Praxis Math Quiz: Interpret Place Value
20 questions · exam conditions
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Interpret Place ValueQuestion 1 of 20

A cashier mistakenly enters $4.50 for an item that costs $45.00. The value the cashier entered is what fraction of the correct value?

12\frac{1}{2}
15\frac{1}{5}
110\frac{1}{10}
1100\frac{1}{100}
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Praxis Math Quiz

Praxis Math Quiz: Interpret Place Value

Practice Interpret Place Value in Praxis Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Interpret Place Value, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A cashier mistakenly enters $4.50 for an item that costs $45.00. The value the cashier entered is what fraction of the correct value?

  1. 12\frac{1}{2}
  2. 15\frac{1}{5}
  3. 110\frac{1}{10} (correct answer)
  4. 1100\frac{1}{100}
Explanation: To find the fraction, divide the entered value by the correct value: 4.5045.00\frac{4.50}{45.00}. This simplifies to 4.545\frac{4.5}{45}. Since 4.5×10=454.5 \times 10 = 45, the fraction is equivalent to 110\frac{1}{10}. The error was a shift of one place value, which corresponds to a factor of 10.

Question 2

Let K be the largest 4-digit number that can be formed using the digits 3, 1, 9, 6, each used once. Let L be the smallest 4-digit number that can be formed using the same digits. What is the value of K - L?

  1. 7,962
  2. 8,262 (correct answer)
  3. 8,338
  4. 8,532
Explanation: To form the largest number K, arrange the digits in descending order: 9,631. To form the smallest number L, arrange the digits in ascending order: 1,369. The difference is K−L=9631−1369=8262K - L = 9631 - 1369 = 8262.

Question 3

The value of the digit 7 in the number 471.3 is 70. If this number is divided by 1,000, what is the value of the digit 7 in the new, resulting number?

  1. 0.7
  2. 0.07 (correct answer)
  3. 0.007
  4. 70
Explanation: First, perform the division: 471.3÷1,000=0.4713471.3 \div 1,000 = 0.4713. In the new number, 0.4713, the digit 7 is in the hundredths place. Therefore, its value is 7×11007 \times \frac{1}{100}, which is 0.07.

Question 4

The number 0.47 is multiplied by 200. In the original number, the value of the digit 4 is 0.4. What is the value of the digit 4 in the product?

  1. 0.4
  2. 4 (correct answer)
  3. 40
  4. 80
Explanation: First, find the product: 0.47×200=940.47 \times 200 = 94. In the resulting number, 94, the digit 4 is in the ones place. Therefore, its value is 4.

Question 5

How many tens are in the number 4,582?

  1. 8
  2. 58
  3. 458 (correct answer)
  4. 4580
Explanation: This question asks for the total number of groups of 10 that can be made from 4,582. This is equivalent to dividing 4,582 by 10. 4582÷10=458.24582 \div 10 = 458.2. This means there are 458 full groups of ten in the number 4,582.

Question 6

The decimal 0.375 represents the fraction 3751000\frac{375}{1000}. Which of the following is this fraction expressed in simplest form?

  1. 38\frac{3}{8} (correct answer)
  2. 1540\frac{15}{40}
  3. 75200\frac{75}{200}
  4. 37100\frac{37}{100}
Explanation: To simplify the fraction 3751000\frac{375}{1000}, find the greatest common divisor (GCD) of 375 and 1000. Both numbers are divisible by 125. 375÷125=3375 \div 125 = 3 and 1000÷125=81000 \div 125 = 8. Therefore, the fraction in simplest form is 38\frac{3}{8}.

Question 7

A number with two decimal places is rounded to the nearest tenth, giving 6.5. In the original number, the digit in the hundredths place is an odd number that is also a factor of the digit in the tenths place. What was the original number?

