Course 2 1-3 Metric Measurements 1-3 Metric Measurements Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course 2

1-3 Metric Measurements1-3 Metric Measurements

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

1-3 Metric Measurements

Warm UpFind each value.

1. 10 2. 10

3. 100 4. 100

100 10,000

10,000 1,000,000

2 4

2 3

Course 2


Problem of the Day

Which is larger, 100 or 100 ? How do you know?

1004 is larger; the power of 100 is greater.

3 4

Course 2


Learn to identify, convert, and compare metric units.

Course 2


Course 2


Choose the most appropriate metric unit for each measurement. Justify your answer.

A. The amount of water a runner drinks eachday

Meters—The length of a boat is similar to the length of several doorways.

Liters—The amount of water a runner drinks each day is similar to the amount of water in a large water bottle.

Kilograms—The mass of a car is similar to the mass of several hundred textbooks.

Additional Example 1: Choosing the Appropriate Metric Unit

C. The mass of a car

B. The length of a boat

Course 2


Choose the most appropriate metric unit for each measurement. Justify your answer.

A. The amount of liquid in 10 teardrops

B. The mass of a pencil eraser

C. The length of 15 soccer fields

Check it Out: Example 1

Grams—The mass of a pencil eraser is similar to the mass of a few paperclips.

Milliliters—The amount of liquid in 10 teardrops is similar to the amount of liquid in several eyedroppers.

Kilometers—The length of 15 soccer fields is similar to the length of 10 football fields.

Course 2


The prefixes of metric units correlate to place values in the base-10 number system. The table shows how metric units are based on powers of 10.

You can convert units within the metric system by multiplying or dividing powers of 10. To convert to a smaller unit, you must multiply. To convert to a larger unit, you must divide.

Course 2


Move the decimal point 2 places left: 530.

Convert the measure.

530 cL to liters

530 cL = (530 ÷ 100) L100 cL = 1L, so divide by 100.

= 5.3 L

Additional Example 2A: Converting Metric Units

Course 2


Additional Example 2B: Converting Metric Units

1,070 g = (1070 1000) mg1 g = 1000 mg, so multiply by 1000.

= 1,070,000 mgMove the decimal point 3 places right: 1,070,000.


1,070 g to milligrams

Course 2


Check It Out: Example 2A

980 dm = (980 ÷ 10) m10 dm = 1m, so divide by 10.

= 98 m Move the decimal point 1 places left: 980.


980 dm to meters

Course 2


Check It Out: Example 2B

580 g = (580 100) cg1 g = 100 cg, so multiply by 100.

= 58,000 cgMove the decimal point 2 places right: 58,000.


580 g to centigrams

Course 2


Additional Example 3: Using Unit Conversions t to Make Comparisons

Elizabeth purchases one pumpkin that weighs 3 kg and another that weighs 2,150 g. Which pumpkin weighs more? Use estimation to explain why your answer makes sense.

You can convert the mass of Elizabeth’s pumpkin to grams.

1 kg = 1000 g, so multiply by 1,000.

3 kg = (3 1,000) g

Move the decimal point 3 places right: 3.000.

= 3,000 g

2,150 g is about 2 kg. Since 2 kg < 3 kg, Elizabeth’s 3 kg pumpkin weighs more.

Course 2


Check It Out: Additional Example 3

Tyesha purchases a bag of potatoes that weighs 2.5 kg and another bag that weighs 3,850 g. Which bag weighs more? Use estimation to explain why your answer makes sense.You can convert the mass of Tyesha’s bag to grams.

1 kg = 1000 g, so multiply by 1,000.

2.5 kg = (2.5 x 1,000) g

Move the decimal point 3 places right: 2.500.

= 2,500 g

3,850 g is about 4 kg. Since 4 kg > 2.5 kg, Tyesha’s 3,850 g bag weighs more.

Course 2


Lesson QuizConvert each measure.

1. 1,270 g to kilograms

2. 890 cm to millimeters

3. 750 mL to liter

4. 122 km to meters

5. 800 mg to grams

1.27 kg

8,900 mm

0.75 L

122,000 m

0.8 g

6. Rosa walks 1.5 km to the library. Meghan walks 2,200 m to the library. Who walks farther? Use estimation to explain why your answer makes sense. Meghan walks farther. 2,200 m = 2.2 km

Course 2

1-3 Metric Measurements1-4 Applying Exponents

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2


Warm UpFind each value.

