In the number 4,708.35, what is the value of the digit 7?
Show answer and reasoning
Correct answer: A. 700
Correct. The 7 sits in the hundreds place (4 thousands, 7 hundreds, 0 tens, 8 ones), so its value is 7 x 100 = 700.
- B: 7,000 would require the 7 to be in the thousands place; the thousands digit is 4.
- C: 7 is the digit itself, not its place value. Place value multiplies the digit by the power of ten for its position.
- D: 70 would be the value if the 7 were in the tens place; the tens digit here is 0.
Source: Praxis 5003: Numbers and Operations, I.A place value and number systems
What is 10 times 0.46?
A. 4.06
B. 0.046
C. 4.6
D. 46
Show answer and reasoning
Correct answer: C. 4.6
Correct. Multiplying by 10 shifts every digit one place to the left, so 0.46 becomes 4.6.
- A: 4.06 inserts a zero between the digits; a place value shift never changes the order or spacing of the digits.
- B: 0.046 is the result of dividing by 10 (shifting one place to the right), not multiplying.
- D: 46 is 100 times 0.46, a shift of two places rather than one.
Source: Praxis 5003: Numbers and Operations, I.A place value and number systems
Which number equals 3 x 1,000 + 5 x 10 + 8 x 0.01?
A. 3,508
B. 3,058
C. 3,050.8
D. 3,050.08
Show answer and reasoning
Correct answer: D. 3,050.08
Correct. 3 x 1,000 = 3,000; 5 x 10 = 50; 8 x 0.01 = 0.08. The sum is 3,050.08.
- A: 3,508 treats the 8 as 8 ones and drops the empty hundreds place; 8 x 0.01 is 0.08, not 8.
- B: 3,058 puts the 8 in the ones place instead of the hundredths place.
- C: 3,050.8 places the 8 in the tenths place, but 8 x 0.01 is eight hundredths.
Source: Praxis 5003: Numbers and Operations, I.A place value and number systems
Round 63,449 to the nearest thousand.
A. 63,400
B. 60,000
C. 64,000
D. 63,000
Show answer and reasoning
Correct answer: D. 63,000
Correct. The hundreds digit is 4, which is less than 5, so the thousands digit stays 3 and everything after it becomes zero: 63,000.
- A: 63,400 is the number rounded to the nearest hundred, not the nearest thousand.
- B: 60,000 is the number rounded to the nearest ten thousand.
- C: 64,000 would require the hundreds digit to be 5 or more. A common error is rounding 449 up to 500 first and then rounding again.
Source: Praxis 5003: Numbers and Operations, I.E computation strategies and estimation
Which list orders 0.305, 0.35, 0.3, and 0.053 from least to greatest?
A. 0.053, 0.3, 0.305, 0.35
B. 0.35, 0.305, 0.3, 0.053
C. 0.053, 0.305, 0.3, 0.35
D. 0.3, 0.053, 0.305, 0.35
Show answer and reasoning
Correct answer: A. 0.053, 0.3, 0.305, 0.35
Correct. Compare place by place: 0.053 has 0 tenths, so it is smallest. Then 0.300, 0.305, and 0.350.
- B: This is the correct order reversed, greatest to least.
- C: This treats 0.305 as smaller than 0.3, but 0.305 = 0.3 + 0.005, so it is larger.
- D: This puts 0.3 before 0.053, but 0.3 = 0.300 is larger than 0.053, which has 0 tenths.
Source: Praxis 5003: Numbers and Operations, I.A place value and number systems
