UNIT 1A
NAME:______________________
PERIOD:_____________________
TEACHER:
Ms. Schmidt
_
Place Value
Classwork Day 1
Example 1
Write the place value of the underlined digit. Then write its value.
a. 205, 300, 005, 001____________________________________________________________________
b. 689, 525,917,143_____________________________________________________________________
Example 2
a. What is thirteen million, five thousand in standard form? _____________________________________
b. Write the word name for 20,030,010,000. __________________________________________________
Example 3
Write 3,007,000,091,806 in expanded form.
Standard Form
3,007,000,091,806
Expanded Form
Place Value
Classwork Day 1
Practice
Write the place of the underlined digit. Then write its value.
1. 670,901,230,001,400 __________________________________________________________________
2. 80,030,438,550_______________________________________________________________________
3. 427,321,040,229,320___________________________________________________________________
Write the word name for each number
4. 20,000,006,400 _______________________________________________________________________
5. 10,340,532 __________________________________________________________________________
6. 9,203,212,321 ________________________________________________________________________
Write each number in standard form.
7. One hundred twelve trillion
8. Three hundred and eight billion
9. Ninety-one trillion, three thousand
11. 20,000,000 + 4,000,000 + 30,000 + 300
10. 90,000,000,000 + 30,000,000 + 100,000
12. 42,000 + 400 + 50 + 1
Write each number in expanded form.
13. 52,905 ______________________________________________________________________________
14. 840,500 _____________________________________________________________________________
15. 2,000,201,032 ________________________________________________________________________
16. A megabyte holds about 1,000,000 characters of data. A gigabyte holds about 1,000 times as much data
as a megabyte. About how many characters of data does a gigabyte hold?
CHALLENGE: What is another name for a thousand million?
Place Value
Homework Day 1
Use the number 64, 310, 420, 069, 346. Name the digit in the given place.
1. Millions
3. Hundred billions
2. Trillions
4. Ten trillions
5. Write 3,007,000,091,806 in expanded form.
6. Write 20,000,000 + 5,000,000 + 3,000 + 200 in written form.
7. What is 23,000,400,000,158 in written form?
a. Twenthy-three milion, four hundred thousand, one hundred fifty-eight
b. Twenty-three billion, four hundred million, one hundred fifty-eight
c. Twenty-three tillion, four hindred million, one hundred fifty-eight
d. Two trillion, three billion, four million, one hundred fifty-eight
Ellen wrote three statements about the place values in the box. Tell whether each of her statements is true or
false. Explain your thinking.
16,079,653, 234,032
8. My trillion digit is 9.
9. My hundred thousand digit is 2.
10. My ten billion digit is 1 more than my ten
million digit.
11. My millions digit is the same as my ten
thousands digit and my tens digit.
Place Value Decimals
Classwork Day 2
Example 1
Write the place value of the underlined digit. Then write its value.
a. 9.8693 _______________________________________________________________________
b. 672. 92835 _____________________________________________________________________
Example 2
c. What is two thousand ten hundred thousandths in standard form? _______________________________
d. Write the word name for 8.0408. __________________________________________________
Example 3
Write 0.045608 in expanded form.
Standard Form
0.045608
Expanded Form
Place Value Decimals
Classwork Day 2
Practice
Write the place of the underlined digit. Then write its value.
1. 322.0357 __________________________________________________________________
2. .18202 _______________________________________________________________________
3. 42.73257 ___________________________________________________________________
Write the word name for each number
4. 20,000.032 _______________________________________________________________________
5. 10.495 __________________________________________________________________________
6. 9,200,000.09537 ____________________________________________________________________
Write each number in standard form.
7. Eighty and thirteen ten thousandths
8. Fourteen hundred thousandths
9. Nine-hundred and 7 millionths
11. 2,000,000 + .3 + .005 + .00007
10. 90,000,000,000 + 100,000 + .005 + .00009
12. 42,000 + 400 + 50 + 1 + .05 + .002
Write each number in expanded form.
