Section C: Practice Problems Compare, Order, and Round
In this section, we learned to compare, order, and round numbers up to 1,000,000.
We started by using what we know about place value to compare large whole numbers. For instance, we know that 45,892 is less than 407,892 because the 4 in 45,892 represents four ten-thousands and the 4 in 407,892 represents four hundred-thousands.
Next, we found multiples of 1,000, 10,000, and 100,000 that are closest to given numbers—at first with the help of number lines, and later without. For example, for 407,892, we know that:
408,000 is the nearest multiple of 1,000
410,000 is the nearest multiple of 10,000
400,000 is the nearest multiple of 100,000
Finally, we used what we know about finding nearest multiples to round large numbers to the nearest thousand, ten-thousand, and hundred-thousand.
Problem 1 (Lesson 12)
Jada writes the same digit in the two blanks to make the statement true. Which digits could she write?
Problem 2 (Lesson 13)
Order these numbers from least to greatest:
How did you pick the smallest number? Explain your reasoning.
Problem 3 (Lesson 14)
Which multiple of 10,000 is closest to 132,256?
Which multiple of 100,000 is closest to 132,256?
Which multiple of 100,000 is closest to the number labeled A?
Problem 4 (Lesson 15)
For the number 583,642:
What is the nearest multiple of 100,000?
What is the nearest multiple of 10,000?
What is the nearest multiple of 1,000?
What is the nearest multiple of 100?
What is the nearest multiple of 10?
Problem 5 (Lesson 16)
Describe the numbers that are 460,000 when rounded to the nearest 10,000.
Where are these numbers located on the number line?
Problem 6 (Lesson 17)
When rounded to the nearest 1,000, Airplane X is flying at 30,000 feet, Airplane Y at 31,000 feet, and Airplane Z at 32,000 feet.
Could Airplanes X and Y be within 1,000 feet of each other? If you think so, give some examples. If you don’t think so, explain why not.
Explain why Airplanes X and Z could not be within 1,000 feet of each other. Use a number line if you find it helpful.
Problem 7 (Exploration)
Rounded to the nearest 10 pounds, one bag of sand weighs 50 pounds.
Jada wants at least 1,000 pounds of sand for a sandbox. How many bags of sand does Jada need to buy to be sure that she has enough sand?
Problem 8 (Exploration)
You will need a set of digit cards 0–9 for this exploration.
Shuffle your cards and stack them face down. Turn over 6 digit cards.
Can you put the 6 digits in the blanks so that all three statements are true?
Problem 9 (Exploration)
To answer these riddles, think about rounding to the nearest 10, 100, 1,000, or 10,000. Use a number line if it is helpful.
I can be rounded to 100 or to 140. What number could I be?
I can be rounded to 7,500 or to 8,000. What number could I be?
I can be rounded to 60,000 or to 57,000. What number could I be?