Decimal Fractions' Meaning: From words to numbers

To solve this problem, let's follow these steps:

• Step 1: Understand the fraction given as "eight tenths."
• Step 2: Recognize this as $\frac{8}{10}$.
• Step 3: Convert the fraction to a decimal format.

Now, let's go through in detail:
Step 1: "Eight tenths" is a fractional term where the numerator is 8, and the denominator is 10, so the fraction is $\frac{8}{10}$.
Step 2: To convert the fraction $\frac{8}{10}$ to a decimal, consider that tenths are represented by the first place right of the decimal point.
Step 3: $\frac{8}{10}$ means eight parts of ten, which can be written as 0.8 in decimal form, since 8 is in the tenths place.

Therefore, the solution to the problem is $0.8$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information in verbal form as a decimal.
• Step 2: Understand the place value indicated by "hundredths."
• Step 3: Convert the verbal phrase into a numerical decimal form.

Now, let's work through each step:
Step 1: The problem gives us the phrase "ninety-two hundredths," which numerically is expressed as $92$.
Step 2: The term "hundredths" implies that $92$ should be divided by $100$, positioning the number in the hundredths place.
Step 3: To convert $92$ hundredths into a decimal, we divide $92$ by $100$, which gives us $0.92$.

Therefore, the decimal fraction of ninety-two hundredths is $0.92$, which corresponds to choice number 1.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Convert the phrase into numerals
• Step 3: Position the numerals correctly based on place value

Now, let's work through each step:
Step 1: The problem gives us the phrase "five hundred and twenty-three thousandths."
Step 2: The number in the phrase is 523, which we need to represent as a decimal fraction.
Step 3: Since the phrase uses "thousandths," 523 must be placed in the position representing thousandths in a decimal. This requires placing 523 starting from the third decimal place:
In decimal form, each digit represents a power of ten. For thousandths, we use the position three places to the right of the decimal point.
Writing this in decimal form involves placing 523 in the "thousandths" column: $0.523$.

Therefore, the solution to the problem is $0.523$.

To convert "nine hundred and thirty-six thousandths" into a decimal fraction, we should understand the components of this phrase:

• The term "hundred" in "nine hundred" means the number 936 must be calculated with consideration.
• "Thousandths" indicates that the value is part of a thousand, or three spaces to the right of the decimal point.

Let's break it down:

When you hear "nine hundred and thirty-six thousandths," you can think of it as being the number 936 over 1000. This can be expressed as $\frac{936}{1000}$.

Writing $\frac{936}{1000}$ as a decimal fraction involves placing the decimal point correctly to reflect the thousandths place. As the denominator is 1000, we must move the decimal three places to the left of the integer 936. Hence, it becomes:

$0.936$

Therefore, the decimal fraction of "nine hundred and thirty-six thousandths" is $0.936$.

To solve this problem, we will convert the verbal form "two tenths" into a decimal:

• Step 1: Understand that "two tenths" means $\frac{2}{10}$.
• Step 2: Convert the fraction $\frac{2}{10}$ into decimal form by performing the division $2 \div 10$.

Now, let's calculate:

Step 1: Identify the fraction: "two tenths" corresponds to the fraction $\frac{2}{10}$.

Step 2: Divide $2$ by $10$, which yields $0.2$.

Thus, two tenths written as a decimal fraction is $0.2$.

To solve this problem, we'll translate the verbal description "three ones and twenty-three thousandths" into a decimal fraction.

Let's break this down:

• The phrase "three ones" refers to the number 3.
• The phrase "twenty-three thousandths" represents the decimal value 0.023, since "thousandths" means we are considering the value in the thousandths place (three decimal places).

Combining these parts:

• We start with 3 for the "three ones."
• Then, we add 0.023 for the "twenty-three thousandths."

Therefore, when we combine 3 and 0.023, we get the decimal 3.023.

Conclusively, the decimal fraction representation of "three ones and twenty-three thousandths" is $3.023$.

To solve this problem, we will follow these steps:

• Step 1: Recognize that a "thousandth" refers to the fraction $\frac{1}{1000}$.
• Step 2: Convert the fraction $\frac{1}{1000}$ to its decimal representation.
• Step 3: Determine which of the given options matches this decimal representation.

Now, let's examine each step:
Step 1: A fraction representing a thousandth is $\frac{1}{1000}$.
Step 2: When we convert $\frac{1}{1000}$ into a decimal, we see that it equals $0.001$ because it requires moving the decimal three places to the left, indicating three zeros before the digit 1.
Step 3: Among the choices provided, option 4 identifies a decimal representation of $0.001$, which correctly reflects a single thousandth place.

Therefore, the solution to the problem is $0.001$.

To solve this problem, we'll follow the steps outlined below:

• Step 1: Recognize that the fraction "seven tenths" is mathematically represented by $\frac{7}{10}$.
• Step 2: Convert this fraction into a decimal by performing the division of 7 by 10.

Now, let's go through these calculations:
Step 1: Write down the fraction $\frac{7}{10}$. Step 2: Divide 7 by 10. This is equivalent to $7 \div 10 = 0.7$. Because we express fractions like $\frac{7}{10}$ with decimals, we see that the number falls at the tenths place, confirming the conversion is accurate.

Upon examining the given choices:

• Choice 1: $7.0$ - Represents seven, but not as a fraction of tenths.
• Choice 2: $0.070$ - Represents seventy thousandths, not tenths.
• Choice 3: $0.70$ - Correctly represents seven tenths.
• Choice 4: $0.700$ - Either represents seven tenths or seven hundred thousandths, but the simplest form for "seven tenths" is $0.7$, which equates with $0.70$.

The number $0.70$ correctly describes "seven tenths" in its simplest and most precise form, as requested by the problem.

Therefore, the solution to the problem is $0.70$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the whole number part from the phrase.
• Step 2: Convert the fractional phrase to a decimal.
• Step 3: Combine the whole number and decimal parts.

Now, let's work through each step:

Step 1: The phrase "one" corresponds to the whole number $1$.

Step 2: The phrase "twenty-five hundredths" refers to the decimal $0.25$. "Hundredths" means the second place to the right of the decimal point.

Step 3: Combine the whole number and the fractional part to form the decimal fraction, which is $1.25$.

Thus, one and twenty-five hundredths written as a decimal fraction is $1.25$, which matches choice 2.

To solve this problem, we need to understand the phrase "one and four thousandths" and convert it to decimal form.

• First, the word "one" represents the whole number part, which is simply $1$.
• The word "and" in the context of numbers usually indicates that a decimal point is to be placed. Therefore, we have $1$ followed by a decimal point, making it $1.$.
• The phrase "four thousandths" gives us the fractional part. In decimal form, thousandths is represented by the third position to the right of the decimal. Thus, four thousandths is written as $0.004$.

Combining these, "one and four thousandths" is written as the decimal fraction $1.004$.

Therefore, the solution to the problem, stated clearly, is that "one and four thousandths" as a decimal fraction is $1.004$.