13. 59,300.036 __________________________________________________________________________
14. 840.826 _____________________________________________________________________________
15. 2,000,201,000.0809 ___________________________________________________________________
Write the whole number portion.
16. 59.403
17. 206,059,083.84083
Write the decimal portion.
18. 95.3083
19. 103,206,705.028305
Place Value Decimals
Homework Day 2
1. Write 39.0948 in written form.
_________________________________________________________________________________
2. Write 8.7029 in expanded form.
________________________________________________________________________________
3. Write two thousand ten hundred thousandths in standard and expanded form.
Standard _______________________________________________________________
Expanded ______________________________________________________________
The slowest growing tree is a White Cedar in Canada. It grew about 0.0658 centimeters per year in 100 year
Use this information to answer 4 and 5.
4. To what decimal place value is the yearly growth measured?
____________________________________________________________________________________
5. How would you write this number in word form?
____________________________________________________________________________________
6. Write a decimal that has a 6 in the hundredths place and the ten thousandths place.
____________________________________________________________________________________
7. What is the written form for 16.011?
a. Sixteen and eleven thousandths
b. Sixteen and eleven tenths
c. Sixteen and eleven ten thousandths
d. Sixteen and eleven millionths
Use the number 49,003,948.052961. Name the digit in the given place.
8. Millionths
9. Ten thousandths
10. Thousand
Comparing and Ordering
Classwork Day 3
Place where you think the following fall on the number line.
1. 3.23
2. 4.74
3. .6
4. 1.3
5. 3.6
6. 4.9
Comparing Numbers
To show a number is greater than another number we use _________________.
To show a number is less than another number we use ___________________.
To show a number is equal to another number we use ____________________.
When comparing numbers, we should line up the decimals to make it easier!!!
Example: Compare 0.42 and 0.548.
Step 1:
Step 2:
Step 3:
You can also use a number line to help compare numbers!
Comparing and Ordering
Classwork Day 3
Practice
Compare the following.
1. 0.46 ______ 0.39
4. 9,325 ______ 9,325,000
2. 0.709 ______ 0.921
5. 9.8 ______ 9.80
3. 3 trillion ______ 9 million
6. 0.01 ______ 0.10
Write in order from greatest to least.
7. 300 thousand; 300 billion; 3 trillion; 30 million
__________________________________________________________________________________
8. 0.75; 0.3; 0.26;0.353
__________________________________________________________________________________
9. 6,074,232; 6,234,921; 6,243,219
__________________________________________________________________________________
10. 0.5478; 0.546; 0.5462; 0.5593
__________________________________________________________________________________
Write in order from least to greatest
11. 0.1211; 0.12; 0.121; 0.0911
__________________________________________________________________________________
12. 2,095,536; 2,095,563; 2,095,526; 209,553
__________________________________________________________________________________
13. 2.7993; 0.0803; 0.0779; 0.2396
__________________________________________________________________________________
14. 349 trillion; 34 million; 349 billion; 39 thousand
__________________________________________________________________________________
Comparing and Ordering
Classwork Day 3
Order the decimals in the table from least to greatest.
15.
16.
Batting Averages
Masses of Objects
Ira
0.278
A
0.206
Henry
0.302
B
2.7564
Sam
0.099
C
0.2
Steve
1.00
D
0.8384
Mario
0.525
E
2.76
_______________________________________
_______________________________________
17. Which decimal is greater than 3.33 but less than 3.34?
a. 2.3349
b. 3.305
c. 3.329
d. 3.336
18. If you plot these numbers on a number line, which one will be in the middle and why? 105,394;
150,494; 115,054
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
Comparing and Ordering
Homework Day 3
Compare the following:
1. 4 trillion ______ 4,000 billion
3. 2.34 ______ 2.3513
2. 0.421 ______ 0.4205
4. 9,035 ______9,035,000
Write in order from least to greatest.
5. 7 trillion; 7 thousand; 70 million; 70 billion
___________________________________________________________________________________
6. 8.134; 8.215; 8.2156; 8.2056
___________________________________________________________________________________
Write in order from greatest to least.
