Number and Place Value:
- Reading, writing, ordering, and comparing numbers to 10,000,000
- Rounding numbers to nearest 10, 100, 1,000, 10,000, and 100,000
- Understanding the place value of digits (thousands, hundreds, tens, ones)
- Adding and subtracting large numbers
- Multiplying and dividing by 10, 100, and 1,000
Reading, Writing, Ordering, and Comparing Numbers to 10,000,000
Q: Write the number three million, four hundred fifty-six thousand, seven hundred eighty-nine.
A: 3,456,789
Q: Read the number 8,201,005.
A: Eight million, two hundred one thousand, five.
Q: Order these numbers from least to greatest: 2,345, 1,987,654, 5,231.
A: 2,345, 5,231, 1,987,654
Q: Which number is greater, 7,890,123 or 7,890,023?
A: 7,890,123
Q: Compare 4,567,890 and 4,567,800. How are they different?
A: They differ only in the ones place; 4,567,890 is greater by 90.
Rounding Numbers to Nearest 10, 100, 1,000, 10,000, and 100,000
Q: Round 3,248 to the nearest 100.
A: 3,200
Q: Round 87,562 to the nearest 10,000.
A: 90,000
Q: Estimate the sum of 4,123 and 2,879 by rounding each number to the nearest 1,000.
A: 4,000 + 3,000 = 7,000 (estimate)
Q: A recipe calls for 543 grams of flour. You only have a 500-gram bag. Is 500 grams rounded to the nearest 100 enough?
A: Yes, 500 grams rounded to the nearest 100 is still 500, which is sufficient for the recipe.
Q: The population of a town is estimated to be around 125,890. Rounding to the nearest 100,000 gives what population estimate?
A: 120,000
Understanding the Place Value of Digits
Q: In the number 6,342, what digit is in the thousands place?
A: 6
Q: The value of the 5 in 5,821 is how many times greater than the value of the 5 in 2,507?
A: 100 times (5 in 5,821 = 5,000; 5 in 2,507 = 50)
Q: What number is ten times bigger than 3,456?
A: 34,560 (Move the decimal one place to the right)
Q: If the digit 7 in the number 7,205 is replaced with a 0, what is the difference in value?
A: 7,000 (The value of 7 in the thousands place)
Q: Write the number 42, using only the digits 2 and 0. How many times is the value of the first 2 different from the second 2?
A: 10 times (20 - 2 = 18)
Adding and Subtracting Large Numbers
Q: Solve: 3,456,789 + 2,109,876
A: 5,566,665
Q: Find the difference between 8,765,432 and 1,234,567.
A: 7,530,865
Q: A company has 4,231,567 units in stock. They sold 1,876,345 units. How many units are left in stock?
A: Left in stock = Starting stock - Units sold
Left in stock = 4,231,567 - 1,876,345 = 2,355,222
Q: Estimate the sum of 5,423,178 and 2,890,654 by rounding each number to the nearest million.
A: 5,000,000 + 3,000,000 = 8,000,000 (estimate)
Q: Sarah needs 7,231,456 points to win a game. She has already collected 3,872,901 points. How many more points does she need?
A: Points needed = Total points - Points collected
Points needed = 7,231,456 - 3,872,901 = 3,358,555
Multiplying and Dividing by 10, 100, and 1,000
Q: Multiply 4,235 by 100.
A: 423,500 (Move the decimal two places to the right)
Q: Divide 8,765 by 10.
A: 876.5 (Move the decimal one place to the left)
Q: A recipe requires 3 cups of flour. How many cups are needed if the recipe is doubled?
A: Doubled recipe = 3 cups/serving * 2 servings = 6 cups
Q: The distance between two cities is 5,230 kilometers. Express the distance in meters. (1 kilometer = 1,000 meters)
A: Distance in meters = Distance in kilometers * Conversion rate
Distance in meters = 5,230 km * 1,000 m/km = 5,230,000 meters
Q: A factory produces 2,100 water bottles per hour. How many bottles can they produce in 8 hours?
A: Total bottles = Production rate/hour * Number of hours
Total bottles = 2,100 bottles/hour * 8 hours = 16,800 bottles
Understanding Place Value (continued):
Q: What is the value of the digit 8 in the number 8,421,356?
A: 8,000,000 (The digit 8 is in the millions place)
Q: Arrange the following numbers in descending order based on the value of the digit 3: 2,345, 7,132, 53,809
A: 53,809, 7,132, 2,345 (The value of 3 decreases from left to right)
Q: Decompose the number 6,247,381 into its place values.
A: 6,247,381 = 6,000,000 (Millions) + 200,000 (Hundred Thousands) + 40,000 (Ten Thousands) + 7,000 (Thousands) + 300 (Hundreds) + 80 (Tens) + 1 (Ones)
Q: If the digit 9 in 4,729,105 is erased, what is the new number?
A: New number = Original number - Erased digit value
New number = 4,729,105 - 9 = 4,729,104
Q: Compare 3,456,789 and 3,456,879. What is the difference in the value due to the difference in the digits? A: The difference is 90. The digit 8 in the ten thousandths place (3,456,879) has a value 90 greater than the digit 7 in the same place (3,456,789).
