Understand Place Value Relationships
Help Questions
4th Grade Math › Understand Place Value Relationships
Keisha says the value 500 is 10 times the value 50 because the 5 moved one place left. Is Keisha correct?
No, because $500 \div 50 = 100$.
No, because $500 - 50 = 10$.
Yes, because $500 \div 50 = 10$.
Yes, because the digit is 5 in both numbers.
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, the values 500 (5 hundreds) and 50 (5 tens) require students to recognize that 500 is 10 times 50, as the digit 5 moves one place to the left. Choice A is correct because dividing the larger value by the smaller value: 500 ÷ 50 = 10, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice B represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Based on the division equation, $7,000 \div 700 = \ ?$ What does this show about the digit 7 in adjacent places?
0.1
7
10
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, the division 7,000 ÷ 700 requires students to calculate the quotient and recognize it shows the multiplicative relationship between the thousands and hundreds places for the digit 7. Choice C is correct because dividing the larger value by the smaller value: 7,000 ÷ 700 = 10, recognizing that each place is 10 times the place to its right. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations or think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 7,770, the digit 7 in the hundreds place represents how many times what the digit 7 in the tens place represents?
7
10
100
770
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 7,770, the digit 7 appears in the hundreds place (value 700) and the tens place (value 70), requiring students to calculate 700 ÷ 70 to identify the multiplicative relationship. Choice B is correct because dividing the larger value by the smaller value: 700 ÷ 70 = 10, recognizing that each place is 10 times the place to its right. Choice C represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations or think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 4,440, the digit 4 in the thousands place represents how many times what it represents in the hundreds place?
4
10
40
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 4,440, the digit 4 appears in the thousands place (value 4,000) and the hundreds place (value 400), requiring students to calculate 4,000 ÷ 400 to identify the multiplicative relationship. Choice C is correct because dividing the larger value by the smaller value: 4,000 ÷ 400 = 10, recognizing that each place is 10 times the place to its right. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 2,222, the digit 2 in the tens place represents what value compared to the digit 2 in the ones place?
It is 2 times as much.
It is the same value.
It is 100 times as much.
It is 10 times as much.
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 2,222, the digit 2 appears in the tens place (value 20) and the ones place (value 2), requiring students to recognize that 20 is 10 times 2. Choice A is correct because calculating that 20 is 10 times 2 demonstrates understanding that adjacent place values have a 10-to-1 relationship. Choice B represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Based on place value, what is $800 \div 80$?
0.1
10
100
720
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, the values 800 (8 hundreds) and 80 (8 tens) require students to calculate 800 ÷ 80 to identify the multiplicative relationship between hundreds and tens places. Choice A is correct because dividing the larger value by the smaller value: 800 ÷ 80 = 10, recognizing that each place is 10 times the place to its right. Choice B represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations or think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 8,880, the digit 8 in the hundreds place represents how many times what the digit 8 in the tens place represents?
8
10
100
800
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 8,880, the digit 8 appears in the hundreds place (value 800) and the tens place (value 80), requiring students to calculate 800 ÷ 80 to identify the multiplicative relationship. Choice A is correct because dividing the larger value by the smaller value: 800 ÷ 80 = 10, recognizing that each place is 10 times the place to its right. Choice C represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Compare the values in 3,330. How many times greater is the value of the digit 3 in the hundreds place than the digit 3 in the tens place?
3
10
30
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens ($\times$10), tens become hundreds ($\times$10), hundreds become thousands ($\times$10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place ($700$) is 10 times the 7 in the tens place ($70$). In the number 3,330, the digit 3 appears in the hundreds place (value $300$) and the tens place (value $30$), requiring students to calculate $300 \div 30$ to identify the multiplicative relationship. Choice B is correct because dividing the larger value by the smaller value: $300 \div 30 = 10$, recognizing that each place is 10 times the place to its right. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: $700 \div 70 = 10$, $5,000 \div 500 = 10$, $30 \div 3 = 10$ (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Look at the number 3,333. The digit 3 in the tens place represents how many times what it represents in the ones place?
2
10
30
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 3,333, the digit 3 appears in the tens place (value 30) and the ones place (value 3), requiring students to recognize that 30 is 10 times 3. Choice C is correct because dividing the larger value by the smaller value: 30 ÷ 3 = 10, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 6,600, the digit 6 in the thousands place represents how many times what the digit 6 in the hundreds place represents?
6
10
60
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 6,600, the digit 6 appears in the thousands place (value 6,000) and the hundreds place (value 600), requiring students to recognize that 6,000 is 10 times 600. Choice B is correct because dividing the larger value by the smaller value: 6,000 ÷ 600 = 10, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.