What is place value from value of a number?

Answer 1

The concept of "place values" applies only to systems that have "places", and only when at least some of those "places" are given numeric "values".
Examples: (1) temperatures at all spots on the earth's surface; (2) bumpers within pinball machines; (3) prices at all locations on grocery store shelves; (4) sequential places as used with Arabic numerals -- the place values are powers of ten.

Like the MH Sci-Tech dictionary, most authors of curricular materials badly confuse the numeric values of PLACES, with the values of whatever QUANTITIES occur in those places. At $2 per can, the quantity, 7 cans, has a (quantity) value of $14 ... but the (place) value on the shelf is $2.

The Arabic numeral for 456 uses 3 places ... for (4, 5, 6) ... with digits being entered into each of the ( _, _, _ ) places. The 3 place-values, right to left, are 1 and 10 and 100. Using 4 in the 100-place expresses the QUANTITY 4(100s) ... whose quantity-value is 400. The "serial" value of (4,5,6) comes from adding the quantity-values of 4(100s) and 5(10s) and 6(1s) ... as 400+50+6 or 456.