Understand Place Value Relationships - 4th Grade Math

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?
Answer: 10 times The digit 7 in the hundreds place has a value of 700, and the digit 7 in the tens place has a value of 70, and 700 divided by 70 is 10, so Choice B is correct. Choice A, 100 times, would be the ratio between the hundreds place and the ones place, not the tens place. Choice C, 770 times, is just the number formed by the two digits together, not a ratio of their place values. Choice D, 7 times, mistakenly compares the digits themselves instead of their place values.
Look at this pattern: $9 \times 1 = 9$ , $9 \times 10 = 90$ , $9 \times 100 = 900$ . Based on place value relationships, which statement explains why $900 \div 90$ equals $10$ ?
Answer: Because $9$ in the hundreds place represents $10$ times what $9$ represents in the tens place This directly applies the place value relationship: a digit in one place represents 10 times what it represents in the place to its right. Here, 9 in the hundreds place (900) represents 10 times what 9 represents in the tens place (90). Choice B incorrectly suggests 900 is 100 times larger than 90. Choice C shows the multiplication pattern but doesn't explain the place value relationship. Choice D incorrectly describes place values as being '10 more' rather than '10 times' what the place to the right represents.
Look at the number 3,333. The digit 3 in the hundreds place has a value how many times greater than the digit 3 in the ones place?
Answer: 100 The 3 in the hundreds place represents 300, and the 3 in the ones place represents 3. Dividing 300 by 3 gives 100, so the hundreds-place digit is 100 times the value of the ones-place digit. Choice A does not reflect a place-value multiplying relationship. Choice B matches a tens-to-ones comparison, not hundreds-to-ones. Choice D is too small for comparing hundreds to ones.
What is $6,000 \div 600$ ?
Answer: 10 6,000 ÷ 600 = 10, because 600 × 10 = 6,000. Choice B is one less than the correct quotient. Choice C would be the result of dividing by 60 instead of 600. Choice D confuses division with finding a fraction less than one.
In the number $58,347$ , Carlos multiplied the value of the $8$ by a certain number and got $80,000$ . Then he divided the value of the $3$ by that same number. What was his result?
Answer: $30$ The digit 8 is in the thousands place, so its value is 8,000. To get 80,000, Carlos multiplied by 10 (since 8,000 × 10 = 80,000). The digit 3 is in the hundreds place, so its value is 300. Dividing by the same number: 300 ÷ 10 = 30. Choice B gives just the digit 3, not its place value divided by 10. Choice C gives the original place value of 3 without dividing. Choice D would result from incorrectly thinking 3 ÷ 10 = 0.3 instead of using the place value 300.
Marcus says, " $300$ is 10 times $30$ ." Is Marcus correct?
Answer: Yes, because $300 \div 30 = 10$ . Dividing 300 by 30 gives 10, confirming that 300 is indeed 10 times as many as 30, so Marcus is correct. Choice B uses addition instead of division, which does not test the times-as-many relationship. Choice C reflects a division error, since 300 divided by 30 is 10, not 100. Choice D uses subtraction, which also does not test a multiplicative comparison.
In the number $4,440$ , how many times greater is the value of the digit 4 in the thousands place than the digit 4 in the hundreds place?
Answer: 10 times The digit 4 in the thousands place has a value of 4,000, and the digit 4 in the hundreds place has a value of 400, and 4,000 divided by 400 is 10, so Choice C is correct. Choice A, 100 times, would be the ratio between the thousands place and the tens place, not the hundreds place. Choice B, 1 time, would mean the two place values are equal, which they are not. Choice D, 4 times, mistakenly compares the digits themselves instead of their place values.
Which statement correctly describes the relationship between $400$ and $40$ ?
Answer: $400$ is 10 times $40$ . The correct answer is B because $400 = 10 \times 40$ , matching the place-value relationship between the two numbers. Choice A is incorrect since 400 and 40 are different values. Choice C overstates the relationship, confusing it with a jump across two place values instead of one. Choice D describes a difference rather than a multiplicative relationship, which is what the question asks about.
Based on place value, what is $800 \div 80$ ?
Answer: 10 The correct answer is 10, because 800 divided by 80 equals 10 when you think of it as 8 hundreds divided by 8 tens. Choice A, 720, comes from subtracting 80 from 800 instead of dividing. Choice B, 0.1, comes from flipping the division and finding 80 divided by 800 instead. Choice C, 100, comes from mistakenly dividing by 8 instead of 80.
In the number $6,660$ , the value of the digit 6 in the hundreds place is how many times the value of the digit 6 in the tens place?
Answer: 10 The digit 6 in the hundreds place has a value of 600, and the digit 6 in the tens place has a value of 60; dividing 600 by 60 shows the hundreds-place value is 10 times the tens-place value. Choice A overstates the relationship, as if the two places were 100 times apart instead of 10. Choice C confuses the place value with the digit itself, ignoring what each place is actually worth. Choice D comes from subtracting the two place values instead of dividing them. Choice B correctly compares the two place values using division.
