Question

in the number below, the digit 2 appears three times.
325,012.782
which of the following are the correct places in which the digit 2 appears?
a. the thousands, ones, and thousandths places
b. the ten thousands, tens, and thousandths places
c. the thousands, tens, and hundredths places
d. the ten thousands, ones, and thousandths places

Explanation:

Step1: Identify digit positions

First, let's write the number \( 325,012.782 \) with place values. The left side of the decimal is the whole number part:

• From right to left (before decimal): units (ones), tens, hundreds, thousands, ten - thousands, hundred - thousands.
• After decimal: tenths, hundredths, thousandths.

Breaking down \( 325,012.782 \):

• The first 2 (from left in whole number part): In \( 325,012 \), the digits are (from left) 3 (hundred - thousands), 2 (ten - thousands), 5 (thousands), 0 (hundreds), 1 (tens), 2 (ones).
• The second 2: In the ones place (the last digit before the decimal).
• The third 2: After the decimal, in the thousandths place (the third digit after the decimal, since the first is tenths (\(7\)), second is hundredths (\(8\)), third is thousandths (\(2\))).

Step2: Match with options

Now let's check each option:

• Option A: thousands (no, the first 2 is ten - thousands), ones (yes), thousandths (yes). So A is wrong.
• Option B: ten - thousands (yes, the first 2), tens (no, the digit in tens place is 1), thousandths (yes). So B is wrong.
• Option C: thousands (no), tens (no), hundredths (no, hundredths is 8). So C is wrong.
• Option D: ten - thousands (yes, the first 2), ones (yes, the second 2), thousandths (yes, the third 2). So D matches.

Answer:

D. the ten thousands, ones, and thousandths places