If the decimal number 57.3507 is written in place-value form as 5 × A + 7 ÷ B…
2024
If the decimal number 57.3507 is written in place-value form as 5 × A + 7 ÷ B + 3 × C + 5 ÷ D + 7 × E, then the value of 5 × A + 3 × B + 6 × C + D + 3 × E is:
Answer: C. 153.6003 — CONCEPTIn decimal place value, each position is ten times the position immediately to its right. A digit therefore contributes digit × place value; division…
- A.
53.603
- B.
213.003
- C.
153.6003
- D.
55.6003
Attempted by 7 students.
Show answer & explanation
Correct answer: C
CONCEPT
In decimal place value, each position is ten times the position immediately to its right. A digit therefore contributes digit × place value; division by 10, 100, and so on represents tenths, hundredths, and smaller places.
Reading a decimal from left to right identifies the multiplier or denominator attached to each digit before any new expression is evaluated.
APPLICATION
Match 57.3507 with 5 × A + 7 ÷ B + 3 × C + 5 ÷ D + 7 × E.
The digit 5 is in the tens place, so A = 10; the digit 7 is in the ones place, so B = 1.
The digit 3 is in the tenths place, so C = 0.1; the digit 5 is in the hundredths place, so D = 100 because 5 ÷ 100 = 0.05.
The final digit 7 is in the ten-thousandths place, so E = 0.0001.
Substitute these values: 5 × 10 + 3 × 1 + 6 × 0.1 + 100 + 3 × 0.0001 = 50 + 3 + 0.6 + 100 + 0.0003 = 153.6003.
CROSS-CHECK
Reconstructing the original number gives 5 × 10 + 7 ÷ 1 + 3 × 0.1 + 5 ÷ 100 + 7 × 0.0001 = 50 + 7 + 0.3 + 0.05 + 0.0007 = 57.3507, confirming the place-value assignments.
RESULT
The required value is 153.6003.