1. Scientific Notation, Conversions and Significant Digits
Learning Goals …
… convert numbers to scientific notation
… convert measurements using the metric system
… identify the number of significant digits in a
measurement

2. Try working on Practice Questions …
Scientific Notation
Ex) Convert the following to scientific notation:
(a) = ______________________
(b) = ____________________
(c) (2.63 x 10-9)(5.06 x 103) = ______________
Note: use the exponent button on your calculator
EXP, E, EE
5.3 x 10-5
4.0 x 107
1.33 x 10-5
Try working on Practice Questions …

3. Practice Questions:
Express the following numbers in scientific notation:
= _________________________
= _________________________
58.23 = _________________________
= _________________________
12452 = _________________________
Express the following numbers to decimal notation:
1.77 x 107 = ________________________
2.552 x 10-9 = _________________________
1.18 x 103 = _________________________
4.44 x 10-1 = _________________________
1.399 x 100 = _________________________
Express the results of the following operations in scientific notation:
1.39 x x 10-4 = _________________________
1.17 x x 102 = _________________________
(1.81 x 10-3) (1.06 x 1020) = _________________________
(5.77 x 10-4)  (1.71 x 10-11) = _________________________
1.003 x 1012
3.998 x 10-10
5.823 x 101
2.038 x 10-1
x 104
1180
0.444
1.399
1.42 x 10-2
1.13 x 104
1.92 x 1017
3.37 x 107

4. Cubic units (m3, cm3, mm3) Vs. Capacity units (mL, L, kL)
Volume
Cubic units (m3, cm3, mm3) Vs. Capacity units (mL, L, kL)
Cubic units can be converted to capacity units
(and vice versa) using the following conversions:
1 cm3 = 1mL
1000 cm3 = 1000 mL = 1 L
1 m3 = 1000 L
1 m3 = (100cm)(100cm)(100cm)
1 m3 = cm3 = mL
1 m3 = 1000 L

5. The Metric System:
Convert the following:
3.15 m = __________ cm g) mg = ____________ g
955 g = ___________ kg h) 1620 km = ___________ dm
1630 mL = _________ L i) 144 kg = _____________ mg
20.0 hg = __________ mg j) mm = __________ cm
178 mm = _________ cm k) cm3 = ____________ L
2000 L = ______ m3 l) 126 m3 = ____________ cm3
x x move decimal to
the right  k
(kilo) h
(hecta) da
(deca)
unit d
(deci) c
(centi) m
(milli)
÷ ÷  move decimal to
the left
315
0.0155
0.955
1.630
17.8
3.450 2

6. Significant Digits
Non-zero digits are always significant.
(eg) 22 ______ significant digits
22.3 ______ significant digits
With zeros, the situation is more complicated:
Zeros placed before other digits are not significant (place holders)
(eg) ______ significant digits
(eg) g ______ significant digits
Zeros placed between other digits are always significant.
(eg) L ______ significant digits
(eg) kg ______ significant digits 2 3 2 4 4 4

7. Zeros that exist after the decimal place to demonstrate
Zeros that exist after the decimal place to demonstrate accuracy are significant.
(eg) ______ significant digits
(eg) ______ significant digits
Zeros that exist at the end of a number are significant only if they are behind a decimal point. If the zeros at the end of a number do not follow a decimal point, they are not significant (place holders)
(eg) ______ significant digits
(eg) ______ significant digits 4 4 3 7

8. Ex. 5 cats 10 chairs 60 min/h 1000m/km
Measurement
Certainty
522.3 cm
sig digs cm
12 m/s
3.10 x 105 m/s
0.005 km m 4 3 3 2 1 4
If you have an exact value or defined value, the significant digits are infinite
Ex. 5 cats 10 chairs min/h 1000m/km

9. ROUNDING
If the digit after the digit to be retained as significant is a
greater than 5, round up
If the digit after the digit to be retained as significant is a 4 or less, round down
If the digit after the digit to be retained as significant is
exactly 5:
if the digit to be retained is odd, round up
if the digit to be retained is even, round down
Round the following to a whole number:
91.8  _______ d)  _______
52.3  _______ e)  _______
37.53  _______ f)  _______ 92 79 52 42 38 38

10. CALCULATIONS INVOLVING SIGNIFICANT DIGITS ADDITION AND SUBTRATION
Precision Rule – Precision is defined as the place value of the last digit obtained from a measurement or calculation
When adding or subtracting, the final answer has the same number of decimal places as the number with the least number of decimal places.
The least number of decimal places is ____
(eg) m m m = __________________ 1
26.1

11. Multiplication and Division
When multiplying or dividing, the final answer must have the same number of significant figures as the original number with the fewest significant figures (we can’t be any more certain than we were to begin with)
(eg) Calculate the volume of a box with sides measuring
5.05 cm, 3.87 cm and 4.7 cm
V = (5.05 cm x 3.87 cm x 4.7 cm)
= cm3
= 92 cm3

12. WS “Significant Digits” Complete any Practice Questions
CAN I …
… convert numbers to scientific notation
… convert measurements using the metric system
… identify the number of significant digits in a
measurement
HOMEWORK
WS “Significant Digits”
Complete any Practice Questions