ROUND & ROUND
BOUND TO HAPPEN
SCIENTIFICALLY SPEAKING
MEASURE UP!
IB SAYS...
100
Round 38.7462 to 2 decimal places.
38.75
100
A length is recorded as 8cm to the nearest cm. State its lower bound.
7.5 cm
100
Write 4,500,000in scientific notation.
4.5×106
100
Is the statement “The desk is exactly 1.2 m long” describing an exact or approximate measurement?
Approximate. Physical measurements have a degree of uncertainty.
100
STATE the number of significant figures: 0.00340
3 significant figures
200
Round 0.007846 to 3 significant figures.
0.00785
200
A mass is recorded as 42.6g to the nearest 0.1g. State its upper bound.
42.65 g
200
Write 7.21×10-4 as an ordinary decimal.
0.000721
200
Which is more precise?
A. 8cm
B. 8.2cm
C. 8.24cm
C. 8.24cm
It is given to the greatest precision.
200
A measurement has an exact value of 50cm and an approximate value of 48cm.
CALCULATE the percentage error.
300
How many significant figures are in 0.04050?
4 significant figures
300
A length is 15.2cm correct to 1 decimal place. Write the interval containing the actual length x.
15.15 ≤ x < 15.25
300
Calculate and give your answer in scientific notation:
(3×105)(4×103)
1.2×109
300
A student estimates the height of a classroom door as 20 m.
Is this value reasonable? Explain.
No. A typical classroom door is only a few metres high, so 20 m is an unreasonable estimate.
300
A length is given as 72cm correct to the nearest cm.
DETERMINE the interval containing the actual length L.
71.5≤ L <72.5
400
A distance is calculated as 12.4968 km. Give the answer to 3 significant figures.
12.5 km
400
A rectangular field has a length of 40m and width of 25m, both measured to the nearest metre. What values should be used to calculate the greatest possible area?
Length = 40.5 m
Width = 25.5 m
400
Calculate:
4×106
400
A tablet screen is advertised as 8.0 inches (20.32 cm).
Explain why these two measurements appear to have different levels of precision even though they describe the same screen.
They are expressed using different units and have been rounded differently.
Changing units does not change the actual physical length.
400
A measurement is reported as 3.7281946kg.
EXPLAIN why giving all of these calculator digits may be inappropriate.
The measuring instrument may not have enough precision to justify all of those digits. The answer should be rounded to an appropriate degree of accuracy based on the context or measurement.
500
A calculator gives 0.99996 L. Give the value to 4 decimal places AND 4 significant figures.
1.0000 L (4 d.p)
1.000 L (4 s.f.)
500
A square has side length 6.4cm correct to 1 decimal place. Determine the lower and upper bounds for its area.
6.35 ≤ s < 6.45
6.352 ≤ A < 6.452
40.3225 ≤ A < 41.6025
500
A spacecraft travels 2.4×108km. It travels at an average rate of 6.0×104km/h.
Estimate the travel time in hours and answer in scientific notation.
4.0×103 hours
500
A company advertises that its battery lasts 24 hours.
A customer tests it and gets 22.7 hours.
Does this necessarily mean the company's measurement is wrong? Explain.
No. Battery life is an approximate measurement and can depend on conditions such as usage. The advertised value may also have been rounded or obtained under different testing conditions.
500
A scientist measures the diameter of a cell as
0.0000124837 m.
She reports the measurement as
1.25×10-5 m.
JUSTIFY whether her reported value is reasonable.
Yes. The value has been correctly written in scientific notation and rounded to 3 significant figures.
0.0000124837 = 1.24837×10-5
which rounds to
1.25×10-5 m