Place-value basics — local (place) value query: What is the local value of the digit 7 in the numeral 5679032?

Introduction / Context:
This question focuses on local (place) value, which equals a digit multiplied by its positional weight. Unlike face value (the digit itself), local value depends entirely on where the digit sits within the numeral.

Given Data / Assumptions:

• Number: 5679032
• Digit of interest: 7
• We apply standard base-10 place values: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions, etc.

Concept / Approach:
Write the number with place markers to identify the position of the 7. In 5,679,032 the digits correspond to millions (5), hundred-thousands (6), ten-thousands (7), thousands (9), hundreds (0), tens (3), ones (2). Therefore, the 7 is in the ten-thousands place, giving a local value of 7 * 10000.

Step-by-Step Solution:
1) Position mapping: 5 (millions), 6 (hundred-thousands), 7 (ten-thousands), 9 (thousands), 0 (hundreds), 3 (tens), 2 (ones).2) Identify the 7 as ten-thousands place.3) Compute local value: 7 * 10000 = 70000.4) Conclude that the local value is 70000.

Verification / Alternative check:
Expand the number: 5*10^6 + 6*10^5 + 7*10^4 + 9*10^3 + 0*10^2 + 3*10 + 2. The contribution from the 7 term is 70000, confirming the reasoning.

Why Other Options Are Wrong:
7: That is the face value, not the place value.10000: Misses the multiplier 7; it is only the positional weight.5070000: Combines multiple digits and positions incorrectly.

Common Pitfalls:
Confusing the thousand and ten-thousand positions; overlooking the commas that separate groups; or mistaking face value for place value.

Final Answer:
70000