rounding and estimating
DESCRIPTION
Rounding and Estimating. PRE-ALGEBRA LESSON 3-1. Round each number to the underlined place value. a. 89.63. c. 0.83476. b. 579,122. 90. 600,000. 0.8348. 3-1. Rounding and Estimating. PRE-ALGEBRA LESSON 3-1. (For help, go to Skills Handbook page 727.). - PowerPoint PPT PresentationTRANSCRIPT
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
3-1
Round each number to the underlined place value.
a. 89.63 b. 579,122 c. 0.83476
90 600,000 0.8348
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
(For help, go to Skills Handbook page 727.)
Use the number 27.3865. Write the value of the given digit.
1. 2 2. 3
3. 8 4. 6
Check Skills You’ll Need
3-1
Solutions
1. 27.3865; 2 tens 2. 27.3865; 3 tenths
3. 27.3865; 8 hundredths 4. 27.3865; 6 thousandths
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
3-1
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
a. Round 8.7398 to the nearest tenth.
8.7398
tenths place
less than 5
8.7
Round down to 7.
3-1
(continued)
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
b. Round 8.7398 to the nearest integer.
8.7398
nearest integer is ones place
5 or greater
9
Round up to 9.
Quick Check
3-1
Estimate to find whether each answer is reasonable.
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
a. Calculation
+$ 59.98
$ 83.21
$115.67
$258.86+$ 60
$ 80
$120
Estimate
$260
The answer is close to the estimate. It is reasonable.
3-1
(continued)
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
b. Calculation
–$ 39.34
$176.48
$147.14
Estimate
–$ 40
$180
$140
The answer is not close to the estimate. It is not reasonable.
Quick Check
3-1
Add thefront-end digits.
You are buying some fruit. The bananas cost $1.32,
the apples cost $2.19, and the avocados cost $1.63. Use
front-end estimation to estimate the total cost of the fruit.
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
5.10=
The total cost is about $5.10.
+
Estimate byrounding.
.60
.20
.30
1.10
Quick Check
3-1
Estimate the total electricity charge: March: $81.75; April: $79.56; May: $80.89.
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
240=
The total electricity charge is about $240.00.
The values cluster around $80. 80
3 months
• 3
Quick Check
3-1
Round to the underlined place.
1. 6.557 2. 3.0448
Estimate.
3. $4.95 + $.89 4. 4.589 + 5.098 + 5.179
Rounding and EstimatingRounding and EstimatingPRE-ALGEBRA LESSON 3-1PRE-ALGEBRA LESSON 3-1
about $6.00
6.6 3.04
about 15
3-1
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
3-2
Round to the nearest whole number and to the nearest tenth.
a. 4.07 b. 0.708 c. 364.825
4, 4.1 1, 0.7 365, 364.8
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
(For help, go to Lesson 3-1.)
Round to the nearest one.
1. 145.89 2. 199.27
3. 101.06 4. 28.45
Check Skills You’ll Need
3-2
Solutions
nearest integer nearest integer 1. 145.89 2. 199.27
5 or greater; round up to 6 less than 5; do not change
146 199
nearest integer nearest integer3. 101.06 4. 28.45
less than 5; do not change less than 5; do not change
101 28
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
3-2
Estimate 6.43 • 4.7.
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
Multiply.6 • 5 = 30
6.43 6 4.7 5 Round to the nearest integer.
6.43 • 4.7 30
Quick Check
3-2
Joshua bought 3 yd of fabric to make a flag. The fabric
cost $5.35/yd. The clerk said his total was $14.95 before tax.
Did the clerk make a mistake? Explain.
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
Multiply 5 times 3, the number ofyards of fabric.
5 • 3 = 15
5.35 5 Round to the nearest dollar.
The sales clerk made a mistake. Since 5.35 > 5, the actual cost should be more than the estimate. The clerk should have charged Joshua more than $15.00 before tax.
Quick Check
3-2
The cost to ship one yearbook is $3.12. The total cost
for a shipment was $62.40. Estimate how many books were in
the shipment.
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
3.12 3 Round the divisor.
The shipment is made up of about 20 books.
62.40 60 Round the dividend to a multiple of 3 that is close to 62.40.
60 ÷ 3 = 20 Divide.
Quick Check
3-2
Is 3.29 a reasonable quotient for 31.423 ÷ 5.94?
