Warm-Up: Find the value of x in each diagram. 1. ∆ABC ~ ∆MLK 34 2. RSTU ~ WXYZ7 3. A girl that...

Warm-Up:Find the value of x in

each diagram.

1. ∆ABC ~ ∆MLK 34

2. RSTU ~ WXYZ 7

3. A girl that is 5 ft tall casts a shadow 4 ft long. At the same time, a tree casts a shadow 24 ft long. How tall is the tree?

4. Order the measurements from smallest to largest: inch, mm, foot, cm, km, mile

30 ft

mm, cm, in, ft, km, mi

Warm Up Continued

Find each absolute value.

5. |–2| 6. |8.1|

7. |3 – 1.2| 8. |7 – 10|2

1.8 3

8.1

HW Checkp. 42 (1 – 4) (6 – 8) (14 – 17)1. They are the same shape, but not necessarily the same size.2. 5.6 m3. 10 ft

6. 8m7. 7 in8. 14. 9m15. 2.8ft16. 8.75 ft17. 4cm

If every dimension of a figure is multiplied by the same number, the result is a similar figure. The multiplier is called a scale factor.

If every dimension of the figure is multiplied by a scale factor:• Ratio of perimeters = scale factor• Ratio of Areas = (scale factor)2

• Ratio of Volumes = (scale factor)3

Example 3A: Changing Dimensions

The radius of a circle with radius 8 in. is multiplied by 1.75 to get a circle with radius 14 in. How is the ratio of the circumferences related to the ratio of the radii? How is the ratio of the areas related to the ratio of the radii?

Example 3B: Changing DimensionsEvery dimension of a rectangular prism with length 12 cm, width 3 cm, and height 9 cm is multiplied by to get a similar rectangular prism. How is the ratio of the volumes related to the ratio of the corresponding dimensions?

Helpful Hint

A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.

Check It Out! Example 3A rectangle has width 12 inches and length 3 inches. Every dimension of the rectangle is multiplied by to form a similar rectangle. How is the ratio of the perimeters related to the ratio of the corresponding sides? How is the ratio of the areas related to the ratios of the corresponding sides?

Example 4A rectangle has an area of 300 square centimeters. After every dimension of the rectangle is multiplied by a scale factor, the new area is 2700 square centimeters. What was the scale factor?

Post-It Check

The lengths of the sides of a square are multiplied by 2.5. How is the ratio of the areas related to the ratio of the sides?

The ratio of the areas is the square of the ratio of the sides: (2.5)2 = 6.25

A precision is the level of detail in ameasurement and is determined by thesmallest unit or fraction of a unit that youcan reasonably measure.

The accuracy of a measurement is the closeness of a measured value to the actual or true value.

Tolerance describes the amount by which a measurement is permitted to vary from a specified value.

A. 0.8 km; 830.2 m

A tenth of a meter is smaller than a tenth of a kilometer, so 830.2 m is more precise.

Example 1: Comparing Precision of Measurements

B. 2.45 in.; 2.5 in.

Choose the more precise measurement in each pair.

0.8 km Nearest tenth of a kilometer

830.2 m Nearest tenth of a meter

A hundredth of an inch is smaller than a tenth of an inch, so 2.45 in. is more precise.

A centimeter is smaller than a meter, so 100 cm is more precise.

Example 1: Continued

C. 100 cm; 1 m

2.45 in.

2.5 in.

Nearest hundredth of an inch

Nearest tenth of an inch

100 cm

1 m

Nearest centimeter

Nearest meter

Choose the more precise measurement in each pair.

Check It Out! Example 1

1a. 2 lb; 17 oz.

An ounce is smaller than a pound, so 17 oz is more precise.

1b. 7.85 m; 7.8 m.

2 lb

17 oz

Nearest pound

Nearest ounce

Check It Out! Example 1 Continued

A hundredeth of a meter is smaller than a meter, so 7.85 m is more precise.

1c. 6 kg; 6000 g.

A gram is smaller than a kilogram, so 6000 g is more precise.

7.85 m

7.8 m

Nearest hundredth of a meter

Nearest meter

6 kg

6000 g

Nearest kilogram

Nearest gram

A. Which scale is the most precise?

Ida works in a deli. She is testing the scales at the deli to make sure they are accurate. She uses a weight that is exactly 1 poundand gets the following results:Scale 1: 1.019 lbScale 2: 1.01 lbScale 3: 0.98 lb

Scales 2 and 3 measure to the nearest hundredth of a pound. Scale 1 measures to the nearest thousandth of a pound.

Example 2 : Comparing Precision and Accuracy

B. Which scale is the most accurate?.

Because 0.01 < 0.019 < 0.02, Scale 2 is the most accurate.

Example 2 : Continued

Because a thousandth of a pound is smaller than a hundredth of a pound, Scale 1 is the most precise.

For each scale, find the absolute value of the difference of the standard mass and the scale reading.

Scale 1: |1.000 – 1.019| = 0.019Scale 2: |1.000 – 1.01| = 0.01 Scale 3: |1.000 – 0.98| = 0.02

A standard mass of 16 ounces is used to test three postal scales.The results are shown below.

Check It Out! Example 2

A. Which scale is the most precise?

Scales A and B measure to the nearest tenth of an ounce.

Check It Out! Example 2 Continued

B. Which scale is the most accurate?

Scale C measures to the nearest hundredth of an ounce.

Because a hundredth of an ounce is smaller than a thousandth of an ounce, Scale C is the most precise.

For each scale, find the absolute value of the difference of the standard mass and the scale reading.

Check It Out! Example 2 Continued

Because 0.07 < 0.2 < 0.3, Scale C is the most accurate.

Scale 1: |16.00 – 16.3| = 0.3Scale 2: |16.00 – 15.8| = 0.2 Scale 3: |16.00 – 16.07| = 0.07

1. Choose the more precise measurement: 2.4 km; 2430 m 2430 m

Lesson Quiz :

2. Jorge works in a mail room. To test the accuracy of the scales in the mail room, he uses a weight that is exactly 8 oz. and gets the following results:

Scale 1: 8.02 ozScale 2: 7.8988 ozScale 3: 8.015 oz

a. Which scale is the most precise?

b. Which scale is the most accurate?

2

3

Classwork:

• P. 33 (4 – 5)• P. 34 (1 – 4) • P. 39 (1 – 6), (13 – 14)

Closing/HW:

• Closing: You will have a vocabulary quiz tomorrow. Write down the words that you will be responsible for knowing.

• HW: Textbook p. 44 (23) p. 49 (19 – 27) ALL