Place Value
Comparing
Decimals
Computation
Rounding
100
Model the number 8.88 on the place value chart.
Use words, numbers, and your model to explain why each of the digits has a different value. Be sure to use “ten times as large” and “one tenth as large” in your explanation.
The place value of 8 is in the ones place it has a value of 8 ones or 8 wholes and is ten times as large as 0.8. It is equal to 8x1
The second 8 is in the tenths place it has a value of 8/10 (8 parts out of ten) It is equal to 8x 1/10
The 3rd 8 is the hundredths place and has a value of 8/100 (8 parts out of 100) It is one tenth as large as the 8 in the tenths place. It is equal to 8x 1/100
100
Compare using >, <, or =.
2 thousandths + 4 hundredths 
0.036
Which number is greater?
0.042
100
Mr. Pham wrote 2.619 on the board. Christy says it is two and six hundred nineteen thousandths. Amy says it is 2 ones 6 tenths 1 hundredth 9 thousandths. Who is right? Use words and numbers to explain your answer.
Who is right?
All are right because there are two wholes 6 in the tenths place one in the hundredths place and nine in the thousandths place.
100
2. Subtract vertically, showing all work.
a. 84.637 – 28.56 =
What is 56.077
100
Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.
Circle all the measurements below that could be the actual measurement of the rainfall.
2.251 cm 2.349 cm 2.352 cm 2.295 cm
Which numbers can be rounded to 2.3 cm
2.251cm 2.349cm 2.295 cm
200
Average annual rainfall totals for cities in New York are listed below.
Rochester 0.97 meters Ithaca 0.947 meters Saratoga Springs 1.5 meters New York City 1.268 meters
Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in word form and expanded form.
1. 0.947, 0.97, 1.268, 1.5
What is expanded notation of 0.947?
0.90+ 0.400+0.7000
What is the word form of 0.947
nine hundred forty seven thousands
200
4×103 + 2×100+3× 110 4×1000+2×102 +3× 1
Which number is greater?
942 < 4207
200
1. Express nine thousandths as a decimal.
2. Express twenty-nine thousandths as a fraction.
3. Express 24.357 in words.
a. Write the expanded form using fractions or decimals.
b. Express in unit form.
1. 0.009
2. 29/1000
3. twenty four and three hundred fifty seven thousandths
a. 20+4+3/10+5/100+7/1000
b. 20 tens 4 ones 3 tenths 5 hundredth 7 thousandths
(2x10)+(4x1)+(3x1/10)+(5x1/100)+(7x1/1000)
200
1. Subtract. You may use a place value chart.
341.84 – 21.92 =
What is
319.92
200
Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine.
a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount?
c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.
d. Round the weight of one dose to the nearest gram.
What is
10.4g +12.1g + 7.5g = 30.0g
300
1. Solve.
a. 4 hundredths + 8 hundredths = ______ hundredths = ______ tenth(s) _______ hundredths
b. 64 hundredths + 8 hundredths = ______ hundredths = ______ tenths _______ hundredths
a. 4 hundredths + 8 hundredths =12 hundredths
12 hundredths = one tenth and 2 hundredths
b. 64 hundredths + 8 hundredths = 72 hundredths
72 hundredths = 7 tenths and 2 hundredths
300
1. Show the numbers on the place value chart using digits. Use >, <, or = to compare.
Explain your thinking in the space to the right.
34.223 ---------------------- 34.232
0.8 ------------------------- 0.706
34,223 < 34,232
The three in the tens place is greater than the 2 in the tens place
0.8 > 0.706
8 tenths is larger that 7 tenths
300
Mrs. Fan wrote 5 tenths minus 3 hundredths on the board. Michael said the answer is 2 tenths because 5 minus 3 is 2. Is he correct? Explain.
0.50 - 0.03 = 0.47
You cannot minus 3 from 5 because they do not have the same place value
300
4. Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths because 8 minus 5 is 3. Is she correct? Explain.
What is
0.8 - 0.05 = 0.75
No the place value is not the same so you cannot minus 5 from 8
300
A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the
result is 13.7.
