METRIC CONVERSIONS LADDER METHOD

T. Trimpe 2008 http://sciencespot.net/

KILO1000Units

HECTO100

Units

DEKA10

UnitsDECI

0.1Unit

CENTI0.01Unit

MILLI0.001Unit

MetersLitersGrams

Ladder Method

How do you use the “ladder” method?

1st – Determine your starting point.

2nd – Count the “jumps” to your ending point.

3rd – Move the decimal the same number of jumps in the same direction.

4 km = _________ m

12

3

How many jumps does it take?

Starting Point Ending Point

4.1

__.2

__.3

__. = 4000 m

Try these conversions using the ladder method.

1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm

14 km = _______ m 109 g = _______ kg 250 m = _______ km

Conversion Practice

Compare using <, >, or =.

56 cm 6 m 7 g 698 mg

Scientific Notation

How do I write numbers in scientific How do I write numbers in scientific notation?notation?

How do I calculate with scientific notation?How do I calculate with scientific notation?

When would I use scientific notation?When would I use scientific notation?

Scientific Notation Essential Scientific Notation Essential QuestionsQuestions

The table shows relationships between several powers of 10.

• Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left.

• Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.

A. 14 104

Multiply.

14.0 0 0 0Since the exponent is a positive 4, move the decimal point 4 places to the right.

Additional Example 1: Multiplying by Powers of Ten

140,000

B. 3.6 105

0 0 0 0 3.6Since the exponent is a negative 5, move the decimal point 5 places to the left.

0.000036

Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.

Additional Example 2: Writing Numbers in Scientific Notation

Think: The number is less than 1, so the exponent will be negative.

A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10.

7.09 103

Write the number in scientific notation.

So 0.00709 written in scientific notation is 7.09 10–3.

Additional Example 2: Writing Numbers in Scientific Notation

Think: The number is greater than 1, so the exponent will be positive.

B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10.

2.3 1010

Write the number in scientific notation.

So 23,000,000,000 written in scientific notation is 2.3 1010.

SIGNIFICANT SIGNIFICANT FIGURES (SIG. FIGURES (SIG. FIGS)FIGS)Rules:

All non-zero #’s are significant

Some zeros are significant; others are place holders

SIG FIGS

Only measurements have sig figs.Counted numbers are exactA dozen is exactly 12A piece of paper is measured 11

inches tall.Being able to locate, and count

significant figures is an important skill.

ATLANTIC-PACIFIC RULE

Ask yourself: self, is there a decimal?

PACIFIC ATLANTIC

(Present) (Absent)

Start from LEFT Start from RIGHT

& count all #’s from & count all #’s from

first nonzero first nonzero

How many sig How many sig figs?figs?

PRESENTStart from LEFT and count

all #’s from first nonzero

4.0010.0203 100.

ABSENTStart from RIGHT and count

all #’s from first nonzero

4001503000100

PRACTICE MAKES PERFECT!

4

3

3

4

3

1

SIG. FIGS IN SCIENTIFIC NOTATIONAll #’s (excluding x 10xx) ARE significant

How many sig. figs?How many sig. figs?:: 3.2 x 103 3.20 x 103

Put 0.08400 in scientific notation w/ sig. figs

SIG. FIG. CALCULATIONS

Multiplication/DivisionRules:The measurement w/ the smallest # of sig.

figs determines the # of sig. figs in answer

Let’s Practice!!!6.221cm x 5.2cm = 32.3492 cm2 4 2 How many sig figs in final answer??? And the answer is…. 32 cm2

ROUNDING RULES

look at the number behind the one you’re rounding.

If it is 0 to 4 don’t change it

If it is 5 to 9 make it one bigger

round 45.462 to four sig figs

to three sig figs

to two sig figs

to one sig fig