  1. 6.45
  2. 6.49
  3. 6.51 (correct answer)
  4. 6.53
Explanation: If a number rounds to 6.5, it must be in the range [6.45, 6.55). Let the number be 6.AB. If A=4, the number is 6.4B. It rounds to 6.5 only if B ≥ 5. The odd digits for B are 5, 7, 9. None of these are factors of A=4. So, the tenths digit cannot be 4. If A=5, the number is 6.5B. It rounds to 6.5 only if B < 5. The odd digits for B are 1, 3. We check if these are factors of A=5. 1 is a factor of 5. 3 is not a factor of 5. Therefore, the hundredths digit B must be 1. The original number is 6.51.

Question 8

In the number 74,712, the value of the digit 7 in the ten thousands place is how many times the value of the digit 7 in the hundreds place?

  1. 10
  2. 100 (correct answer)
  3. 1,000
  4. The values are the same.
Explanation: The digit 7 in the ten thousands place has a value of 70,000. The digit 7 in the hundreds place has a value of 700. To find how many times greater the first value is than the second, divide them: 70,000÷700=10070,000 \div 700 = 100. Therefore, the value is 100 times greater.

Question 9

If the number 543.21 is multiplied by 100, the value of the digit 4 increases by what amount?

  1. 3,960 (correct answer)
  2. 4,000
  3. 396
  4. 40
Explanation: In the original number, 543.21, the digit 4 is in the tens place, so its value is 40. When the number is multiplied by 100, the result is 54,321. In this new number, the digit 4 is in the thousands place, so its new value is 4,000. The increase in value is the difference between the new value and the original value: 4,000−40=3,9604,000 - 40 = 3,960.

Question 10

A number has the form ABC.DE, where A, B, C, D, and E are non-zero digits. The value of the digit A is 1,000 times the value of the digit D. Which of the following statements must be true?

  1. The digit A is equal to the digit D. (correct answer)
  2. The digit A is equal to the digit E.
  3. The digit B is equal to the digit D.
  4. The digit A is 10 times the digit D.
Explanation: The digit A is in the hundreds place, so its value is A×100A \times 100. The digit D is in the tenths place, so its value is D×110D \times \frac{1}{10}. The problem states that A×100=1000×(D×110)A \times 100 = 1000 \times (D \times \frac{1}{10}). Simplifying the right side gives A×100=100×DA \times 100 = 100 \times D. Dividing both sides by 100 yields A=DA = D.

Question 11

Let N be the number 843.15. A new number, M, is created by swapping the digit in the tens place of N with the digit in the tenths place of N. What is the positive difference between N and M?

  1. 9.99
  2. 27.00
  3. 29.70 (correct answer)
  4. 39.60
Explanation: In the number N=843.15, the tens digit is 4 and the tenths digit is 1. Swapping them creates the number M=813.45. The difference is N−M=843.15−813.45=29.70N - M = 843.15 - 813.45 = 29.70.

Question 12

In which of the following numbers does the digit 8 represent a value that is 1100\frac{1}{100} of the value represented by the digit 8 in the number 18,234?

  1. 2,815
  2. 3,482 (correct answer)
  3. 81,432
  4. 5.08
Explanation: In the number 18,234, the digit 8 is in the thousands place, so its value is 8,000. We need to find a number where the value of the digit 8 is 1100×8,000=80\frac{1}{100} \times 8,000 = 80. A digit 8 has a value of 80 when it is in the tens place. In the number 3,482, the digit 8 is in the tens place.

Question 13

In the subtraction problem 5,M32−2,4N1=3,1715,M32 - 2,4N1 = 3,171, M and N represent single digits. What is the value of the expression 10M+N10M + N?

  1. 56
  2. 65
  3. 66 (correct answer)
  4. 12
Explanation: You can solve this by working backwards with addition: 3,171+2,4N1=5,M323,171 + 2,4N1 = 5,M32. In the tens place, 7+N7+N must result in a number ending in 3, so 7+N=137+N=13 and N=6N=6. Carry the 1 to the hundreds place. In the hundreds place, 1+1+4=M1+1+4 = M, so M=6M=6. The expression 10M+N10M + N becomes 10(6)+6=60+6=6610(6) + 6 = 60 + 6 = 66.

