| Digital Quiz 1 |
How many significant digits are there in 456.678 ?
See Explanation.
All non-zero digits in a number are significant.
This is likely the easiest of the rules. Simply put, if it is a non-zero digit,
it is significant.
Examples:
123,456 has 6 significant digits.
6 has 1 significant digit.
1.234567 has 7 significant digits.
Zeros at the beginning of a number are NOT significant.
This is likely the most difficult of the rules to understand.
Zeros at the beginning are simply place holders. They don't tell us anything about
the precision of a number. For example, if I say that my shoe is 0.025 meters long,
I have not added any precision to the measurement with the zeros. I could have just
as easily stated that my shoe is 25 centimeters long and not changed the significance
of my measurements by dropping the zeros. If I had said that my shoe was 0.0250 meters,
the zero at the end adds a level of confidence to my measurement. Converted to centimeters
the value would be 25.0cm since 0.0250 meters has 3 significant digits.
Examples:
0.000012 has 2 significant digits.
058 has 2 significant digit.
0.00200
has 3 significant digits. (The red zeros are not significant)
Zeros between other digits are significant.
Anytime you have a zero between other digits it is counted as significant. I'm not sure
exactly what to say. It is as if that zero was simply trapped there. Always count
trapped zeros, it's not there fault they are there...it just happened.
Examples:
1006 has 4 significant digits.
1.003 has 4 significant digit.
1.040 has 4 significant digit.
0.000607
has 3 significant digits. (The red zeros are not significant)
Zeros at the end of a decimal value are significant.
Zeros at the end of a decimal value add confidence to a number.
As a scientist, if I say that you are holding about 1 gram of sugar, I am not giving
much significance to that number. It is just an estimate..not very significant.
If I say you are holding 1.00 grams of sugar, I am saying with pretty good confidence
that you are holding 1.00 grams of sugar..but it might be maybe 1.001 or 1.002 or 1.003 or..well
you get the picture. I'm sure you have 1.00 grams of sugar because that is the best I could measure.
If I say that you are holding 1.0000000 grams of sugar, well..cheese and crackers!..I have
taken really amazing care in measuring your sugar! As a scientist,
that is a lot of confidence in measuring and I think you better darn well count the zeros!
Examples:
1.0 has 2 significant digits.
2.0000 has 5 significant digit.
2.22000 has 6 significant digit.
0.00020
has 2 significant digits. (The red zeros are not significant)
This number has two rules to follow.
Zeros at the end of a decimal value are significant and....
Zeros between other digits are significant.
Zeros at the end of a decimal value add confidence to a number and zeros in the middle are just
stuck. Either way, they both get counted.
Examples:
1.010 has 4 significant digits.
2.0100 has 5 significant digit.
2.22002 has 6 significant digit.
0.00020
has 2 significant digits. (The red zeros are not significant)
Milli means thousandths.
So, there are 1000 milliliters in a liter.
There are 1000 millimeters in a meter.
There are 1000 milligrams in a gram.
A simple sort of equation to remember is...To remove the milli from milliliter move
the decimal point three spaces left.
So.... 456ml becomes 0.456 liter
To add a milli to a liter move the decimal point three spaces right.
So... 0.456 liter becomes 456ml
The same rule applies with anything starting with milli..milligram, millimeter or milliliter.
Examples:
1.0 liter = 1000 ml
0.001 liter = 1 ml
345ml = 0.345 liter
1 mm= 0.001m
0.010 meter= 10mm
Centi means hundredths.
There are 100 cents in a dollar
So, there are 100 centimeters in a meter.
A simple sort of equation to remember is...To remove the centi from centimeter move
the decimal point two spaces left.
So.... 45cm becomes 0.45 meters.
To add a centi to a meter move the decimal point two spaces right.
So... 0.35 meter becomes 35cm.
Examples:
0.01 meter = 10cm
20cm = 0.2 meter
300cm= 3 meters
5.5 meters= 550cm