7. 4,085,239; 4,085,293; 4,085,240; 4,085,239,000
__________________________________________________________________________________
8. 639.087; 639.078; 639.088; 639
__________________________________________________________________________________
9. Which circle has the greatest diameter? (The diameter is the line that goes through the center of the
circle)
10. I am a decimal. I am more than 2 tenths greater than 0.29. I am between 0.2 and 0.3. What number am I?
Decimals to Fractions
First Method:
Second Method:
Step 1:
Step 2:
Step 3:
Classwork Day 4
Decimals to Fractions
Example 1: Convert 0.25 to a fraction.
First Method:
Second Method:
Example 2: Express 0.333 to a fraction.
First Method:
Second Method:
Example 3: Express 1.625 as a fraction.
First Method:
Second Method:
Classwork Day 4
Decimals to Fractions
Classwork Day 4
Practice
Using any method, express each of the following decimals as fractions.
1. 0.007
4. 1.7
2. 0.930
5. 0.42
3. 0.375
6. 0.75
7.
About 0.65 of the students in the after school program have a cell phone. Which fraction is equivalent
to the decimal?
a.
b.
13
200
650
10
8. Write the decimal and fraction for the shaded region below.
c.
d.
130
20
13
20
Decimals to Fractions
Homework Day 4
Write each decimal as a fraction in simplest form.
1. 0.15
5. 1.75
2. 0.27
6. 5.36
3. 0.82
7. 0.98
4. 0.380
8. 0.425
Fractions to Decimals
First Method:
Second Method:
2
Example: Express as a decimal.
5
First Method:
Second Method:
Classwork Day 5
Fractions to Decimals
Classwork Day 5
Practice
Write each fraction as a decimal.
1.
2.
3.
50
4.
100
9
5.
50
90
6.
200
9
25
7
8
5
16
7. Write the shaded region below as a fraction.
8.
2
3
of the class will complete their homework tonight. Which decimal represents this fraction?
a. 0.6
b. 0.66
c. 0.6666666
d. 0.667
Fractions to Decimals
1.
2.
3.
4.
99
100
90
150
20
200
6
20
Homework Day 5
5.
6.
7.
8.
3
8
8
55
39
64
7
5
Rounding
Example: Round 93.496326 to the hundredths place.
Classwork Day 6
Rounding
Classwork Day 6
Activity:
1.
11.
2.
12.
3.
13.
4.
14.
5.
15.
6.
16.
7.
17.
8.
18.
9.
19.
10.
20.
Rounding
1. Round to the nearest tenth. 8.54
2. Round to the nearest whole number. 99.59
3. Round to the nearest tenth. 310.286
4. Round to the nearest whole number. 6.46
5. Round to the nearest whole number. 6.805
6. Round to the nearest tenth. 9.725
7. Round to the nearest hundredth. 118.380
8. Round to the nearest millionth. 90.69907
9. Round to the nearest thousandth. 65.8591
10. Round to the nearest whole number. 70.597
Homework Day 6
Estimating
Estimating Sums and Differences
Front End Estimation:
Rounding:
Example: Estimate the following: 93.36 – 45.09
Estimating Products and Quotients
Compatible Numbers
Rounding
Example 2: Estimate the following 257 ÷ 8
Classwork Day 7
Estimating
Classwork Day 7
Practice
Estimate the following using rounding to the nearest whole number. Indicate if it is an overestimate or
underestimate.
1. 4.36 – 2.95
3. 13.09 – 10.55
2. 8.59 + 9.12
4. 1.5 + 59.2
Estimate the following by rounding to the nearest tenth. Indicate if it is an overestimate or underestimate.
5. 21.48 + 1.2743
7. 83.164 + 5.657
6. 11.363 – 5.385
8. 43.55 – 24.2499
Estimate each answer by rounding. Indicate if it is an overestimate or underestimate.
9. 3.48 x 4.78
11. 20.43 x 2.33
10. 10.23 x 4.743
12. 1.984 x 3.793
Estimate each answer by using compatible numbers. Indicate if it is an overestimate or underestimate.