Question 14

How many hundredths are equivalent to the number 2.7?

  1. 2.7
  2. 27
  3. 270 (correct answer)
  4. 2700
Explanation: The number 2.7 can be written as the fraction 2710\frac{27}{10}. To find the equivalent number of hundredths, we need to find an equivalent fraction with a denominator of 100. 2710=27×1010×10=270100\frac{27}{10} = \frac{27 \times 10}{10 \times 10} = \frac{270}{100}. This means 2.7 is equivalent to 270 hundredths.

Question 15

A computer performs a calculation in 0.00000035 seconds. What is the place value of the digit 3 in this number?

  1. Millionths
  2. Ten-millionths (correct answer)
  3. Hundred-thousandths
  4. Billionths
Explanation: To identify the place value, count the places to the right of the decimal point. The first place is tenths, then hundredths, thousandths, ten-thousandths, hundred-thousandths, millionths, and the seventh place is ten-millionths. The digit 3 is in the seventh decimal place, which is the ten-millionths place.

Question 16

The numbers X=0.505X=0.505, Y=0.55Y=0.55, and Z=0.5Z=0.5 are to be placed in order from least to greatest. Which of the following is the correct order?

  1. Z, X, Y (correct answer)
  2. X, Z, Y
  3. Z, Y, X
  4. Y, X, Z
Explanation: To compare decimals, it is helpful to write them with the same number of decimal places. X=0.505X = 0.505, Y=0.550Y = 0.550, and Z=0.500Z = 0.500. Now, comparing the numbers as if they were whole numbers (505, 550, 500), the order from least to greatest is 500, 505, 550. This corresponds to the order Z, X, Y.

Question 17

A number is expressed in expanded form as 7×103+4×101+6×10−2+1×10−37 \times 10^3 + 4 \times 10^1 + 6 \times 10^{-2} + 1 \times 10^{-3}. What is this number written in standard decimal form?

  1. 7,400.61
  2. 7,040.61
  3. 7,040.061 (correct answer)
  4. 740.061
Explanation: Evaluate each term based on its power of 10: 7×103=70007 \times 10^3 = 7000; 4×101=404 \times 10^1 = 40; 6×10−2=0.066 \times 10^{-2} = 0.06; 1×10−3=0.0011 \times 10^{-3} = 0.001. Summing these values gives 7000+40+0+0.06+0.001=7040.0617000 + 40 + 0 + 0.06 + 0.001 = 7040.061.

Question 18

A certain decimal number has a tenths digit that is twice its hundredths digit. Its hundredths digit is 3. Its ones digit is the sum of its tenths and hundredths digits. What is the number?

  1. 3.69
  2. 9.36
  3. 6.93
  4. 9.63 (correct answer)
Explanation: Let's determine each digit. The hundredths digit is 3. The tenths digit is twice the hundredths digit, so it is 2×3=62 \times 3 = 6. The ones digit is the sum of the tenths and hundredths digits, so it is 6+3=96 + 3 = 9. Assembling the number with the digits in their correct places gives 9.63.

Question 19

For the number 2,781.9, what is the sum of the value of the digit in the hundreds place and the value of the digit in the tenths place?

  1. 16
  2. 70.9
  3. 700.9 (correct answer)
  4. 709
Explanation: The question asks for the sum of the values of the digits, not the sum of the digits themselves. The digit in the hundreds place is 7, and its value is 700. The digit in the tenths place is 9, and its value is 0.9. The sum of these values is 700+0.9=700.9700 + 0.9 = 700.9.

Question 20

In the number 6,194,382.57, one digit has a value of 90,000 and another digit has a value of 0.07. What is the sum of these two digits?

  1. 2
  2. 16 (correct answer)
  3. 79
  4. 97
Explanation: First, identify the digits from their values. The digit with a value of 90,000 is 9 (in the ten thousands place). The digit with a value of 0.07 is 7 (in the hundredths place). The question asks for the sum of these two digits, which is 9+7=169 + 7 = 16.