(COP) Significant Digits Lesson

Significant Digits

When we express measured values, we can only list as many digits as we initially measured with our measuring tool plus one estimated digit.  For example, if you use a ruler to measure the length of a stick, you may measure it to be 36.7 cm. You could not express this value as 36.7123 cm because your measuring tool was not precise enough to measure or estimate this many places after the decimal.

pencil getting measured by ruler

Please watch the videos below while filling in the guided notes on how to determine the number of significant digits.

Assignment Check

Factor-Label Method for Converting

When converting metric units to other metric units, you can choose the method you would like to use to find the final answer.  However, when using the English system of measurements in which moving the decimal point is not the solution; using the factor-label method is essential.  Look at the table below for conversion factors within the English system.

Conversion Factors

Length

Weight

Volume

Time

12 in = 1 ft

1 kg = 2.2 lbs

32 oz = 1 qt

1 day = 24 hours

3 ft = 1 yd

16 oz = 1 lb

4 qts = 1 gal

1 hour = 60 mins

1760 yds = 1 mile

2000 lbs = 1 ton

1 L = 1.06 qts

1 min = 60 seconds

1 mile = 1.61 km

1 oz = 28.35 g

1 qt = 2 pints

365 days = 1 yr

Please watch the videos below explaining step-by-step how to use the factor-label method to convert between units.  

Fill in the Guided Video Notes Links to an external site. as you watch the videos.

In summary, it is important to follow the steps below:

  1. Place the given quantity as a fraction.
  2. Insert the necessary conversion factors as fractions.
  3. Cross out units that cancel out.
  4. Perform the math calculation

Example:   How many hours are in 18 weeks?

  18 weeks = _______ hours

LaTeX: \frac{18 \text{ weeks}}{1}\times\frac{7 \text{ days}}{1\text{ week}}\times\frac{24 \text{ hours}}{1\text{ day}} = 3,024 \text{ hours}18 weeks1×7 days1 week×24 hours1 day=3,024 hours

Practice Questions

Scientific Notation

Can you read this number?

5,973,600,000,000,000,000,000,000

(Earth's Mass in Kilograms)

What about this number?

0.000000000000000000000000000000910938

(Mass of an electron in Kilograms)

Scientists often have to work with very large or very small numbers.  It can be too cumbersome to write out these large or small numbers.  The scientific notation is a shorthand representation of these very large or very small numbers.  When written in scientific notation, a number is expressed as a decimal number between 1 and 10 that is multiplied by a power of 10.  

Look at the two simulations below to explain how to convert large numbers to scientific notation and then small numbers to scientific notation.

 

Practice Problems

[CC BY 4.0] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION