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

2. Warm Up
Find each value. 2 4
100
10,000 2 3
10,000
1,000,000

3. Which is larger, 100 or 100 ? How do you know?
Problem of the Day
Which is larger, 100 or 100 ? How do you know? 3 4
1004 is larger; the power of 100 is greater.

4. Learn to identify, convert, and compare metric units.

6. Additional Example 1: Choosing the Appropriate Metric Unit
Choose the most appropriate metric unit for each measurement. Justify your answer.
A. The amount of water a runner drinks each day
Liters—The amount of water a runner drinks each day is similar to the amount of water in a large water bottle.
B. The length of a boat
Meters—The length of a boat is similar to the length of several doorways.
C. The mass of a car
Kilograms—The mass of a car is similar to the mass of several hundred textbooks.

7. Check it Out: Example 1
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
Milliliters—The amount of liquid in 10 teardrops is similar to the amount of liquid in several eyedroppers.
Grams—The mass of a pencil eraser is similar to the mass of a few paperclips.
Kilometers—The length of 15 soccer fields is similar to the length of 10 football fields.

8. 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.

9. Additional Example 2A: Converting Metric Units
Convert the measure.
530 cL to liters
100 cL = 1L, so divide by 100.
530 cL = (530 ÷ 100) L
Move the decimal point 2 places left: 530.
= 5.3 L

10. Additional Example 2B: Converting Metric Units
Convert the measure.
1,070 g to milligrams
1 g = 1000 mg, so multiply by 1000.
1,070 g = (1070  1000) mg
Move the decimal point 3 places right: 1,070,000.
= 1,070,000 mg

11. Check It Out: Example 2A
Convert the measure.
980 dm to meters
10 dm = 1m, so divide by 10.
980 dm = (980 ÷ 10) m
Move the decimal point 1 places left: 980.
= 98 m

12. Check It Out: Example 2B
Convert the measure.
580 g to centigrams
1 g = 100 cg, so multiply by 100.
580 g = (580  100) cg
Move the decimal point 2 places right: 58,000.
= 58,000 cg

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

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

15. Meghan walks farther. 2,200 m = 2.2 km
Lesson Quiz
Convert each measure.
1. 1,270 g to kilograms
cm to millimeters
mL to liter
km to meters
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

16. 1-4 Applying Exponents Warm Up Problem of the Day Lesson Presentation
Course 2
Warm Up
Problem of the Day
Lesson Presentation

17. Warm Up
Find each value.
1. 92
3. 152
5. 103 81
2. 122
144
225
4. 102
100
1,000
6. 104
10,000

18. 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

19. Learn to express large numbers in scientific notation.

20. Vocabulary
scientific notation

21. The distance from Venus to the Sun is over 100,000,000 kilometers
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

22. The table shows several powers of ten.
Power of 10
Meaning
Value
101 10 10
102
10 · 10
100
103
10 · 10 · 10
1,000
104
10 · 10 · 10 · 10
10,000

23. Additional Example 1A: Multiplying by Powers of Ten
Method 1: Evaluate the power.
Multiply 10 by itself 3 times.
14 · 103 = 14 · (10 · 10 · 10)
= 14 · 1,000
Multiply.
= 14,000

24. Additional Example 1B: Multiplying by Powers of Ten
Method 2: Use mental math.
Move the decimal point 3 places.
(You will need to add 3 zeros.)
14 · 103 =
3 places
= 14,000

25. Check It Out: Example 1A
Multiply 12 · 102.
Method 1: Evaluate the power.
Multiply 10 by itself 2 times.
12 · 102 = 12 · (10 · 10)
= 12 · 100
Multiply.
= 1,200

26. Check It Out: Example 1B
Multiply 12 · 102.
Method 2: Use mental math.
Move the decimal point 2 places.
(You will need to add 2 zeros.)
12 · 102 = 12.00
2 places
= 1,200

27. 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 7
1.79
x 10
A number greater than or equal to 1 but less than 10
A power of 10

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

29. Additional Example 2: Writing Numbers in Scientific Notation
Write the number 4,340,000 in scientific notation.
6 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
4,340,000 = 4,340,000
= 4.34  106
The exponent is equal to
the number of places the
decimal point is moved.

30. Check It Out: Example 2
Write the number 8,421,000 in scientific notation.
6 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
8,421,000 = 8,421,000
The exponent is equal to
the number of places the
decimal point is moved.
=  106

31. Additional Example 3: Writing Numbers in Standard Form
The population of China in the year 2000 was estimated to be about  109. Write this number in standard form.
Since the exponent is 9, move the decimal
point 9 places to the right.
1.262  109 =
= 1,262,000,000
The population of China was about 1,262,000,000
people.

32. 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.
Since the exponent is
8, move the decimal
point 8 places to the
right.
1.5  108 =
= 150,000,000
The distance from the Earth to the Sun is about 150,000,000 kilometers.

33. Additional Example 4: Comparing Numbers in Scientific Notation
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?
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 < So 1.06  108 < 1.86  108
Brazil has more people living there.

34. Check It Out: Additional Example 4
The number of coins in Ty’s jar was 0.76  104 and number of coins in Laurel’s jar was  103. In which jar are there more coins?
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  Laurel’s jar: .93  103
Notice that 4 > 3. So .76  104 > .93  103
Ty’s jar has more coins in it.

35. Lesson Quiz: Part I
Multiply.
1. 25  102
2,500
2. 18  104
180,000
 102
11,000
 103
3,742

36. Lesson Quiz: Part II
Write each number in scientific notation.
5. 7,400,000
6. 45,000
7. Earth is about  107 miles from the Sun. Write this number in standard form.
7.4  106
4.5  104
92,920,000