Question

relating place value. 10 or \\(\frac{1}{10}\\) of
3.45
4.35
777
777

Explanation:

To analyze the place value relationships:

For 3.45 and 4.35:

• In \( 3.45 \), the underlined digit \( 3 \) is in the ones place (value \( 3\times1 = 3 \)).
• In \( 4.35 \), the underlined digit \( 3 \) is in the tenths place (value \( 3\times\frac{1}{10}=0.3 \)).
• The relationship: The \( 3 \) in \( 4.35 \) (tenths place) is \( \frac{1}{10} \) of the \( 3 \) in \( 3.45 \) (ones place), since \( 0.3=\frac{1}{10}\times3 \).

For the two "777" numbers:

• Let the first \( 777 \) have the underlined \( 7 \) in the tens place (value \( 7\times10 = 70 \)).
• Let the second \( 777 \) have the underlined \( 7 \) in the hundreds place (value \( 7\times100 = 700 \)).
• The relationship: The \( 7 \) in the tens place is \( \frac{1}{10} \) of the \( 7 \) in the hundreds place (since \( 70=\frac{1}{10}\times700 \)), or vice versa (the \( 7 \) in the hundreds place is \( 10 \) times the \( 7 \) in the tens place).

(Note: The exact place - value relationship depends on the specific underlining of the "7" digits, but the general principle of place - value scaling by factors of \( 10 \) or \( \frac{1}{10} \) applies.)

Answer:

To analyze the place value relationships:

For 3.45 and 4.35:

• In \( 3.45 \), the underlined digit \( 3 \) is in the ones place (value \( 3\times1 = 3 \)).
• In \( 4.35 \), the underlined digit \( 3 \) is in the tenths place (value \( 3\times\frac{1}{10}=0.3 \)).
• The relationship: The \( 3 \) in \( 4.35 \) (tenths place) is \( \frac{1}{10} \) of the \( 3 \) in \( 3.45 \) (ones place), since \( 0.3=\frac{1}{10}\times3 \).

For the two "777" numbers:

• Let the first \( 777 \) have the underlined \( 7 \) in the tens place (value \( 7\times10 = 70 \)).
• Let the second \( 777 \) have the underlined \( 7 \) in the hundreds place (value \( 7\times100 = 700 \)).
• The relationship: The \( 7 \) in the tens place is \( \frac{1}{10} \) of the \( 7 \) in the hundreds place (since \( 70=\frac{1}{10}\times700 \)), or vice versa (the \( 7 \) in the hundreds place is \( 10 \) times the \( 7 \) in the tens place).

(Note: The exact place - value relationship depends on the specific underlining of the "7" digits, but the general principle of place - value scaling by factors of \( 10 \) or \( \frac{1}{10} \) applies.)