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
Since 3.29 is not close to 5, it is not reasonable.
5.94 6 Round the divisor.
31.423 30 Round the dividend to a multiple of 6 that is close to 31.423.
30 ÷ 6 = 5 Divide.
Quick Check
3-2
Estimating Decimal Products and QuotientsEstimating Decimal Products and QuotientsPRE-ALGEBRA LESSON 3-2PRE-ALGEBRA LESSON 3-2
Estimate each product or quotient.
1. $4.78 ÷ 0.891 2. 983.24 • 2.41
3. –5.89 ÷ (–2.7) 4. 24.69 • 0.7
5. 20.498 • 4.908
about 100
about $5 about 2,000
about 2 about 25
3-2
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
3-3
Order from greatest to least: 0.677, 0.855, 0.760, 0.078, 0.541
0.855, 0.760, 0.677, 0.541, 0.078
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
(For help, go Skills Handbook page 723.)
Write the numbers from least to greatest.
1. 8, 6, 4, 9, 3, 5, 6 2. 72, 68, 69, 71, 72
3. 112, 101, 98, 120, 101 4. 3.74, 3, 3.7, 3.3, 37
Check Skills You’ll Need
3-3
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
Solutions
1. 3, 4, 5, 6, 6, 8, 9 2. 68, 69, 71, 72, 72
3. 98, 101, 101, 112, 120 4. 3, 3.3, 3.7, 3.74, 37
3-3
Six elementary students are participating in a one-week
Readathon to raise money for a good cause. Use the graph. Find
the (a) mean, (b) median, and (c) mode of the data if you leave
out Latana’s pages.
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
a. Mean:
40 + 45 + 48 + 50 + 505=
2335=
46.6=
The mean is 46.6.
sum of data valuesnumber of data values
3-3
(continued)
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
b. Median: 40 45 48 50 50 Write the data in order.
The median is the middle number, or 48.
c. Mode: Find the data value that occurs most often.
The mode is 50.
Quick Check
3-3
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
a. $1.10 $1.25 $2.00 $2.10 $2.20 $3.50
No values are the same, so there is no mode.
b. 1 3 4 6 7 7 8 9 10 12 12 13
How many modes, if any, does each have? Name them.
c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape
There is one mode.
Both 7 and 12 appear more than the other data values.
Cherry appears most often.
Since they appear the same number of times, there are two modes.
3-3
Quick Check
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
a. Which data value is an outlier?
Use the data: 7%, 4%, 10%, 33%, 11%, 12%.
The data value 33% is an outlier.
b. How does the outlier affect the mean?
The outlier raises the mean by about 5.5 points.
12.8 – 7.3 = 5.5
It is an outlier because it is 21% away from the closest data value.
Find the mean with the outlier.776 12.8
Find the mean without the outlier.446
7.3
3-3
Quick Check
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
a. the monthly amount of rain for a year
Which measure of central tendency best describes
each situation? Explain.
since the average monthly amount of rain for a year is not likely to have an outlier, mean is the appropriate measure.
Mean;
b. most popular color of shirt
Mode;
When the data have no outliers, use the mean.
When determining the most frequently chosen item, or when the data are not numerical, use the mode.
since the data are not numerical, the mode is the appropriate measure.
3-3
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
c. times school buses arrive at school
(continued)
since one bus may have to travel much farther than other buses, the median is the appropriate measure.
Median;
When an outlier may significantly influence the mean, use the median.
3-3
Quick Check
Mean, Median, and ModeMean, Median, and ModePRE-ALGEBRA LESSON 3-3PRE-ALGEBRA LESSON 3-3
Which measure of central tendency best describes each situation?
1. numbers of legs on the animals in a zoo
2. favorite digits (from 0 to 9) of the students in a class
3. numbers of days-per-student that students are absent from school
4. test scores
median
mode
mode
mean
3-3
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
3-4
Evaluate each expression for r = 4, s = 6, t = 2.
a. 4r b. 18 ÷ s + t c. (r + s) • 2
16 5 20
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
(For help, go to Lesson 1-3.)
Evaluate each expression for x = 3 and y = 4.