1. 92

3. 152

5. 103

81 144

225

2. 122

4. 102 100

6. 1041,000 10,000

Course 2


Problem of the Day

Each day, Lowell runs one more lap than he did the day before. After seven days he has run a total of 77 laps. How many laps did he run on the first day? 8

Course 2


Learn to express large numbers in scientific notation.

Course 2


Vocabulary

scientific notation

Course 2


The distance from Venus to the Sun is over 100,000,000 kilometers. You can write this number as a power of ten by using a base of ten and an exponent.

10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108

Power of ten

Course 2


The table shows several powers of ten.

Power of 10 Meaning Value

101

10 · 10 · 10 · 10

10 · 10 · 10

10 · 10

10 10

100

1,000

10,000

102

103

104

Course 2


Multiply 14 · 103.

Additional Example 1A: Multiplying by Powers of Ten

14 · 103 = 14 · (10 · 10 · 10)

= 14 · 1,000

= 14,000

Multiply 10 by itself 3 times.Multiply.

Method 1: Evaluate the power.

Course 2


Multiply 14 · 103.

Additional Example 1B: Multiplying by Powers of Ten

14 · 103 = 14.000

3 places

= 14,000

Move the decimal point 3 places.(You will need to add 3 zeros.)

Method 2: Use mental math.

Course 2


Check It Out: Example 1A

Multiply 12 · 102.

12 · 102 = 12 · (10 · 10)

= 12 · 100

= 1,200

Multiply 10 by itself 2 times.Multiply.

Method 1: Evaluate the power.

Course 2


Multiply 12 · 102.

Check It Out: Example 1B

12 · 102 = 12.00

2 places

= 1,200

Move the decimal point 2 places.(You will need to add 2 zeros.)

Method 2: Use mental math.

Course 2


Scientific notation is a kind of shorthand that can be used to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as

A number greater than or equal to 1 but less than 10

A power of 10

Course 2


In scientific notation, it is customary to use a multiplication cross () instead of a dot.

Writing Math

Course 2


Write the number 4,340,000 in scientific notation.

Additional Example 2: Writing Numbers in Scientific Notation

4,340,000 = 4,340,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.

= 4.34 106 The exponent is equal to the number of places the decimal point is moved.

6 places

Course 2


Check It Out: Example 2

Write the number 8,421,000 in scientific notation.

8,421,000 = 8,421,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.

= 8.421 106The exponent is equal to the number of places the decimal point is moved.

6 places

Course 2


The population of China in the year 2000 was estimated to be about 1.262 109. Write this number in standard form.

Additional Example 3: Writing Numbers in Standard Form

1.262 109 = 1.262000000Since the exponent is 9, move the decimalpoint 9 places to the right.

= 1,262,000,000

The population of China was about 1,262,000,000people.

Course 2


Check It Out: Example 3

The distance from the Earth to the Sun is calculated to be 1.5 108 kilometers. Write this distance in standard form.

1.5 108 = 1.50000000 Since the exponent is8, move the decimalpoint 8 places to theright.

= 150,000,000

The distance from the Earth to the Sun is about 150,000,000 kilometers.

Course 2


In 2005, the population of Mexico was 1.06 108

and the population of Brazil was 1.86 108. In which country do more people live?

Additional Example 4: Comparing Numbers in Scientific Notation

To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal portion of the numbers.

Mexico: 1.06 108 Brazil: 1.86 108

Notice that 1.06 < 1.86. So 1.06 108 < 1.86 108

Brazil has more people living there.

Course 2


The number of coins in Ty’s jar was 0.76 104 and number of coins in Laurel’s jar was 0.93 103. In which jar are there more coins?

Check It Out: Additional Example 4

To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal portion of the numbers.

Ty’s jar: 0.76 104 Laurel’s jar: .93 103

Notice that 4 > 3. So .76 104 > .93 103

Ty’s jar has more coins in it.

Course 2


Lesson Quiz: Part I

Multiply.

180,000

2,500

11,000

3,742

1. 25 102

2. 18 104

3. 110 102

4. 3.742 103

Course 2


Lesson Quiz: Part II

Write each number in scientific notation.

5. 7,400,000

6. 45,000

7. Earth is about 9.292 107 miles from the Sun.

Write this number in standard form.

4.5 104

7.4 106

92,920,000

Documents

Course 2 1-3 Metric Measurements 1-3 Metric Measurements Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation