Place value
In the number 5,307, what value does the digit 3 represent?
300
What is 7 × 10?
70
What is 480 ÷ 10? Explain what happens to the digits.
48. Dividing by 10 shifts every digit one place to the right (tens become ones, hundreds become tens).
Convert 500 centimeters to meters.
500 cm = 5 m
35 x10^2
3500
In 8,402, how many times larger is the 8 in the thousands place than the 8 would be in the hundreds place?
10 times larger
Multiply 45 × 100. Show how place value changes.
4,500 (45 × 100 = 45 with two zeros added → 4,500)
Divide 4,500 ÷ 100. Show the place-value move and result.
45. Dividing by 100 shifts digits two places to the right (hundreds→ones).
Convert 2,000 meters to kilometers.
2,000 m = 2 km
452x10^3
452,000
Write a number where the digit 6 in the hundreds place represents 10 times the value it would represent in the tens place and 1/10 of the value it would represent in the thousands place. Give one possible number and explain the place values.
6,600 (6 in the hundreds place = 600; in tens it would be 60 — 600 is 10 times 60; in thousands it would be 6,000 — 600 is 1/10 of 6,000)
Compute 3,208 × 10 and explain which digit(s) move and how the place values change.
32,080. Each digit shifts one place to the left; the ones become tens, tens become hundreds, etc.
Divide 4,500 ÷ 100. Show the place-value move and result
45. Dividing by 100 shifts digits two places to the right (4,500 → 45).
Convert 450 millimeters to centimeters and to meters, using only whole-number results where possible.
5,289x10^4
52,890,000
In the number 42,058, explain how the digit 2 in the ten-thousands and the digit 2 in the thousands relate in value. Which is 10 times the other? Show the values.
The 2 in ten-thousands is 20,000; the 2 in thousands is 2,000. The ten-thousands 2 is 10 times the thousands 2.
Multiply 1,256 × 1000 using place-value reasoning. Show the result and explain why.
1,256,000. Multiplying by 1,000 shifts every digit three places to the left (add three zeros).
Divide 1,256,000 ÷ 1,000. Show the result and explain the rule used.
1,256. Dividing by 1,000 shifts every digit three places to the right (remove three zeros).
A ribbon is 275 centimeters long. How many meters is that using whole-number meters and leftover centimeters?
275 cm = 2 m and 75 cm (since 1 m = 100 cm)
950,000 divided by 10^2
9,500
A digit in a five-digit number is in the hundreds place and has value 700. Where could the same digit be placed so that its value becomes 7,000? Explain using the "10 times" rule.
Place the digit in the thousands place. A digit in the thousands place is 10 times the value in the hundreds place (7,000 is 10 × 700).
A factory produces 2,437 bolts per day. How many bolts are produced in 10 days, 100 days, and 1,000 days? Show each product and explain the pattern you observe.
A warehouse has 2,437,000 nails. If the nails are packed into boxes of 1,000 nails each, how many boxes are there? Then find how many boxes if each box held 10 nails (show both steps: divide by 1,000 and by 10). Explain the relationship between the two quotients.
A baker needs 2,500 milliliters of milk. Milk is sold in 1-L (1,000 mL) containers. How many full 1-L containers are needed and how many milliliters will be left over? Give whole-number answers.
2,500 mL = 2 full 1-L containers (2,000 mL) with 500 mL left over. If only full containers may be purchased, buy 3 containers.
892,000,000 divided by 10^6