Chapter 3, Problem 1VR

Complete each statement with the correct word from the column on the right.

trillion

million

billion

arithmetic numbers

repeating

terminating

A _______decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5. [3.5a]

To determine

To fill: The incomplete sentence, ‘A ___ decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5’.

Answer to Problem 1VR

Solution:

The complete sentence is ‘A repeating decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5’.

Explanation of Solution

Given Information:

The provided incomplete sentence is ‘A ___ decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5’.

The provided choices of words are, trillion, million, billion, arithmetic numbers, repeating, terminating

Explanation:

Consider the provided incomplete sentence, ‘A ___ decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5’.

For fractions with denominators that have numbers with factors other than 2 or 5, the number is not divisible completely, thus, converting the decimals with repeating numbers after the decimal point.

For example,

$\frac{100}{14}$

Perform long division,

$14\begin{array}{c}\hfill 7.\overline{14285}\\ \hfill \overline{)\begin{array}{l}100.00000\\ \frac{98}{\begin{array}{l}20\\ \frac{14}{\begin{array}{l}60\\ \frac{56}{\begin{array}{l}40\\ \frac{28}{\begin{array}{l}120\\ \frac{112}{\begin{array}{l}80\\ \frac{70}{10}\end{array}}\end{array}}\end{array}}\end{array}}\end{array}}\end{array}}\end{array}$

After this, the numbers in the quotient are repeated, and the quotient is $7.\overline{14285}$.

Hence, the complete sentence is ‘A repeating decimal occurs when we convert a fraction to a decimal and the denominator of the fraction has at least one factor other than 2 or 5’.