Scientific Notation & Significant figures
Standard SCSh5 d: Express appropriate
numbers of significant figures for calculated
data.
Scientific Notation
• Do you know this number?
–300 000 000 m/s
–It’s the speed of light.
• Do you know this number?
–0.000 000 000 752kg
–It’s the mass of a dust particle.
Scientific Notation
• Instead of counting zeroes and getting confused, we use
scientific notation to write really big or small numbers.
– 3.00 × 108 m/s (300 000 000 m/s)
– 7.53 × 10-10 kg (0.000 000 000 752kg)
– The 1st number is the COEFFICIENT- it is always a number
between 1 and 10.
– The 2nd number is the BASE- it is the number 10 raised to
a power, the power being the number of decimal places
moved.
Significant Figures
• In science, we describe a value as having a
certain number of significant figures or digits.
– Includes all the #’s that are certain and 1 uncertain
digit.
– 1:30 has 2, 1:28 has 3, and 1:28:28 has 5
– There are rules that dictate which #’s are
considered significant!
Rules for Significant Figures
• Zeroes! Continued
– Any zeroes after numbers may or may not be significant.
• If there is a decimal point in the number, then YES, they
are significant!
– Ex. 12.000 has 5 sig. figs.
– Ex. 0.1200 has 4 sig. figs.
– Ex. 530.0000 has 7 sig. figs.
• If there is no decimal point in the number, then NO,
they aren’t significant!
– Ex. 120 has 2 sig. figs.
– Ex. 430 000 000 000 has 2 sig. figs.
Rules for Significant Figures
• Any non-zero # is considered significant
• Zeroes!
– Any zeroes between 2 numbers is significant
• Ex. 205 has 3 sig. figs.
• Ex. 4060033 has 7 sig. figs.
• Ex. 10.007 has 5 sig. figs.
– Any zeroes before a number are NOT significant
• Ex. 0.054 has 2 sig. figs.
• Ex. 0.000 005 has 1 sig. fig.
Adding/ Subtracting and
Significant Figures
• The rule
– When adding or subtracting the only significant
figures you worry about are those after the
decimal point. Your answer can have the same
number of significant figures AFTER the decimal
point as the original number that has the LEAST
number of significant figures after the decimal
point.
Examples
• 17.34 + 4.900 + 23.1 = 45.34
(1 sig. fig after decimal)
= 45.3
• 9.80 – 4.782 = 5.318
(2 sig. figs. After decimal) = 5.32
Multiplying/ Dividing and
Significant Figures
• The rule
–When multiplying or dividing, your
answer must have the same number of
significant figures as the original
number that has the least number of
significant figures total, not just after
the decimal.
Examples
• 3.9 × 6.05 × 420 = 9909.9
(2 sig. figs total) = 9900
= 9.9 × 103
• 14.2 ÷ 5 = 2.82
(1 sig. fig total) = 3