1. 2x + 2y 2. 2x + y
3. 2(x + y) 4.x + y
2
Check Skills You’ll Need
3-4
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
Solutions
1. 2x + 2y = 2(3) + 2(4) 2. 2x + y = 2(3) + (4)
= 6 + 8 = 6 + 4
= 14 = 10
3. 2(x + y) = 2(3 + 4) 4. =
= 2(7)
= 14
x + y
2
3 + 4
2
=
= 3.5
72
3-4
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
Suppose you ride your bike 18 miles in 3 hours.
Use the formula d = r t to find your average speed.
d = r t Write the formula.
18 = (r )(3) Substitute 18 for d and 3 for t.
Divide each side by 3.183 =
3r
3
Simplify.6 = r
Your average speed is 6 mi/h.
Quick Check
3-4
Use the formula F = + 37, where n is the number
of chirps a cricket makes in one minute, and F is the
temperature in degrees Fahrenheit. Estimate the temperature
when a cricket chirps 76 times in a minute.
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
n4
The temperature is about 56°F.
F = + 37n4 Write the formula.
F = + 37764 Replace n with 76.
F = 19 + 37 Divide.
F = 56 Add.
Quick Check
3-4
Find the perimeter of a rectangular tabletop with a
length of 14.5 in. and width of 8.5 in. Use the formula for the
perimeter of a rectangle, P = 2 + 2w.
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
The perimeter of the tabletop is 46 in.
P = 2 + 2w Write the formula.
P = 46 Add.
P = 2(14.5) + 2(8.5) Replace with 14.5 and w with 8.5.
P = 29 + 17 Multiply.
Quick Check
3-4
Using FormulasUsing FormulasPRE-ALGEBRA LESSON 3-4PRE-ALGEBRA LESSON 3-4
Use the formula P = 4s to find the perimeter of a square with side s.
1. s = 5.6 m 2. s = 9.3 in.
3. Find the side of a square with a perimeter of 164 yd.
41 yd
22.4 m 37.2 in.
3-4
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
3-5
Separate the digits 1 through 9 into three groups that have the same sum.
1, 5, 9; 2, 6, 7; 3, 4, 8
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
(For help, go to Skills Handbook page 730.)
Simplify.
1. 2.8 + 7.06 2. 0.65 + 1.8
3. 4.52 – 2.48 4. 3.7 – 0.62
Check Skills You’ll Need
3-5
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
Solutions
1. 2.80 2. 0.65 + 7.06 + 1.80
9.86 2.45
3. 4.52 4. 3.70– 2.48 – 0.62
2.04 3.08
3-5
Solve 6.8 + p = –9.7.
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
6.8 + p = –9.7
6.8 – 6.8 + p = –9.7 – 6.8 Subtract 6.8 from each side.
p = –16.5 Simplify.
Check 6.8 + p = –9.7
6.8 + (–16.5) –9.7 Replace p with –16.5.
–9.7 = –9.7
Quick Check
3-5
Ping has a board that is 14.5 ft long. She saws off a
piece that is 8.75 ft long. Use the diagram below to find the
length of the piece that is left.
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
The length of the piece that is left is 5.75 ft.
x = 5.75 Simplify.
x + 8.75 – 8.75 = 14.5 – 8.75 Subtract 8.75 from each side.
x + 8.75 = 14.5
Quick Check
3-5
Solve –23.34 = q – 16.99.
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
–23.34 = q – 16.99
–23.34 + 16.99 = q – 16.99 + 16.99 Add 16.99 to each side.
–6.35 = q Simplify.
Quick Check
3-5
Alejandro wrote a check for $49.98. His new account
balance is $169.45. What was his previous balance?
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
Alejandro had $219.43 in his account before he wrote the check.
Simplify.p = 219.43
Add 49.98 to each side.p – 49.98 + 49.98 = 169.45 + 49.98
p – 49.98 = 169.45
Equation p – $49.98 = $169.45
Let p = previous balance.
Words previous balance minus check is new balance
Quick Check
3-5
Solving Equations by Adding or Subtracting DecimalsSolving Equations by Adding or Subtracting DecimalsPRE-ALGEBRA LESSON 3-5PRE-ALGEBRA LESSON 3-5
Solve each equation.
1. a + 10 = 7.9 2. –1.01 = c – 9
3. s – (–2.6) = 1.6 4. 3.02 + d = 2.91
5. –23.7 = 13.3 + g
– 37
– 2.1 7.99
– 1 – 0.11
3-5
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
3-6
Lucinda buys 12 gal of gasoline at $1.95 per gallon. How much does the gas cost?