What is the maximum possible value of this number? Use words and the number line to explain your reasoning. Include the midpoint on your number line.
13.7
13.8
400
Use an area model to explain the product of 4.6 and 3. Write the product in standard form, word form, and expanded form.
What is the standard form, word form, and expanded form of 13.8?
Thirteen and 8 tenths
10 + 3 + 8x1/10
400
5. Lance measured 0.485 liter of water. Angel measured 0.5 liter of water. Lance said, “My beaker has more water than yours because my number has three decimal places and yours only has one.” Is Lance correct? Use words and numbers to explain your answer.
Which number is greater?
0.485 < 0.5
5 tenths is more than 4 tenths. Even though there are three decimal places in 0.485.
But if you round 0.485 both numbers will be equal since 4 tenths will round to 5 tenths since 8 hundredths is more than 5 hundredths.
400
A clipboard costs $2.23. It costs $0.58 more than a notebook. If Lisa bought 2 clipboards and one notebook how much would she spend? She paid with a ten-dollar bill. How much change does Lisa get?
$2.23 - $0.58 = $1.65
Cost of notebook $1.65
$2.23 + $ 2:23 $1.65 = $6.11 total cost of notebook and clipboard
$10.00 - $6.11 = $3.89 Change from $10 bill
400
Tom bought a binder for $3.16 and a math notebook for $4.567. How much more did the math notebook cost than the binder?
What is
$1.407
400
Jen’s pedometer said she walked 2.549 miles. She rounded her distance to 3 miles. Her brother rounded her distance to 2.5 miles. When they argued about it, their mom said they were both right. Explain how that could be true. Use number lines and words to explain your reasoning.
Jen rounded to the ones place since there is a 5 in the tenths place she rounded up so 2.549 rounded to 3
Her brother rounded to the tenths place. Since there is 4 in the hundredths place the tenths place does not change. So 2.549 rounded to 2.5
500
1. Write the following in exponential form and as a multiplication sentence using only 10 as a factor (e.g., 100 = 102 = 10 × 10).
a. 1,000 = ______________ = ______________
b. 100 × 100 = ______________ = ______________
2. Write the following in standard form (e.g., 4 × 102 = 400).
a. 3 × 102 = ______________
b. 16 × 104 = ______________
c. 800 ÷ 103 = ______________
d. 754.2 ÷ 102 = ______________
1a. What is 10x10x10 0r 10 raised to the power of 3
1b. What is 10x10x10x10 or 10 raised to the power of 4
2. What is the standard form of:
2a. 300
2b. 1600
2c. 80000
2d. 754000
500
In a paper airplane contest, Marcel’s plane travels 3.345 meters. Salvador’s plane travels 3.35 meters. Jennifer’s plane travels 3.3 meters. Based on the measurements, whose plane traveled the farthest distance? Whose plane traveled the shortest distance? Explain your reasoning using a place value chart.
Salvador's plane travels the furthest because 5 hundredths is more than 4 hundredths and there is no hundredths place in 3.3
Jennifer's plane travelled the shortest distance since there is no hundredths in 3.3 the other two numbers have 5 and 4 in hundredths place
500
Anna buys groceries for her family. Hamburger meat is $3.38 per pound, sweet potatoes are $0.79 each, and hamburger rolls are $2.30 a bag. If Anna buys 3 pounds of meat, 5 sweet potatoes, and 1 bag of hamburger rolls, what will she pay in all for the groceries?
$3.38X3= $10.14 Cost of meat
$0.79 x 5=$ 3.95 cost of sweet potatoes
$2.30X 1=$2.30 cost of hamburger rolls
$10.14 + $3.95 + $2.30 = $16.39 cost of all the groceries
500
Subtract
8.246 – 5 hundredths
What is 8.196?
500
Round the quantity to the given place value. Draw number lines to explain your thinking. Circle the rounded value on the number line.
a. 13.989 to the nearest tenth
b. 382.993 to nearest hundredth
What is
a. 14.0
b. 382.99