between 36 and 90 are 2 and 3. The lowest power of 2 is 1, as it appears only once in 90. The lowest power of 3 is 2, as it appears twice in both 36 and 90.
Multiply the common prime factors with their lowest powers.
HCF \(= 2^1\times 3^2 = 2 \times 9 = 18.\)
Therefore, the highest common factor (HCF) of 36 and 90 is 18.
Question
Find the lowest common multiple (LCM) of 36 and 48.
Answer/Explanation
Ans:
144
Question
(a) Write 2016 as the product of prime factors.
(b) Write 2016 in standard form.
Answer/Explanation
Ans:
(a) \(2^5 \times 3^2 \times 7\) oe final answer
(b) \(2.016 \times 10^3\)