$23.40
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
(For help, go to Skills Handbook page 765.)
Find each product.
1. 2.6(4.5) 2. 3.2(0.15)
3. 11.03(0.6) 4. 8.003(0.6)
Check Skills You’ll Need
3-6
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
Solutions
1. 2.6 2. 0.15
4.5 3.2 130 30
+ 1040 + 45011.70 = 11.7 0.480 = 0.48
3. 11.03 4. 8.003
0.6 0.66.618 4.8018
3-6
Solve –6.4 = 0.8b.
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
–6.4 = 0.8b
–6.40.8
0.8b0.8= Divide each side by 0.8.
–8 = b Simplify.
Check –6.4 = 0.8b
–6.4 0.8(–8) Replace b with –8.
–6.4 = –6.4
Quick Check
3-6
Every day the school cafeteria uses about 85.8
gallons of milk. About how many days will it take for the
cafeteria to use the 250 gallons in the refrigerator?
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
Let x = number of days.
numberof days
Words times is 250 gallonsdaily milk
consumption
Equation • =85.8 x 250
3-6
(continued)
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
85.8x = 250
The school will take about 3 days to use 250 gallons of milk.
x = 2.914 . . . Simplify.
x 3 Round to the nearest whole number.
85.8x85.8 =
25085.8 Divide each side by 85.8.
Quick Check
3-6
Solve –37.5 = .
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
c–1.2
–37.5 =c
–1.2
Multiply each side by –1.2.–37.5(–1.2) = (–1.2)c
–1.2
45 = c Simplify.
Quick Check
3-6
A little league player was at bat 15 times and had
a batting average of 0.133 (rounded to the nearest thousandth). The
batting average formula is a = , where a is the batting average, h is
the number of hits, and n is the number of times at bat. Use the
formula to find the number of hits she made.
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
hn
a =hn
0.133 =h
15 Replace a with 0.133 and n with 15.
3-6
(continued)
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
0.133(15) = (15)h
15 Multiply each side by 15.
Simplify.1.995 = h
2 h Since h (hits) represents an integer, round to the nearest integer.
The little league player made 2 hits.
Quick Check
3-6
Solving Equations by Multiplying or Dividing DecimalsSolving Equations by Multiplying or Dividing DecimalsPRE-ALGEBRA LESSON 3-6PRE-ALGEBRA LESSON 3-6
Solve each equation.
1. 9b = –30.6 2. –10.8 =
3. 2.45 = –0.7k 4. = 240
5. y ÷ (–0.3) = 146.7
– 44.01
–3.4 27
p–2.5
–3.5
t3.7
888
3-6
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
3-7
Use mental math to find each product or quotient.
a. 8.75 × 100
b. 9.6 × 100
c. 4.6 ÷ 10
d. 0.94 × 100
e. 4.06 ÷ 100
875
960
0.46
94
0.0406
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
(For help, go to Skills Handbook page 734.)
Find each product or quotient.
1. 5 100 2. 14.06 ÷ 1,000
3. 0.294 10 4. 0.9 ÷ 100
Check Skills You’ll Need
3-7
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
Solutions
1. 5 • 100 2. 14.06 ÷ 1000Move the decimal point Move the decimal point2 places to the right. 500. 3 places to the left. 0.01406
5 • 100 = 500 14.06 ÷ 1000 = 0.01406
3. 0.294 • 10 4. 0.9 ÷ 100Move the decimal point Move the decimal point 1 place to the right. 02.94 2 places to the left. 0.009
0.294 • 10 = 2.94 0.9 ÷ 100 = 0.009
3-7
Choose an appropriate metric unit. Explain your choice.
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
a. the width of a textbook
b. the mass of a pair of glasses
c. the capacity of a thimble
Milliliter; a thimble will hold only a small amount of water.
Gram; glasses have about the same mass as many paperclips, but less than this textbook.
Centimeter; the width of a textbook is about two hands, or ten thumb widths, wide.
Quick Check
3-7
Choose a reasonable estimate. Explain your choice.
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
a. capacity of a drinking glass: 500 L or 500 mL
b. length of a hair clip: 5 m or 5 cm
c. mass of a pair of hiking boots: 1 kg or 1 g
1 kg; the mass is about one half the mass of your math book.
