Measurement and Energy

Question 1

Mass

Answer 1

Mass is a measure of the amount of matter in a body. There is a difference between mass and weight. Weight is the measure of the amount of force acting on the mass due to gravity. However if you’re on the surface of the Earth and not moving, mass and weight can be considered to be the same in everyday contexts. If you change your location with respect to gravity, mass will remain unchanged, but weight will not.

Question 2

Converting area units

Answer 2

To convert are units, change the side length units and compare the value for area
1m2 =100×100=10000cm2
1m2 =10000cm2
1 cm2 = 1m2
10 000

Question 3

Accuracy in measurements

Answer 3

Accuracy in measurements
The smallest unit on the measuring instrument is called the precision or limit of reading. For example, a 30 cm ruler with a scale for millimetres has a precision of 1 mm. The accuracy of a measurement
is restricted to plus or minus half (± 12 )of the precision. For example,
if the measurement on the ruler is 10 mm then the range of errors is 10 ± 0.5 mm. Here the upper bound is 10 + 0.5 mm or 10.5 mm and the lower bound is 10 – 0.5 mm or 9.5 mm.

Every measurement is an approximation and has an error. The absolute error is the difference between the actual value and the measured value indicated by the instrument. The maximum value
for an absolute error is 12 of the precision.

Question 4

Precision

Answer 4

Smallest unit on measuring instrument or limit of reading

Question 5

Absolute error

Answer 5

Measured value – Actual value
± 12 × precision

Question 6

Upper Bond

Answer 6

Measurement + Absolute error

Question 7

Lower Bond

Answer 7

Measurement - Absolute error

Question 8

Relative error

Answer 8

±Absolute error
Measurement

Question 9

Percentage error

Answer 9

±Absolute error × 100% Measurement

Question 10

Converting volume units

Answer 10

To convert volume units, change the side length units and compare the values for volume.
1m3 = 100 × 100 × 100 = 1000000cm3
1m3 = 1000 000 cm3

1 cm = 1 m3
1000 000

Question 11

Standard form

Answer 11

Standard form or scientific notation is used to write very large or very small numbers more conveniently. It consists of a number between 1 and 10 multiplied by a power of 10. For example, the number 4 100 000 is expressed in scientific notation as 4.1 × 106. The power of 10 indicates the number of tens multiplied together. For example:
4.1×106 = 4.1× (10 ×10 ×10 ×10 ×10 ×10) = 4100000
When writing numbers in scientific notation, it is useful to remember that large numbers have a positive power of 10 and small numbers have a negative power of 10.

Question 12

Writing number in standard notation

Answer 12

1. Find the first two non-zero digits.
2. Place a decimal point between these two digits. This is the number between 1 and 10.
3. Count the digits between the new and old decimal point. This is the power of 10.
4. Power of 10 is positive for larger numbers and negative for small numbers.

Question 13

Significant figures

Answer 13

Significant figures are used to specify the accuracy of a number. They are often used to round a number. Significant figures are the digits that carry meaning and contribute to the accuracy of the number. This includes all the digits except the zeros at the start of a number and zeros at the end of a number without a decimal point. These zeros are regarded as placeholders and only indicate the size of the number. Consider the
following examples.

• 51.340 has five significant figures: 5, 1, 3, 4 and 0.
• 0.00871 has three significant figures: 8, 7 and 1.
• 56091 has five significant figures: 5, 6, 0, 9 and 1.
  The significant figures in a number not containing a decimal point can sometimes be unclear. For example, the number 8000 may be correct to one, two, three or four significant figures. To prevent this problem, the last significant figure of a number can be underlined. For example, the number 8000 has two significant figures. If the digit is not underlined the context of the problem is a guide to the accuracy of the number.

Question 14

Writing number to significant figures

Answer 14

1. Write the number in standard form.
2. Count the digits in the number to determine its accuracy (ignore zeros at the end, except
   after a decimal point).
3. Round the number to the required number of significant figures.

Question 15

Food Energy

Answer 15

Food energy is measured in kilojoules (kJ). (1calorie = 4.184 kilojoules)

Question 16

Energy Consumption

Answer 16

Energy is the capacity to do work. Energy exists in numerous forms, such as heat. The joule (symbol J) is the unit of energy used by the International System of Units (SI). Heat energy, such as that produced by burning natural gas in the home, is usually measured in megajoules (one million joules), symbol MJ.

Question 17

Power

Answer 17

Power is the rate at which energy is generated or consumed. The watt is the SI unit of power and is equal to one joule per second. The symbol for the watt is W. As for the joule, the standard SI prefixes such as milli, kilo, mega, giga and tera are then added and commonly used to measure power.

Question 18

Electric energy (energy consumption)

Answer 18

Electrical Energy = Power x Time. The total amount of electrical energy used depends on the total power used by all your electrical devices and the total time they are used in your home. One kilowatt hour is equal to 1000 watts of power used for one hour of time.