Express the following numbers as a basic numeral:
Complete the following equations:
Express the following numbers in scientific notation:
10^{5} is equal to:
1 million
10 thousand
10 million
100 thousand
Determine whether the following numbers are equivalent to 0.00045:
4.5 \times 10^{ - 4 }
45 \times 10^{ - 4 }
4.5 \times 10^{ - 6 }
0.45 \times 10^{ - 3 }
4.5 \times 10^{ - 3 }
45 \times 10^{ - 5 }
Of the expressions selected in part (a), which one is in scientific notation?
For each of the following pair of numbers:
State the largest number.
Find the factor by which it is greater.
For each of the following set of numbers:
State the largest number.
State the smallest number.
7.27 \times 10^{ - 7 }
2.22 \times 10^{ - 7 }
4.76 \times 10^{ - 7 }
- 1.25 \times 10^{ - 2 }
- 1.25 \times 10^{ - 6 }
- 1.25 \times 10^{2}
- 9.37 \times 10^{ - 4 }
- 6 \times 10^{ - 4 }
- 6 \times 10^{ - 9 }
- 7.31 \times 10^{ - 9 }
- 5.13 \times 10^{ - 9 }
- 8.31 \times 10^{ - 9 }
- 2.93 \times 10^{ - 2 }
- 7.88 \times 10^{2}
- 7.88 \times 10^{ - 2 }
- 8.99 \times 10^{ - 3 }
- 1.99 \times 10^{ - 6 }
- 8.99 \times 10^{ - 6 }
- 4.7 \times 10^{2} \times 10^{3}
- 4.7 \times 10^{ - 8 } \times 10^{8}
- 4.7 \times 10^{9} \times 10^{8}
- 2.12 \times 10^{ - 1 } \times 10^{7}
- 2.12 \times 10^{ - 7 } \times 10^{4}
- 2.12 \times 10^{7} \times 10^{2}
Evaluate the following, giving your answers in scientific notation:
A calculator dislays scientific notation in the form aEb, express the following numbers as a basic numeral:
5.81 E 5
3.16 E \left( - 4 \right)
2.5 E 6
7.05 E \left( - 3 \right)
Use your calculator to find the value of the following:
A calculator displays 3.35 E 5 as the correct final answer when solving the following problem. Find the missing values in the problem to produce the given answer.
"At any particular time, approximately 2.32 \times 10^{⬚} aircraft are registered as being in flight over ⬚ \times 10^{10} square metres of air space. On average, how much air space does each aircraft have?"
A number is represented in the form 2 E \left( - 6 \right). Which of the following could this number represent?
The mass of an ant in grams
Earth’s population
The distance in kilometres between two planets
The diameter of a human cell
The world's oceans hold approximately 1\,332\,000\,000 cubic kilometres of water.
Bone marrow in a person’s body produces 2.3 \times 10^{6} red blood cells each second.
Which of the following would be the closest rounded value for this number?
20 million each second
2 million each second
2 hundred thousand each second
Hence, estimate the number of red blood cells produced each minute.
The tiny tubes in our kidneys measure about 1.2 \times 10^{ - 5 } metres in diameter.
Which of the following would be the closest rounded value for this number?
1 ten-thousandth of a metre
1 millionth of a metre
1 hundred thousandth of a metre
Hence, estimate the diameter of the tubes in millimetres.
A country’s land size is approximately 250\,000 square kilometres and its population is approximately 68 million people.
Express the number of square kilometres in scientific notation.
Express the population in scientific notation.
Hence, determine the population density measured in persons per square kilometre. Express your answer in scientific notation.
Consider the following:
- A plane is travelling eight hundred thousand metres per hour.
- An asteroid travelling at 8 \times 10^{8} metres per hour.
Express the speed of the plane in scientific notation.
How many times faster is the asteroid travelling? Express your answer as a basic numeral.
Two stars, A and B, in neighbouring galaxies have masses of 2.7 \times 10^{41} \text{ kg} and \\ 8.91 \times 10^{44} \text{ kg} respectively. How many times more massive is star B than star A? Express your answer as a basic numeral.
The mass of the largest mammal on Earth is approximately 1.5 \times 10^{3} times greater than the mass of an average adult human who weighs 90 \text{ kg}. According to this information, find the approximate mass of the largest mammal on Earth. Express your answer as a basic numeral.
An insect has an average mass of 0.2 gram. During a plague, it was estimated that there were 100 million insects in a particular area. Find the total mass of insects in scientific notation.
An estimated 9.1 \times 10^{7} people watched the final of the last World Cup, while an estimated 6.8 \times 10^{7} people watched the final of the World Cup four years before. Find the average number of people who watched the final of the World Cup the last two times it occurred.
Last year, the total \text{CO}_2 emissions of a country was approximately 7 \times 10^{11} \text{ kg} and the country had approximately 3.5 \times 10^{8} citizens. Find the average \text{CO}_2 emissions for each citizen of the country.
The mass of an atom of helium is 6.6465 \times 10^{ - 24 } grams and each litre of helium weighs 145 grams. A balloon is pumped with 11 litres of helium.
Find the number of grams of helium in the balloon.
One mole \left(\text{mol}\right) of an element consists of approximately 6.02 \times 10^{23} atoms.
Find the number of atoms in 3.5 \text{ mol} of element X. Express your answer in scientific notation.
If 3.5 \text{ mol} of element X weighs 31.5 \text{ g}, find the mass of 1 \text{ mol} of element X.
Planet A has a radius of 8.2 \times 10^{18} \text{ km}, while planet B has a radius of 4.1 \times 10^{23} \text{ km}. How many times greater than the volume of planet A is the volume of planet B? Express your answer in scientific notation. The volume of a sphere is given by V = \dfrac{4}{3} \pi r^{3}.
Outcomes
9.B2.1
Analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powers.