unit 1

Non-Zero Digits: All non-zero digits are considered significant. For example, in the number 348, all three digits
(3, 4, and 8) are significant.

Zeros between Non-Zero Digits: Zeros that are between non-zero digits are considered significant. For example,
in the number 503, all three digits are significant.

Leading Zeros: Leading zeros (zeros to the left of the first non-zero digit) are not considered significant. For
example, in the number 0.0456, the significant figures are 4, 5, and 6.

Trailing Zeros in a Decimal Number: Trailing zeros in a decimal number (after the last non-zero digit and after the
decimal point) are considered significant. For example, in the number 7.500, all four digits are significant.

Trailing Zeros in Whole Numbers: Trailing zeros in a whole number (without a decimal point) are not considered
significant unless they are indicated by a decimal point or scientific notation. For example, in the number 1200,
the significant figures are 2 and 1.

Exact Numbers: Counting numbers (e.g., 1, 2, 3) and defined constants have an infinite number of significant
figures. For example, there are 100 centimeters in 1 meter; this relationship has an exact value.

Rules
1.

Numbers that are not zero are significant. 1-9 are called digits

2.

Zeroes between non-zero digits are significant

3.

Leading zeroes. Zeroes that are in the front are NOT significant.

4.

Trailing zeroes with decimals. Where there is a decimal, zeroes

are significant

5.

Trailing zeroes with no decimals - These zeroes will be NOT

significant.

0.0050830

Sentence stems

1.

The number of significant figures for ___________ are ___________.

2.

Question _______ has _________ significant figures.

3.

There are ___________ significant figures because of rules ____________ .

Today’s Objective

500

500.

0.000500

How many significant figures do these three numbers have?

500 1

500. 3

0.000500 3

How many significant figures do these three numbers have?
Answers!

Rounding Multiplication/ Division

Find out the significant figures of each number and have your answer have the same amount of sig figs as the one with the fewest.

▪ Example:

6.43ml x 2.015ml = 12.95645 → 13.0

▪ Example:

2.50g/0.04cm = 62.5 → 60

Examples

1.310 x 2.3 = 3.013 →

▪ 513.57 x 2.1 = 1078.497 →

▪ 20.2 / 0.005 = 4040 →

Answers!

1.310 x 2.3 = 3.013 → 3.0

▪ 513.57 x 2.1 = 1078.497 →1100

▪ 20.2 / 0.005 = 4040 →4000

Rounding Addition/Subtraction

Results are rounded off so that the final digit is in the same decimal place as the measurement with the least spaces after the decimal.

▪ Example:

213.67 + 98.111 = 311.781 —---> 311.78

▪ Example:

78.995 – 23.8= 55.195 —-----> 55.2

Examples

▪ 6.201 cm + 7.4 cm + 0.68 cm +12.0 cm = 26.281 cm

▪ 8.264 g - 7.8 g = 0.464 g

▪ 10.4168 m - 6.0 m = 4.4168 m

Answers

6.201 cm + 7.4 cm + 0.68 cm +12.0 cm = 26.281 cm
→ 26.3

▪ 8.264 g - 7.8 g = 0.464 g —---> 0.5g

▪ 10.4168 m - 6.0 m = 4.4168 m —----> 4.4m

Scientific Notation

This is a secret technique used to write numbers that are too big or too
small.

Example 1

A blue whale can weigh up to 136,000 kilograms. Write this number in scientific
notation.

Example 2

There are 7,888,000,000 people in the world. Write this number in scientific
notation.

Example 4

An ant is 0.00025 meters tall. Write this number in scientific notation.

Example 3

Write this number is scientific notation. 0.00067

Example 5

A hummingbird flaps its wing 4000 times a minute. Write that number in scientific
notation.