Question
(a) Write 2.8 × 102 as an ordinary number.
(b) Work out 2.5 × 108× 2 × 10–2.
Give your answer in standard form.
▶️Answer/Explanation
(a)In scientific notation, a number is written as a product of a decimal number between 1 and 10. To convert 2.8\times 10^{2} to an ordinary number, we need to move the decimal point 2 places to the right, since the power of 10 is positive.
\(2.8\times 10^{2}=280\)
Therefore, \(2.8\times 10^{2} \)is equivalent to 280 in ordinary number form.
(b)To multiply numbers in scientific notation, we first multiply the coefficients together and then add the powers of 10:
\(2.5 × 10^8 × 2 × 10–2 = (2.5 × 2) × (10^8× 10^–2)\)
\(= 5 × 10^6\)
Question
A city has a population of five hundred and six thousand.
Write the size of the population
(a) in figures,
▶️Answer/Explanation
The size of the population in figures is 506,000.
(b) in standard form.
▶️Answer/Explanation
To express the population in standard form, we write the number so that it is between 1 and 10, and then multiply it by the appropriate power of 10. Now,we move the decimal point five places to the left to get 5.06, which is between 1 and 10. Then we multiply by 10^5, since we moved the decimal point five places to the left.The population of the city in standard form is:\(5.06\times 10^{6}\)
Question
(a) Write 82600 in standard form.
(b) Calculate \(\frac{6.02\times 10^{8}-5\times 10^{6}}{3\times 10^{6}}\) .
Give your answer in standard form.
▶️Answer/Explanation
(a)To write a number in standard form, we write it in the form of \(a\times 10^b\), where a is a number between 1 and 10, and b is an integer.
82600 in standard form is:
\(8.26 \times 10^4\)
(b)First, let’s simplify the numerator\(:6.02\times 10^{8}-5\times 10^{6}\)
Take \(10^{6}\) as common,it simplifies to:
\(\frac{10^{6}\left ( 6.02\times 10 ^{2}-5\right )}{3\times 10^{6}}\)
Now \(10^{6} \)cancels out from both numerator and denominator,
\(\Rightarrow \frac{6.02\times 10^{2}-5}{3}=\frac{602-5}{3}\)
\(=\frac{597}{3}\)
=199
In standrad form \(1.99\times 10^{2}\)
Question
(a) Write 2016 as the product of prime factors.
(b) Write 2016 in standard form.
▶️Answer/Explanation
(a)(a)The prime factorization of 2016 is:
2016 = 2 × 2 × 2 × 2 × 3 × 3 × 7
In exponential form, it can be written as:
\(2016 = 2^4 × 3^2 × 7\)
(b)To write 2016 in standard form, we express it as a number multiplied by a power of 10.
2016 can be written as:
2,016 = 2.016 × 1000
Since 1000 can be expressed as\( 10^3\), we have:
\(2,016 = 2.016 × 10^3\)
Therefore, 2016 in standard form is\( 2.016 × 10^3.\)
Question
(a) Write 629000 in standard form.
(b) Write \(82.1 \times 10^{-3}\) as an ordinary number.
▶️Answer/Explanation
(a) To write 629,000 in standard form, we express it as a number multiplied by a power of 10.
629,000 can be written as:
\(629,000 = 6.29\times 100,000\)
Since 100,000 can be expressed as \(10^5,\) we have:
\(629,000 = 6.29\times 10^5\)
Therefore, 629,000 in standard form is \(6.29\times 10^{5}.\)
(b) To write \(82.1\times 10^{-3} \)as an ordinary number, we move the decimal point to the left by three places, corresponding to the negative exponent of 10:
\(82.1\times 10^{3} \)becomes 0.0821.
Therefore, \(82.1\times 10^{-3}\) as an ordinary number is 0.0821.