5 cm; the length of a hair clip would be about 5 widths of a thumbnail.
500 mL; a drinking glass holds less than a quart of milk.
Quick Check
3-7
Complete each statement.
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
a. 7,603 mL = L
7,603 ÷ 1,000 = 7.603 To convert from milliliters to liters, divide by 1,000.
7,603 mL = 7.603 L
4.57 m = 457 cm
To convert meters to centimeters, multiply by 100.
4.57 100 = 457 cm
b. 4.57 m = cm
Quick Check
3-7
A blue whale caught in 1931 was about 2,900 cm
long. What was its length in meters?
Using the Metric SystemUsing the Metric SystemPRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
Wordscentimeters per meter
length in centimeters ÷
length in meters=
2,900Equation 100 29÷ =
The whale was about 29 m long.
Quick Check
3-7
PRE-ALGEBRA LESSON 3-7PRE-ALGEBRA LESSON 3-7
Write the metric unit that makes each statement true.
1. 23 kg = 23,000 2. 970 cm = 9.7
Complete each statement.
3. g = 42 mg 4. km = 5,000 m
g m
0.042 5
Using the Metric SystemUsing the Metric System
3-7
PRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
Problem Solving Strategy: Act It OutProblem Solving Strategy: Act It Out
3-8
Describe the pattern. Then give the next three terms.3, 6, 12, 24, 48, . . .
Starting with 3, each number is two times the number before it: 96, 192, 384.
PRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
(For help, go to Lesson 1-7.)
Write a rule for each number pattern. Find the next three numbers inthe pattern.
1. 0, 6, 12, 18,… 2. –18, –9, 0, 9,…
3. 0, 2, 1, 3, 2, 4, 3,… 4. 7, 6, 8, 7, 9, 8, 10,…
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Check Skills You’ll Need
3-8
PRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
Problem Solving Strategy: Act It OutProblem Solving Strategy: Act It Out
Solutions
1. 0, 6, 12, 18,…
Start with 0 and add 6 repeatedly.
0, 6, 12, 18, 24, 30, 36+6 +6 +6 +6 +6 +6
2. –18, –9, 0, 9,…
Start with –18 and add 9 repeatedly.
–18, –9, 0, 9, 18, 27, 36
+9 +9 +9 +9 +9 +9
3-8
PRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
Problem Solving Strategy: Act It OutProblem Solving Strategy: Act It Out
3. 0, 2, 1, 3, 2, 4, 3,…
Start with 0. Alternately add 2 and subtract 1.
0, 2, 1, 3, 2, 4, 3, 5, 4, 6
+2 –1 +2 –1 +2 –1 +2 –1 +2
Solutions (continued)
4. 7, 6, 8, 7, 9, 8, 10,...
Start with 7. Alternately subtract 1 and add 2.
7, 6, 8, 7, 9, 8, 10, 9, 11, 10
–1 +2 –1 +2 –1 +2 –1 +2 –1
3-8
Marta gives her sister one penny on the first day of October,
two pennies on the second day, and four pennies on the third day. She
continues to double the number of pennies each day. On what date will
Marta give her sister $10.24 in pennies?
Problem Solving Strategy: Act It OutProblem Solving Strategy: Act It OutPRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
1 2 2 • 2 = 4 4 • 2 = 8 8 • 2 = 1616 • 2 = 32
Number ofpennies
Days after the first
012345
Amount
$0.01$0.02$0.04$0.08 $0.16$0.32
3-8
(continued)
Problem Solving Strategy: Act It OutProblem Solving Strategy: Act It OutPRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 = 1024
You can tell from the pattern in the chart that you just need to count the number of 2’s multiplied until you reach 1,024, which is $10.24 in pennies.
Marta will give her sister $10.24 in pennies on October 11.
10 twos = 10 days after the first penny is given
Quick Check
3-8
PRE-ALGEBRA LESSON 3-8PRE-ALGEBRA LESSON 3-8
Solve using any strategy.
1. On Monday, Jon reads page 45 of his book and continues toread until he finishes page 89. How many page does he readon Monday?
2. Marion put one penny in a bank. Each day after that she put inthe bank double the number of pennies from the previous dayuntil the bank was full. If the bank was full on the 8th day, whenwas the bank only half-full?
89 – 45 + 1, or 45 pages
7th day
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3-8