Study this pattern: $50 \div 5 = 10$ , $500 \div 50 = 10$ , $5,000 \div 500 = 10$ . Based on place value understanding, what should come next in this pattern?
Answer: $50,000 \div 5,000 = 10$ because the pattern continues with each number being $10$ times larger When you see division patterns like this, focus on how the numbers change while the quotient stays the same. Let's examine what's happening in each step of the given pattern. In $50 \div 5 = 10$ , $500 \div 50 = 10$ , and $5,000 \div 500 = 10$ , notice that both the dividend (first number) and divisor (second number) are multiplied by 10 each time. When you multiply both numbers in a division problem by the same amount, the answer stays the same. This is why all three equal 10. Following this pattern, the next step should have $50,000 \div 5,000 = 10$ . Both numbers are again 10 times larger than the previous step, maintaining the same relationship. Answer D correctly identifies this pattern. Answer A jumps too far ahead by making both numbers 10 times larger than what the next logical step should be. Answer B breaks the pattern entirely by changing the divisor incorrectly, which gives a quotient of 100 instead of 10. Answer C disrupts the pattern by keeping the divisor as 5 instead of following the sequence where the divisor should be 5,000. The key insight is recognizing that when both the dividend and divisor increase by the same factor, the quotient remains constant. This demonstrates an important property of division and place value relationships. Remember: In number patterns involving division, look for how both numbers change together. If they change by the same factor, the answer will stay the same.
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?
Answer: 10 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.
In the number 4,440, how many times greater is the value of the digit 4 in the thousands place than the digit 4 in the hundreds place?
Answer: 10 The correct answer is 10, because the digit 4 in the thousands place represents 4,000, and the digit 4 in the hundreds place represents 400, and 4,000 is 10 times 400. Choice A, 1, mistakenly treats the two digits as having the same value. Choice C, 100, jumps two place values instead of the single place value between thousands and hundreds. Choice D, 4, just repeats the digit itself instead of comparing the place values.
In the number $9,990$ , the digit 9 in the tens place represents what value compared to the digit 9 in the ones place?
Answer: It represents 10 times the value. The 9 in the tens place represents 10 times the value of the 9 in the ones place, since 90 is ten times 9. Choice A describes an additive difference, not the correct multiplicative relationship. Choice C would describe the hundreds place compared to the ones place, not the tens place. Choice D is wrong because the two digits represent different place values.
What is $800 \div 80$ ?
Answer: 10 The correct answer is A, 10, because $800 \div 80 = 10$ . Choice B comes from subtracting instead of dividing. Choice C confuses the place-value pattern and adds an extra zero. Choice D flips the division, finding $80 \div 800$ instead.
Marcus compares $800$ and $80$ in a place value chart. How many times greater is $800$ than $80$ ?
Answer: 10 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, students compare 800 (8 hundreds) and 80 (8 tens), requiring them to recognize that 800 is 10 times 80. 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.
In the number 5,550, the digit 5 in the hundreds place represents what value compared to the digit 5 in the tens place?
Answer: It is 10 times as much. 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 5,550, the digit 5 appears in the hundreds place (value 500) and the tens place (value 50), requiring students to recognize that 500 is 10 times 50. Choice B is correct because calculating that 500 is 10 times 50, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice C 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.
Yuki compares $40$ and $4$ . How many times greater is $40$ than $4$ ?
Answer: 10 Dividing 40 by 4 gives 10, so 40 is 10 times greater than 4, making Choice C correct. Choice A, 0.1, is the reciprocal of the correct answer, as if the comparison were flipped. Choice B, 100, would come from squaring the correct ratio instead of dividing directly. Choice D, 36, comes from subtracting 4 from 40 instead of dividing.
In the number $2,460$ , the digit $4$ is in the hundreds place. If that digit moved one place to the right, into the tens place, what value would it represent there?
Answer: $40$ In $2,460$ , the digit $4$ is in the hundreds place, so it represents $400$ . Moving one place to the right puts it in the tens place, where it represents $40$ , one-tenth of its original value. Choice A gives the digit's face value rather than its place value. Choice B repeats the original hundreds-place value without shifting it. Choice D multiplies by 10 instead of dividing by 10.
A digital scoreboard shows $45,630$ points. Due to a malfunction, each digit shifts one place to the right, and a $0$ appears in the ten-thousands place. What number does the scoreboard show now?
Answer: $4,563$ Shifting every digit one place to the right divides the number by 10: $45,630 \div 10 = 4,563$ . Choice B shifts the digits to the left instead, multiplying by 10. Choice C misplaces the comma without actually shifting every digit correctly. Choice D only shifts part of the number, leaving some digits in their original places.

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