Adding and Subtracting Large Numbers (continued):
Q: A library has 1,234,567 books. They borrowed 231,879 books from another library for a special event. How many books are there in total for the event?
A: Total books = Library books + Borrowed books
Total books = 1,234,567 + 231,879 = 1,466,446
Q: John has saved $4,231. He needs $7,890 for a new gadget. How much more money does he need to save?
A: Money needed = Gadget price - Saved money
Money needed = $7,890 - $4,231 = $3,659
Q: Estimate the difference between 9,234,567 and 4,876,123 by rounding each number to the nearest million.
A: 9,000,000 - 5,000,000 = 4,000,000 (estimate)
Multiplying and Dividing by 10, 100, and 1,000 (continued):
Q: A baker needs 5 cups of flour for a cake recipe. If he wants to make 4 cakes, how much flour does he need in total?
A: Total flour = Flour per cake * Number of cakes
Total flour = 5 cups/cake * 4 cakes = 20 cups
Q: There are 8,765 meters of fabric. How many kilometers of fabric is that? (1 kilometer = 1,000 meters)
A: Fabric in kilometers = Fabric in meters / Conversion rate
Fabric in kilometers = 8,765 meters / 1,000 m/km = 8.765 kilometers
Q: A box of cookies costs $2.35. How much would 5 boxes cost?
A: Total cost = Price per box * Number of boxes
Total cost = $2.35/box * 5 boxes = $11.75
Word Problems:
Q: A rectangular garden is 7,234 meters long and 2,100 meters wide. What is the perimeter of the garden? (Perimeter = total length of all sides added together)
A: Perimeter = 2 (length + width)
Perimeter = 2 (7,234 m + 2,100 m) = 18,568 meters
Q: A bus can travel 876 kilometers on a full tank of gas. If the bus travels for 4 hours, and it averages 219 kilometers per hour, how much gas is left in the tank? (Note: This question has extraneous information about the bus's speed that isn't necessary to solve for the remaining gas)
A: Unfortunately, with the given information, we cannot determine the remaining gas in the tank. We only know the travel distance on a full tank (876 km), but not the gas tank capacity or how much gas was used during the 4-hour trip.
Q: A farmer harvests 3,456 apples on Monday and 2,109 on Tuesday. What is the total number of apples harvested in the two days?
A: Total apples = Apples on Monday + Apples on Tuesday
Total apples = 3,456 + 2,109 = 5,565
Q: A movie ticket costs $12.50 for adults and $7.80 for children. How much more expensive is an adult ticket compared to a child's ticket?
A: Price difference = Adult price - Child price
Price difference = $12.50 - $7.80 = $4.70
Q: A rectangular pizza measures 30 centimeters long and 20 centimeters wide. What is the area of the pizza? (Area = length x width)
A: Area = 30 cm x 20 cm = 600 square centimeters
Q: A recipe requires 1/2 cup of milk for every 1 cup of flour. If Sarah uses 3 cups of flour, how much milk does she need?
A: Milk needed = Flour used x Milk per cup of flour
Milk needed = 3 cups * 1/2 cup/cup = 1.5 cups
Q: A train travels 567 kilometers on the first day and 423 kilometers on the second day. What is the total distance traveled in the two days?
A: Total distance = Distance on day 1 + Distance on day 2
Total distance = 567 km + 423 km = 990 kilometers
Q: There are 23 apples in a basket. If Mary takes away 7 apples, how many are left?
A: Apples left = Apples in basket - Apples taken away
Apples left = 23 apples - 7 apples = 16 apples
Q: A rectangular box has a length of 10 centimeters, a width of 5 centimeters, and a height of 8 centimeters. What is the volume of the box? (Volume = length x width x height)
A: Volume = 10 cm x 5 cm x 8 cm = 400 cubic centimeters
Q: Lisa has collected 234 stickers. Sarah has 17 more stickers than Lisa. How many stickers does Sarah have?
A: Sarah's stickers = Lisa's stickers + Difference
Sarah's stickers = 234 stickers + 17 stickers = 251 stickers
Q: A shelf can hold a maximum weight of 10,000 kilograms. Boxes weighing 2,135 kilograms are placed on the shelf. How much weight can still be added without exceeding the limit?
A: Remaining capacity = Maximum weight - Weight of boxes on shelf
Remaining capacity = 10,000 kg - 2,135 kg = 7,865 kg
Q: A square piece of paper measures 15 centimeters on each side. What is the perimeter of the square? (In a square, all sides are equal)
A: Perimeter of square = Side length x 4 (since all sides contribute to the total distance around the shape)
Perimeter = 15 cm x 4 = 60 centimeters
Q: A bag of rice weighs 5 kilograms. How many grams does it weigh? (1 kilogram = 1000 grams)
A: Weight in grams = Weight in kilograms x Conversion rate
Weight in grams = 5 kg * 1000 g/kg = 5,000 grams
Q: There are 7 days in a week. How many days are there in 4 weeks?
A: Total days = Days per week x Number of weeks
Total days = 7 days/week * 4 weeks = 28 days
