Download significant figures

IB Math Studies Yr 1
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Date_______________
12-1 Final Review: Unit 1
Unit 1 – IB Topic Number and Algebra

SCIENTIFIC NOTATION
This involves re-writing a number so that it has the form: a x 10k, where 1 ≤ a < 10 and 𝑘 ∈ Ζ
 A positive exponent means it is a LARGE number
Example: 4.92 x 104 = 49,200
 A negative exponent means it is a SMALL number
Example: 5.98 x 10-4 = .000598

When converting a number into scientific notation:
o Move the decimal so that it is between the first and second number
o Count how many places you moved the decimal (make this your exponent)
 If the original number was large, make the exponent positive
 If the original number was small, make the exponent negative
Examples: Write as decimal numbers.
a) 8.2 × 104
b) 3.76 × 10−2
Write in scientific notation.
a) 3900
b) 0.000071
IB Math Studies Yr 1
SIGNIFICANT FIGURES
This is a way of rounding a number to a specific level of precision. (the number you round to should be
similar or close to the original)
Rules for counting significant figures
- Digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are always significant.
- Zeros within/between numbers are always significant
(Ex: Both 4308 and 40.05 contain four significant figures)
To check the number of sig figs:
1. Write the number in Scientific Notation first!
2. Count the number of significant figures you see
Examples: Round the following values to the requested number of significant figures
a) 12654.543 [3 sig figs]
Example:
Round 34,567.8 to 3 significant figures.
Step 1: 3.4567.8 x 104
b) 0.6572 [2 sig figs]
Step 2: This is the 3rd significant figure
Step 3: Round this number: 3.46 x 104
(all numbers to right of this
number turn to zeros)
c) 0.0046192 [3 sig figs]
Step 4: Take out of scientific notation:
Answer: 34,600
PERCENT ERROR
Error is often expressed as a percentage of the exact value, and in this case we call it percentage error.
Example: A Problem has an exact answer of x = 0.1265
a)
State the value of x given correct to two significant figures.
b)
Calculate the percentage error if x is given correct to 2 significant figures
IB Math Studies Yr 1



UNIT CONVERSION
When converting units, make sure to include the appropriate units of measure for your final answer
(label your answer!)
Always start at the unit you are given, and then count how many places you travel to get to the unit
you are converting to. Move the decimal in the same direction and the same number of places as you
counted.
Use the phrase:
King Henry Doesn't [Usually] Drink Chocolate Milk
kilo- hecto- deka- [unit] deci- centi- milliExample: A large rectangular field has a length of 1.7 X 103 m and a width of 3.2 X 103 m.
a) Find the area of the field in m2.
Helpful Hints:
-Draw a diagram, and
label the sides using
the actual number
(not in scientific
notation)
b) Find the area of the field in km2.
c) Express your answer to (b) in the form a × 10k where 1 ≤ a < 10 and 𝑘 ∈ ℤ
-Convert each side
length first!
-Then calculate the
area of the figure in a
different unit.
IB Math Studies Yr 1
1. Calculate 3.7 × 18.72 – 500, writing your answer
2.
(a)
correct to two decimal places;
(b)
(i)
correct to three significant figures;
(ii)
in the form a × 10k, where 1 ≤ a < 10, k ∈ ℤ
(a) Calculate exactly
77.2 x 33
3.60 x 22
(b)
Write the answer to part (a) correct to 2 significant figures.
(c)
Calculate the percentage error when the answer to part (a) is written correct to 2
significant figures.
(d)
Write your answer to part (c) in the form a x 10k where 1 ≤ a < 10 and k is an integer of
.
IB Math Studies Yr 1
3. (a) A girl’s height is 1.623 m. Write her height to the nearest cm.
(b)
The time taken to fill a tank was 4 hours 13 minutes. Write this time to the nearest 5
minutes.
(c)
The attendance at a show was 1435 people. How many people, to the nearest 100, were
at the show?
(d)
The mean distance of the Moon from the Earth is approximately 384 403 km. Write this
distance in the form a × 10k where 1 ≤ 𝑎 < 10 𝑎𝑛𝑑 𝑘 𝜖 ℤ
4. Convert 5.9 kilograms (kg) to grams (g)
5. A rectangular field is 22 m long and 68 m wide.
a) Calculate the area of the field in m2.
b) Calculate the area of the field in cm2.
c) Express your answer to (b) in the form 𝑎 × 10𝑘 where 1 ≤ 𝑎 < 10 and 𝑘 ∈ ℤ.