13. 19.16 ÷ 3.7
15. 31.047 ÷4.492
14. 14.9 ÷8.432
16. 61.503 ÷ 8.044
17. Dominick wants to buy 2 CD’s for $14.95 each, 3 DVD’s for $19.99 each, and a video game for $36.79.
Which answer could you use to estimate, to the nearest whole number, how much money he needs?
a. 15 + 20 + 26
b. 2(14) + 3(20) + 36
c. 2(15) + 3(20) + 37
d. 2(15) + 3(19) +36
Estimating
Homework Day 7
Estimate the following using rounding to the nearest whole number. Indicate if it is an overestimate or
underestimate.
1. 4.93 – 2.352
2. 9.52 + 10.94
Estimate the following by rounding to the nearest tenth. Indicate if it is an overestimate or underestimate.
3. 0.9952 + 20.352
4. 53.592 – 3.295
Estimate each answer by rounding. Indicate if it is an overestimate or underestimate.
5. 1.293 x 4.932
6. 20.323 x 4.830
Estimate each answer by using compatible numbers. Indicate if it is an overestimate or underestimate.
7. 73.196 ÷ 11.513
8. 123.82 ÷25.937
9. Melissa bought a jar of mustard, a half-gallon of ice cream and two boxes
of popcorn. She gave the clerk a $20 bill. Estimate how many dollars she
received in change.
a. $4
c. $11
b. $9
d. $14
10. The library has a bookshelf 46.725 inches wide for their new encyclopedia. When the encyclopedia
arrived, the librarian found that each of the 24 volumes was 1.65 inches wide. Estimate if the 24 books
ill find on the shelf. How does your rounding affect the answer?
Adding and Subtracting Decimals
Classwork Day 8
When adding or subtracting decimals…
1. Line up the decimal points
2. “Drag” the decimal down
3. Add/Subtract normally!
**Write place holders to the right if needed.
Example: 98.944 + 3.28
Example 2: 5.011 – 4.312
*Remember to estimate your answers before adding or subtracting!
Practice
1. 10.21 – 4.62
3. 2.29 + 10.85
2. 0.03 + 1.85
4. Complete the sequence.
1.0, 2.2, 3.4, ___, ____
Adding and Subtracting Decimals
5. $10.39 + $200.85
Classwork Day 8
6. 40.3024 – 20.49
Use the diagram to the right to answer 7 and 8.
7. How does the cost for 1 tube of glue compare to the cost for 1
roll of tape?
8. What is the difference in cost between 2 packs of markers and 4
sheets of poster board?
Compare the following.
9. 12 – 0.0009 ____ 12- 0.00009
10. 412.089 + 34.71 ____ 498 – 52.075
11. Dean bought a birthday card for $2.95. There was an additional $0.18 tax. Dean paid for his purchase
using a $10 bill. How much change should Dean receive?
12. Hans wants to buy 10 lb. of hamburger meat for a barbecue. He picks out three packages at the
supermarket. Their weights are labeled 2.73 lb., 3.2 lb., and 2.29 lb. how much more mat does Han
need?
Adding and Subtracting Decimals
Homework Day 8
Compute the following.
1. 0.67 + 39
3. 0.49 + 0.006 + 0.213
2. 9.002 – 4,887.56
4. 497.1 – 437.805
5. Compare,
0.051 + 0.3 + 0.44993 ____ 1.2593
6. Find the next two numbers in the sequence. 5.5, 4.7, 3.9, ___, ___, ___
7. Wendy bought shoes for $39.99 and sneakers for $29.99. The tax on her purchase was
$4.90. If Wendy paid using a $100 bill, what was her change?
8. Ellie gets her car’s oil changed every 4,500 miles. Her last oil change was done at
33,798.7 miles. What will the odometer read when Ellie needs to get her next oil change?
9. Trey wrote 9.009 – 0.001 = 9.008. Is his answer correct? Why or why not?