Chapter R.2, Problem 1E

Concept Check In Exercises 1–4, provide the correct response.

In the decimal number 367.9412, name the digit that has each place value.

a. tens

b. tenths

c. thousandths

d. ones or units

e. hundredths

To determine

The digit from the decimal $367.9412$ that has “tens”place value.

Answer to Problem 1E

Solution:

The digit that has tens place value is 6.

Explanation of Solution

Given Information:

The decimal number is $367.9412$.

Consider the decimal,

$367.9412$

Rewrite the decimal as the sum of digits,

$367.9412=3\cdot 100+6\cdot 10+7\cdot 1+9\cdot \left(\frac{1}{10}\right)+4\cdot \left(\frac{1}{100}\right)+1\cdot \left(\frac{1}{1000}\right)+2\cdot \left(\frac{1}{10000}\right)$

For the tens place, the digit is two places left of the decimal point. Here, it is 6. Hence, the digit at the tens place is 6.

To determine

The digit from the decimal $367.9412$ that has “tenths” place value.

Answer to Problem 1E

Solution:

The digit that has tenths place value is 9.

Explanation of Solution

Given Information:

The decimal number is $367.9412$.

Consider the decimal,

$367.9412$

Rewrite the decimal as the sum of digits,

$367.9412=3\cdot 100+6\cdot 10+7\cdot 1+9\cdot \left(\frac{1}{10}\right)+4\cdot \left(\frac{1}{100}\right)+1\cdot \left(\frac{1}{1000}\right)+2\cdot \left(\frac{1}{10000}\right)$

For the tenths place, the digit is one place right of the decimal point. Here, it is 9. Hence, the digit at tenths place is 9.

To determine

The digit from the decimal $367.9412$ that has “thousandths” place value.

Answer to Problem 1E

Solution:

The digit that has thousandths place value is 1.

Explanation of Solution

Given Information:

The decimal number is $367.9412$.

Consider the decimal,

$367.9412$

Rewrite the decimal as the sum of digits,

$367.9412=3\cdot 100+6\cdot 10+7\cdot 1+9\cdot \left(\frac{1}{10}\right)+4\cdot \left(\frac{1}{100}\right)+1\cdot \left(\frac{1}{1000}\right)+2\cdot \left(\frac{1}{10000}\right)$

For the thousandths place, the digit is three places right of the decimal point. Here, it is 1. Hence, the digit at thousandths place is 1.

To determine

The digit from the decimal $367.9412$ that has “ones or units” place value.

Answer to Problem 1E

Solution:

The digit that has ones place value is 7.

Explanation of Solution

Given Information:

The decimal number is $367.9412$.

Consider the decimal,

$367.9412$

Rewrite the decimal as the sum of digits,

$367.9412=3\cdot 100+6\cdot 10+7\cdot 1+9\cdot \left(\frac{1}{10}\right)+4\cdot \left(\frac{1}{100}\right)+1\cdot \left(\frac{1}{1000}\right)+2\cdot \left(\frac{1}{10000}\right)$

For the ones place, the digit is one place left of the decimal point. Here, it is 7. Hence, the digit at ones place is 7.

To determine

The digit from the decimal $367.9412$ that has “hundredths” place value.

Answer to Problem 1E

Solution:

The digit that has Hundredths place value is 4.

Explanation of Solution

Given Information:

The decimal number is $367.9412$.

Consider the decimal,

$367.9412$

Rewrite the decimal as the sum of digits,

$367.9412=3\cdot 100+6\cdot 10+7\cdot 1+9\cdot \left(\frac{1}{10}\right)+4\cdot \left(\frac{1}{100}\right)+1\cdot \left(\frac{1}{1000}\right)+2\cdot \left(\frac{1}{10000}\right)$

For the hundredths place, the digit is two places right of the decimal point. Here, it is 4. Hence, the digit at hundredths place is 4.