Write 72700000 in standard form
Worked Solution & Answer
Standard form is A × 10n where 1 ≤ A < 10.
e.g. 54 000 = 5.4 × 104
7.27 × 107
e.g. 54 000 = 5.4 × 104
7.27 × 107
Answer: 7.27 × 107
Standard form — Notes & Worked Examples Show / Hide
Explanation:
A number in standard form is written as A × 10n, where 1 ≤ A < 10 and n is a whole number (positive for large numbers, negative for small decimals less than 1).
To multiply or divide in standard form, multiply or divide the front numbers and use index laws on the powers of 10 (adjusting the final answer if A is not between 1 and 10). To add or subtract, convert both numbers into ordinary numbers (or the same power of 10) first.
Example 1: Work out (4.5 × 104) × (6 × 105). Give your answer in standard form.
Solution:
Multiply front numbers: 4.5 × 6 = 27
Add powers of 10: 104 × 105 = 109 → 27 × 109
Adjust so 1 ≤ A < 10: 27 = 2.7 × 101
2.7 × 101 × 109 = 2.7 × 1010
Answer: 2.7 × 1010
Example 2: Work out (3.2 × 10−3) + (4.8 × 10−4). Give your answer in standard form.
Solution:
Write as ordinary decimals:
3.2 × 10−3 = 0.0032 and 4.8 × 10−4 = 0.00048
Add decimals: 0.0032 + 0.00048 = 0.00368
Convert back to standard form:
Answer: 3.68 × 10−3
Write 0.00077 in standard form
Worked Solution & Answer
Standard form is A × 10n where 1 ≤ A < 10.
e.g. 54 000 = 5.4 × 104
7.7 × 10-4
e.g. 54 000 = 5.4 × 104
7.7 × 10-4
Answer: 7.7 × 10-4
The table gives information about the population and the total amount of money, in dollars, spent on healthcare for two countries in 2016
Work out how much more was spent per person on healthcare in Luxembourg than in Austria.
Give your answer correct to the nearest whole number.
Give your answer correct to the nearest whole number.
dollars
Worked Solution & Answer
Luxembourg per person = (3.7 × 10⁹) ÷ (6.3 × 10⁵) = $5873.0158.. M1
Austria per person = (4.2 × 10¹⁰) ÷ (8.7 × 10⁶) = $4827.5862.. M1
Difference = 5873.0158 – 4827.5862 = 1045.429... → 1045 dollars. A1
Austria per person = (4.2 × 10¹⁰) ÷ (8.7 × 10⁶) = $4827.5862.. M1
Difference = 5873.0158 – 4827.5862 = 1045.429... → 1045 dollars. A1
Answer: 1045 dollars
The table gives the amount of rice produced by each of two countries in 2020
(a) Write 3.5 × 107 as an ordinary number. [1 mark]
(b) Work out the amount of rice Japan produced in 2020
Give your answer in standard form. [2 marks]
Give your answer in standard form. [2 marks]
tonnes
Worked Solution & Answer
(a)
35 000 000
Answer (a): 35 000 000
(b)
820 000 + 6 780 000 = 7 600 000 = 7.6 × 10⁶ tonnes M1 A1
Answer (b): 7.6 × 106 tonnes
The table shows information about the surface area of each of the world's oceans.
(a) Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form. [2 marks]
Give your answer in standard form. [2 marks]
square kilometres
(b) Work out the value of k.
Give your answer correct to the nearest whole number. [1 mark]
Give your answer correct to the nearest whole number. [1 mark]
k =
Worked Solution & Answer
(a)
1.06 × 10⁸ – 6.86 × 10⁷ = 3.74 × 10⁷ M1 A1
Answer (a): 3.74 × 107 square kilometres
(b)
(1.56 × 10⁸) ÷ (1.41 × 10⁷) = 11.06... = 11 B1
Answer (b): k = 11
The table shows the populations of five countries.
(a) Work out the difference between the population of China and the population of Germany.
Give your answer in standard form. [2 marks]
Give your answer in standard form. [2 marks]
(b) work out the value of k.
Give your answer correct to the nearest whole number. [2 marks]
Give your answer correct to the nearest whole number. [2 marks]
k =
Worked Solution & Answer
(a)
1.4 × 10⁹ − 0.082 × 10⁹ = 1.318 × 10⁹ M1 A1
Answer (a): 1.318 × 109
(b)
(9.9 × 10⁶) ÷ (9.1 × 10⁵) = 10.879... ≈ 11 M1 A1
Answer (b): k = 11
The table shows some information about eight planets.
(a) Write down the name of the planet with the greatest mass. [1 mark]
(b) Find the difference between the mass of Venus and the mass of Mercury. [1 mark]
kg
(c) Is Nishat right?
You must show how you get your answer. [2 marks]
You must show how you get your answer. [2 marks]
Worked Solution & Answer
(a)
1.898 × 10²⁷ is highest power of 10 -> Jupiter B1
Answer (a): Jupiter
(b)
4.869 × 10²⁴ – 3.302 × 10²³ = 4.5388 × 10²⁴ kg B1
Answer (b): 4.5388 × 1024 kg
(c)
(4.35 × 10⁹) ÷ (4.14 × 10⁷) = 105.07... > 100, so Yes M1 A1
Answer (c): Yes, (4.35 × 109) ÷ (4.14 × 107) = 105.07... > 100
The table shows information about the surface area of each of the world's oceans.
(a) Write 1.56 × 108 as an ordinary number. [1 mark]
(b) Which ocean has the least surface area? [1 mark]
(c) Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form. [2 marks]
Give your answer in standard form. [2 marks]
square kilometres
Worked Solution & Answer
(a)
156 000 000
Answer (a): 156 000 000
(b)
Arctic (1.41 × 10⁷) B1
Answer (b): Arctic
(c)
1.06 × 10⁸ – 6.86 × 10⁷ = 3.74 × 10⁷ M1 A1
Answer (c): 3.74 × 107 square kilometres
The table shows the volumes, in km3, of four oceans.
(a) Write 7.18 × 107 as an ordinary number. [1 mark]
(b) Calculate the total volume of these four oceans. [2 marks]
km³
(c) Write 9 880 000 in standard form. [1 mark]
Worked Solution & Answer
(a)
71 800 000
Answer (a): 71 800 000
(b)
1.88×10⁷ + 3.10×10⁸ + 2.64×10⁸ + 7.18×10⁷ = 6.646 × 10⁸ M1 A1
Answer (b): 6.646 × 108 km³
(c)
9.88 × 106
Answer (c): 9.88 × 106
The table shows the population, correct to two significant figures, of each of six countries in April 2016.
(a) Write 9.3 × 107 as an ordinary number. [1 mark]
(b) Which of these countries had the least population? [1 mark]
(c) Work out the difference between the population of China and the population of India in April 2016.
Give your answer in standard form. [2 marks]
Give your answer in standard form. [2 marks]
Worked Solution & Answer
(a)
93 000 000
Answer (a): 93 000 000
(b)
Singapore (5.7 × 10⁶) B1
Answer (b): Singapore
(c)
1.382 × 10⁹ – 1.327 × 10⁹ = 0.055 × 10⁹ = 5.5 × 10⁷ M1 A1
Answer (c): 5.5 × 107