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Scientific Notation & Significant figures

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Scientific Notation & Significant figures

Standard SCSh5 d: Express appropriate numbers of significant figures for calculated data.

- 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.

- 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.

- 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!

- 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.

- If there is a decimal point in the number, then YES, they are significant!

- Any zeroes after numbers may or may not be significant.

- 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.

- Any zeroes between 2 numbers is significant

- 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.

- 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

- 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.

- 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