This page covers the following topics:
1. Standard form
2. Standard units
4. Estimation and approximation
Standard form is a format of providing answers, typically used for very large or very small numbers. It uses powers of 10 to show the number by expressing it in the form a × 10ˢ, where s is a positive or negative integer and a is grater than or equal to 1 and less than 10. s represents the number of places the decimal point moves; if it is positive, the decimal moves to the right, and if it is negative, the decimal moves to the left.
A unit of measurement is one unit of a quantity. There are standard units that are used for different quantities. For length, kilometres (km) and metres (m) are used for long distances, and centimetres (cm) and millimetres (mm) are used for shorter distances. For mass, kilograms (kg) are used for great masses and grams (g) are used for smaller ones. Time can be measured in seconds, minutes or hours. Price can be measured in pounds (£), euros €) or pence/cents (p).
Questions will ask for answers to be given to a specific number of decimal places, which is the number of digits after the decimal point. If the digit after the last one that is kept is greater than or equal to 5, 1 is added to the last digit. Price is always given to 2 decimal places.
When rounding to the nearest 10, 100 etc or to a specific number of decimal places/significant figures, if the digit after the cut−off point is 5 or above, round up − if it’s under 5, round down.
In estimation questions, round values to 1 significant figure to get approximate answers. To calculate bounds, half the degree of accuracy and add it to the estimation for the upper bound while subtract it from the estimation for the lower bound.
Round 2.578 to two decimal places.
8 is the number after two decimal places and is above 5 so round up.
What is the lower bound of 6940 g, measured to the nearest 10 g?
Half the degree of accuracy: 10/2 = 5 g.
For the lower bound, subtract this from the given value: lower bound = 6935 g.
Round 0.005708 to three significant figures.
The first non zero number i.e. significant figure is 5. 8 is the number after three significant figures and is above 5 so round up.
Alice is 1.6 m tall (rounded to the nearest 10 cm), Beth is 158 cm tall (rounded to the nearest 1 cm). What is the smallest possible difference in their heights?
Alice could be 158 cm tall, which rounded to the nearest 10 cm would be 1.6 m. Therefore they could be of an exactly the same height, in which case the minimum height difference between them would be 0 cm.
The radius of a Helium atom is 31 picometers. Given that 1 meter is equivalent 1000000000000 picometers, give the radius of a Helium atom in meters and in standard form.
31 pm = 31 × 10⁻¹² m = 3.1 × 10⁻¹¹ m
3.1 × 10⁻¹¹ m
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