Units Of Measurement Worksheets Page 29
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Units of measurement
= 1 cm, 100 cm = 1 m, 1000 m = 1 km
•
Measures of length: 10 mm
= 1 kg, 1000 kg = 1 t
•
Measures of mass: 1000 g
= 1 L, 1000 L = 1 kL
•
Measures of capacity: 1000 mL
Relative error
•
All measurements are approximations.
•
Every measuring instrument is limited in the degree of accuracy that it allows.
•
The maximum error is half the degree of accuracy used.
•
A true gauge of the accuracy of a measurement is to calculate the maximum error as a percentage of the
measurement we have taken.
Significant figures
•
Rounding to a given number of significant figures is an alternative to rounding to a given number of decimal
places, and is more appropriate for large numbers.
•
Zeros at the beginning or end of any number are not significant but are used to fill place values.
•
The method of rounding off for significant figures is the same as rounding for decimal places. Look at the
first digit after the cut off point. If this digit is 5 or greater the previous digit is increased by 1, other digits
are ignored, and zeros are put in their place if necessary to fill place values.
•
Large numbers will be written in scientific notation and rounded to a set number of significant figures.
•
For such numbers move the decimal point between the first two significant figures and multiply by the
corresponding power of 10 to the number of places moved. This power of 10 will be positive for numbers
greater than 1 and negative for numbers between 0 and 1.
•
When writing the result to such a question do not write all digits, round to the given or an appropriate
number of decimal places.
Rates
•
A rate is a comparison of two quantities of different types.
•
To simplify a rate, we compare the first quantity with one unit of the second quantity.
•
Many problems involve using rates and these questions must be read carefully to determine whether to
multiply or divide to solve the problem.
Percentage change
•
Percentage change involves increasing or decreasing an amount by a percentage.
•
When more than one percentage change is to be done, each must be carried out separately.
Using ratios
•
A ratio is a comparison of two quantities of the same type.
•
Ratios often need to be simplified, and this is done by dividing each part by the highest common factor.
•
When a quantity needs to be divided in a given ratio, we add the parts of the ratio to find the total number of
shares, then divide the quantity by this number to find the value of one share. Each part of the ratio can then
be calculated by multiplying this by the number of shares in each part.
73
Chapter 2
Units of measurement
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