Question

1. in which two numbers below is the value of the underlined digit ten times as great as the value of the circled digit?

□ 667,7ⓞ7
□ ⓞ67,767
□ 6ⓞ7,767
□ 667,ⓞ67
□ 667,76ⓞ

Explanation:

Step1: Analyze the first number (667,7ⓞ7)

The circled digit is 0 in the hundredths place (value = \(0\times\frac{1}{100} = 0\)). The underlined digit is 6 in the hundreds place (value = \(6\times100 = 600\)). \(600\) is not ten times \(0\) (since \(0\times10 = 0\)), so this is not valid.

Step2: Analyze the second number (ⓞ667,767)

The circled digit is 6 in the hundred thousands place (value = \(6\times100000 = 600000\)). The underlined digit is 6 in the ten thousands place (value = \(6\times10000 = 60000\)). \(60000\) is not ten times \(600000\) (since \(600000\times10 = 6000000\)), so this is not valid.

Step3: Analyze the third number (6ⓞ67,767)

The circled digit is 6 in the ten thousands place (value = \(6\times10000 = 60000\)). The underlined digit is 6 in the hundred thousands place (value = \(6\times100000 = 600000\)). Now, check if \(600000 = 10\times60000\). Since \(60000\times10 = 600000\), this is valid.

Step4: Analyze the fourth number (667,ⓞ767)

The circled digit is 7 in the tenths place (value = \(7\times\frac{1}{10} = 0.7\)). The underlined digit is 7 in the ones place (value = \(7\times1 = 7\)). Check if \(7 = 10\times0.7\). Since \(0.7\times10 = 7\), this is valid.

Step5: Analyze the fifth number (667,76ⓞ)

The circled digit is 7 in the thousandths place (value = \(7\times\frac{1}{1000} = 0.007\)). The underlined digit is 7 in the tenths place (value = \(7\times\frac{1}{10} = 0.7\)). Check if \(0.7 = 10\times0.007\). Since \(0.007\times10 = 0.07
eq0.7\), this is not valid.

Answer:

• 6ⓞ67,767 (where the circled digit is in the ten - thousands place and the underlined digit is in the hundred - thousands place)
• 667,ⓞ767 (where the circled digit is in the tenths place and the underlined digit is in the ones place)