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**Metric Conversions Ladder Method**

T. Trimpe

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**How many jumps does it take?**

Ladder Method 1 2 3 KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit Meters Liters Grams CENTI 0.01 Unit MILLI Unit 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 Starting Point Ending Point How many jumps does it take? 4. 1 __. 2 __. 3 __. = 4000 m

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**Conversion Practice 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 Compare using <, >, or =. 56 cm m 7 g mg

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Scientific Notation

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**Scientific Notation Essential Questions**

How do I write numbers in scientific notation? How do I calculate with scientific notation? When would I use scientific notation?

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**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.

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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.

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**Additional Example 1: Multiplying by Powers of Ten**

Since the exponent is a positive 4, move the decimal point 4 places to the right. 140,000 B. 3.6 10-5 Since the exponent is a negative 5, move the decimal point 5 places to the left.

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**Powers of 10 are used when writing numbers in scientific notation**

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.

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**Additional Example 2: Writing Numbers in Scientific Notation**

Write the number in scientific notation. A Think: The decimal needs to move 3 places to get a number between 1 and 10. 7.09 10-3 Think: The number is less than 1, so the exponent will be negative. So written in scientific notation is 7.09 10–3.

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**Additional Example 2: Writing Numbers in Scientific Notation**

Write the number in scientific notation. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10. 2.3 1010 Think: The number is greater than 1, so the exponent will be positive. So 23,000,000,000 written in scientific notation is 2.3 1010.

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**Significant Figures (sig. figs)**

Rules: All non-zero #’s are significant Some zeros are significant; others are place holders

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**Only measurements have sig figs. Counted numbers are exact **

A dozen is exactly 12 A piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill.

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**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

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**Practice Makes Perfect!**

How many sig figs? PRESENT Start from LEFT and count all #’s from first nonzero 4.001 0.0203 100. ABSENT Start from RIGHT and count all #’s from first nonzero 4001 503000 100 4 4 3 3 3 1

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**Sig. Figs in Scientific Notation**

All #’s (excluding x 10xx) ARE significant How many sig. figs?: 3.2 x 103 3.20 x 103 Put in scientific notation w/ sig. figs

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**Sig. Fig. Calculations Multiplication/Division Rules:**

The measurement w/ the smallest # of sig. figs determines the # of sig. figs in answer Let’s Practice!!! 6.221cm x 5.2cm = cm2 4 2 How many sig figs in final answer??? And the answer is… cm2

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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 to four sig figs to three sig figs to two sig figs to one sig fig

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