# Scientific notation and significant figures

### Scientific notation and significant figures

#### Lessons

In this lesson, we will learn:
• Reasons for using significant figures and scientific notation.
• Situations where rounding, scientific notation and significant figures are appropriate.
• Rules for approximating and reporting values in science.

Notes:
• When doing any calculations in science or math, using standard form and significant figures is useful when dealing with extremely large or extremely small numbers.
• These techniques are used to avoid time wasting writing long meaningless numbers when dealing with extreme numerical values.
• A significant figure is any non-zero number in a value, or any zeros between non-zero numbers in a value.
• Standard form, AKA scientific notation, is written in the format a x 10$^b$. Here, a is your original number set between 1 and 10 and b is the number of places the decimal point got moved. To change a number to standard form:
• Step one: Write your original number with the decimal place in, for example 150 written as 150.00.
• Step two: Set your number as between 1 and 10 by moving the decimal place, for example 150.00 becomes 1.5000.
• Step three: Count the number of decimal places your decimal point had to move for step 2. Moving to the left should be counted as 1, moving to the right should be counted as –1. For example 1.5000 from 150.00 was two moves to the left, so 2.
• Working this way means numbers larger than 1-10 have a positive number of decimal places moved and numbers smaller than 1-10 should have a negative number of decimal places moved.
• Step four: Multiply your number from step 2 by 10 to the power of your number in step 3. For example: 1.5000 x 102
• Further examples: 1,650,000 could be written 1.65 x 106 or 0.0000592 could be written 5.92 x 10$^{-5}$.
• If nothing is specifically requested then some general rules are:
• Try not to round your values until the final stage or answer of a calculation.
• Do not round to a large degree at an early stage calculation, then to a small degree (for example, don't round to 3 significant figures then later to 5 S.F.)
• Use scientific notation (standard form) for any values larger than 1 x 10$^3$ or smaller than 1 x 10$^{-3}$ or on those orders of magnitude.
• Introduction
Introduction to significant figures
a)
Significant figures and scientific notation.

b)
How to use very small or very large numbers.

c)
General rounding rules in science.

• 1.
Apply significant figures and scientific notation/standard form to very large and small numbers.
Boltzmann's constant and Avogadro's number are two important constants in chemistry.
The approximate value of Boltzmann's constant is 0.0000000000000000000000138064852
The approximate value of Avogadro's constant is 602214085700000000000000
a)
Round both of these values to 2 decimal places.
Afterward, round both of these values to 3 significant figures.

b)
Round both of these values to 3 significant figures using standard form.