Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Simple conversion to denominator 10, 100, 1000

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

• Step 1: Identify the given fraction $\frac{1}{10}$.
• Step 2: Convert the fraction to a decimal by dividing the numerator by the denominator.
• Step 3: Perform the division and compare with the given choices.

Let's work through the solution:

Step 1: We start with the fraction $\frac{1}{10}$.

Step 2: Perform the division: $1 \div 10 = 0.1$.

Step 3: Therefore, the decimal equivalent of $\frac{1}{10}$ is $0.1$.

Among the given answer choices, 0.1 corresponds to choice 3, which is the correct answer.

Thus, the solution to the problem is $0.1$.

To convert the fraction $\frac{105}{1000}$ to a decimal, note that the denominator, 1000, is $10^3$, which means we need to move the decimal point three places to the left in the numerator.

Let's break it down:

• Start with the numerator, 105, which can be viewed as 105.0 for clarity.
• Since the denominator is 1000, move the decimal three places to the left: $105.0 \rightarrow 10.5 \rightarrow 1.05 \rightarrow 0.105$

This places the decimal correctly according to the denominator's power of ten.

Therefore, the decimal representation of $\frac{105}{1000}$ is 0.105.

To convert the fraction $\frac{346}{1000}$ into a decimal, follow these steps:

• Recognize that the denominator is 1000, which tells us the decimal will have three places after the decimal point.
• Place the number 346 over 1000 directly into decimal form, which involves moving the decimal point three places to the left.

In this case:

$\frac{346}{1000}$ in decimal form is $0.346$.

Therefore, the solution to the problem is $0.346$.

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

• Step 1: Perform the division required to convert the fraction $\frac{26}{100}$ into a decimal.

Now, let's work through the solution:

$\text{Step 1: Calculate } \frac{26}{100} = 26 \div 100 = 0.26$

Therefore, the decimal representation of $\frac{26}{100}$ is 0.26.

To convert the fraction $\frac{93}{100}$ into a decimal, follow these steps:

• Step 1: Recognize that the fraction's denominator is 100, which is $10^2$.
• Step 2: Convert the fraction to a decimal by moving the decimal point two places to the left in the numerator 93 (one place for each zero in 100).
• Step 3: The decimal conversion of $\frac{93}{100}$ is $0.93$.

The resulting decimal is $0.93$, which aligns with choice 2.

To solve this problem, let's convert the fraction $\frac{3}{10}$ into a decimal.

First, identify the given fraction: $\frac{3}{10}$.

Since the denominator is 10, a power of 10, the conversion to a decimal is straightforward. The fraction $\frac{3}{10}$ can be interpreted as dividing 3 by 10.

Perform the division: $3 \div 10 = 0.3$.

This results in the decimal number $0.3$.

Therefore, the decimal conversion of the fraction $\frac{3}{10}$ is $\mathbf{0.3}$.

To solve this problem, we'll convert the decimal 0.1 into a fraction:

• Step 1: Recognize that in the decimal 0.1, the digit "1" is in the tenths place.
• Step 2: Convert 0.1 directly into a fraction by placing 1 over 10. This is because 0.1 means 1 part out of 10, i.e., $\frac{1}{10}$.

Now, let's consider the problem:

Step 1: Observe the decimal 0.1. The "1" is in the tenths place, which means it represents one-tenth.
Step 2: Hence, as a fraction, 0.1 is $\frac{1}{10}$ since there is one digit after the decimal point, implying a denominator of 10.

Therefore, the correct answer to converting 0.1 into a fraction is $\frac{1}{10}$.

To solve this problem, let's convert the decimal 0.3 into a fraction:

• Step 1: Identify the place value of 0.3.
  Since the decimal 0.3 has one digit after the decimal point, it is in the tenths place. This means that 0.3 is equivalent to 3 tenths, or $\frac{3}{10}$.
• Step 2: Write the fraction based on the place value:
  The decimal 0.3 is expressed as $\frac{3}{10}$, where 3 is the numerator and 10 is the denominator, reflective of the tenths place.
• Step 3: Verify the answer using multiple-choice options:
  Among the choices provided, $\frac{3}{10}$ is the correct match, which corresponds to choice 3.

Therefore, the correct fraction representation for 0.3 is $\frac{3}{10}$.

To convert the decimal 0.27 into a fraction, follow these steps:

• Step 1: Identify the number of decimal places in 0.27. There are two decimal places.
• Step 2: Use a denominator of 100, since 10 to the power of 2 (the number of decimal places) is 100.
• Step 3: Write the number without the decimal point as the numerator: 27.
• Step 4: Write the fraction: $\frac{27}{100}$.
• Step 5: Check if the fraction can be simplified. In this case, 27 and 100 have no common factors other than 1, so the fraction $\frac{27}{100}$ is already in its simplest form.

