Powers of 10: Multiplying and Dividing
Move digits by place value to multiply and divide
Powers of 10: Multiplying and Dividing
Move digits by place value to multiply and divide
Math - Grade 4-5
- 1
Find the product: 47 × 10. Explain what happens to the value of each digit.
Multiplying by 10 moves each digit one place to the left.
47 × 10 = 470. Each digit moves one place to the left, so the number becomes 10 times as large. - 2
Find the quotient: 6,300 ÷ 100. Explain your answer.
6,300 ÷ 100 = 63. Dividing by 100 moves each digit two places to the right, so the number becomes one hundredth as large. - 3
Complete the pattern: 8, 80, 800, 8,000, _____.
Look at how many times the value is multiplied by 10 each step.
The next number is 80,000. Each number is multiplied by 10 to get the next number in the pattern. - 4
Use place value to solve: 3.6 × 100.
3.6 × 100 = 360. The digits move two places to the left because 100 has two zeros. - 5
Use place value to solve: 540 ÷ 10.
Dividing by 10 makes a number 10 times smaller.
540 ÷ 10 = 54. The digits move one place to the right because the number is divided by 10. - 6
A school orders 25 boxes of pencils. Each box has 100 pencils. How many pencils does the school order in all?
The school orders 2,500 pencils in all because 25 × 100 = 2,500. - 7
A baker has 4,800 cookies and packs them equally into boxes of 100 cookies. How many full boxes can the baker pack?
Think about how many groups of 100 are in 4,800.
The baker can pack 48 full boxes because 4,800 ÷ 100 = 48. - 8
Fill in the missing number: 72 × _____ = 72,000.
The missing number is 1,000 because 72 × 1,000 = 72,000. - 9
Fill in the missing number: 9,500 ÷ _____ = 95.
Compare 9,500 and 95 to see how many place values the digits moved.
The missing number is 100 because 9,500 ÷ 100 = 95. - 10
Complete the table for multiplying by powers of 10: 14 × 10 = _____, 14 × 100 = _____, and 14 × 1,000 = _____.
14 × 10 = 140, 14 × 100 = 1,400, and 14 × 1,000 = 14,000. Each larger power of 10 moves the digits one more place to the left. - 11
Find the quotient: 7.2 ÷ 10.
The value becomes smaller, so the decimal point will be placed to show a smaller number.
7.2 ÷ 10 = 0.72. Dividing by 10 moves the digits one place to the right in the place value chart. - 12
Which expression has the greatest value: 56 × 10, 56 × 100, or 56 × 1,000? Explain.
56 × 1,000 has the greatest value because multiplying by 1,000 makes 56 larger than multiplying by 10 or 100. - 13
A runner tracks distances in meters. One kilometer is 1,000 meters. How many meters are in 6 kilometers?
Multiply the number of kilometers by 1,000.
There are 6,000 meters in 6 kilometers because 6 × 1,000 = 6,000. - 14
A bottle holds 2,000 milliliters of water. If each cup holds 100 milliliters, how many cups can be filled?
20 cups can be filled because 2,000 ÷ 100 = 20. - 15
Explain the error: A student says 4.5 × 100 = 45. What is the correct answer?
The number 100 has two zeros, so think about two place value moves.
The correct answer is 450. The student only moved the digits one place, but multiplying by 100 moves the digits two places to the left.