This document discusses significant figures and how to determine the number of significant figures in a value. It explains that significant figures are used for estimated or rounded values, not exact values like monetary amounts. The key points made are: - Significant figures can be determined by writing the number in scientific notation. The number of digits in the mantissa is the number of significant figures. - For numbers greater than 1, the power of 10 will be positive. For numbers between 0 and 1, the power of 10 will be negative. - Moving the decimal and dropping unnecessary zeros converts the number to a form to count significant figures. Trailing zeros after a decimal are always significant. - Examples are provided to demonstrate

1. Image Source: http://img.ehowcdn.com

2. Image Source: Google Images
Significant Figures are involved with estimated results.
When we say there were 15 000 people at a car race,
there were not exactly 15 000 people there.
It is a rounded off estimate to two significant figures:
There were 15 thousand people there.

3. Images Source: Google Images
The Significant Rules figures covered in this presentation
must never be applied to “Exact Values”.
• A $15 000 transaction with the Bank is always a 5 Significant
Figures value, because it involves EXACTLY $15 000, and is not
an estimated or rounded off value: ALL FIGURES ARE SIGNIFICANT.
•A Freeway Speed Limit of 100 km/hr is also an Exact Value,
and has three significant figures.
•An Exam Pass cutoff level of 50% is an exact value,
and has two significant figures.

4. Image Source: http://getstartedinscience.weebly.com
Significant Figures can be done using a set of around 5 rules,
With a lot of complications for how to deal with zeroes.

5. It is a lot easier to work out Significant Figures by taking
our number and putting it into Scientific Notation.
The number of resulting figures is the number of Significant Figures.
1.496 x 108
Image Source: http://www.inquisitr.com
149 600 000 km
149 600 000 has FOUR Significant Figures

6. Keep in mind at all times the following:
1.496 x 108
= 149 600 000
Normal Numbers bigger than 1, or large numbers,
always have a POSITIVE Power of 10.
Values smaller than 1, usually decimal values,
always have a NEGATIVE Power of 10.
6.2 x 101
= 62
6.234 x 10-1
= 0.6234
2.31 x 10-3
= 0.00231

7. 1.5  104
1 5 0 0 0
The Number is Greater than 10,
so the Exponent will be Positive.15 000
= Move the Decimal point to the LEFT
to create a number between 1 and 10.
Remove Zeroes that are not needed.1.5 0 0 0=
=
15 000 has TWO Significant Figures
Count how many digits are present.
4 places

8. 1.502  104
1 5 0 2 0
The Number is Greater than 10,
so the Exponent will be Positive.15 020
= Move the Decimal point to the LEFT
to create a number between 1 and 10.
Remove Zeroes that are not needed.1.5 0 2 0=
=
15 020 has FOUR Significant Figures
Count how many digits are present.
4 places

9. 1.5025  104
1 5 0 2 5
The Number is Greater than 10,
so the Exponent will be Positive.15 025
= Move the Decimal point to the LEFT
to create a number between 1 and 10.
Remove Zeroes that are not needed.1.5 0 2 5=
=
15 025 has FIVE Significant Figures
Count how many digits are there.
4 places

10. 4.3  10-3
0 .0 0 4 3
The Number is a decimal less than 1,
so the Exponent will be Negative.0.0043
=
Move the Decimal point to the RIGHT
to create a number between 1 and 10.
Remove Zeroes that are not needed.0 0 0 4.3=
=
0.0043 has TWO Significant Figures
Count how many digits are there.
3 places

11. 5.0  10-3
0 .0 0 5 0
The Number is a decimal less than 1,
so the Exponent will be Negative.0.0050
= Move the Decimal point to the RIGHT
to create a number between 1 and 10.
Remove Zeroes that are not needed.
NEVER REMOVE ZEROES THAT
CAME AFTER A DECIMAL POINT.
0 0 0 5.0=
We moved 3 places so
Power of 10 is three : 10-3
=
2 Significant Figures
3 places

12. 2.70  10-2
0 .0 2 7 0
The Number is a decimal less than 1,
so the Exponent will be Negative.0.0270
=
Move the Decimal point to the RIGHT
to create a number between 1 and 10.
Remove Zeroes that are not
needed, but not ones from after a
Decimal Pt.
0 0 0 2.70=
=
0.0270 has THREE Significant Figures
Count how many digits are there.
2 places

13. 1.539  103
1 5 3 9
1539
=
1.539=
=
1539 is 1500
v
3 is zero to four
“Do No More”
1.5  103=
7.36  10-3
0 .0 0 7 3 6
0.00736
=
0 0 0 7.36=
=
6 is 5 or bigger so
Round up by +1
0.00736 is 0.0074
7.4  10-3
=
Now Convert this to a number. Now Convert this to a number.

14. 1.539  103
1 5 3 9
1539
=
1.539=
=
1539 is 1540
v
2 is zero to four
“Do No More”
1.54  103=
7.362  10-3
0 .0 0 7 3 6 2
0.007362
=
0 0 0 7.362=
=
9 is 5 or bigger so
Round up by +1
0.007362 is 0.00736
7.36  10-3
=
Now Convert this to a number. Now Convert this to a number.

15. http://passyworldofmathematics.com
Visit our Site for Free Mathematics PowerPoints