Therefore, the decimal 0.27 as a fraction is $\frac{27}{100}$.

To convert the decimal 0.15 into a fraction, we will follow these steps:

• Step 1: Identify the decimal places
  The number 0.15 has two decimal places.

• Step 2: Express the decimal as a fraction with a denominator of a power of 10
  Since there are two decimal places, we write 0.15 as $\frac{15}{100}$.

• Step 3: Compare with given choices
  Among the provided choices, $\frac{15}{100}$ matches the initial conversion of the decimal without simplification.

Therefore, the solution to the problem in the context of the choices provided is $\frac{15}{100}$.

To convert the decimal 0.93 into a fraction, observe the following steps:

• Step 1: Recognize that 0.93 is in the hundredths place. Thus, it can be directly expressed as $\frac{93}{100}$. The number 93 is the numerator, and 100 is the denominator, reflecting the decimal's position.
• Step 2: Consider simplifying the fraction. Since 93 and 100 have no common factors other than 1, $\frac{93}{100}$ is already in its simplest form.
• Step 3: Check if the fraction matches the multiple-choice options provided. In this case, $\frac{93}{100}$ is the correct choice.

Therefore, the decimal 0.93 is equivalent to the fraction $\frac{93}{100}$.

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

• Step 1: Identify the decimal number given as 0.55.
• Step 2: Express 0.55 as a fraction using its place value.
• Step 3: Verify which choice this corresponds to among the provided options.

Let's work through each step:

Step 1: We have the decimal 0.55.

Step 2: In the decimal number 0.55, the first '5' is in the tenths place, and the second '5' is in the hundredths place, so this can be expressed as:
$0.55 = \frac{55}{100}$ This places 55 over 100 to correspond with its placement in the hundredths position in decimal terminology.

Step 3: Comparing the resulting fraction $\frac{55}{100}$ with the choices provided, this matches choice number two. Therefore, choice number two is the correct answer.

Hence, the solution to the problem is $\frac{55}{100}$.

To solve this problem of converting the decimal 0.7 into a fraction, follow these clear steps:

• Step 1: Understand the place value of the decimal number 0.7. The digit 7 is in the tenths place, which means it can be expressed as a fraction over 10.
• Step 2: Write down the fraction as $\frac{7}{10}$. Here, 7 is the numerator, representing the part, and 10 is the denominator, representing the whole.
• Step 3: Check if the fraction $\frac{7}{10}$ can be simplified. Since 7 and 10 have no common divisors other than 1, the fraction is already in its simplest form.

Therefore, the decimal 0.7 is equivalent to the fraction $\frac{7}{10}$.

Comparing this result with the given choices, the correct answer is choice 2: $\frac{7}{10}$.

Thus, the solution to the problem is $\frac{7}{10}$.

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

• Step 1: Identify the decimal place value.
• Step 2: Write the decimal as a fraction based on the place value.
• Step 3: Check if the fraction can be simplified.

Now, let's work through each step:
Step 1: The given decimal is 0.07. The digit 7 is in the hundredths place, which indicates that the denominator should be 100.
Step 2: We write 0.07 as a fraction: $\frac{7}{100}$.
Step 3: Check for simplification. The fraction $\frac{7}{100}$ is already in its simplest form since 7 is a prime number and cannot be divided further by 100.

Thus, the fraction form of 0.07 is $\frac{7}{100}$.

Considering the multiple-choice options:

• Choice 1: $\frac{7}{10}$ - Incorrect, as this corresponds to the decimal 0.7.
• Choice 2: $\frac{7}{1000}$ - Incorrect, as this corresponds to the decimal 0.007.
• Choice 3: $\frac{7}{100}$ - Correct, as this matches the calculation we performed.
• Choice 4: $\frac{70}{100}$ - Incorrect, as this can be simplified to $\frac{7}{10}$.

Therefore, the correct answer is $\frac{7}{100}$, corresponding to choice 3.

To convert the fraction $\frac{67}{1000}$ into a decimal, we recognize that the denominator 1000 implies that this fraction can be expressed in the thousandths place of a decimal.

• Step 1: Identify that the fraction $\frac{67}{1000}$ needs to be expressed with three decimal places.
• Step 2: Understand that each place value after the decimal corresponds to tenths, hundredths, and thousandths, respectively. Since we have 67 thousandths, the decimal will have three digits after the decimal point.
• Step 3: Place 67 into the decimal system by placing it three places to the right of the decimal point:

We write it as $0.067$. Here, "0.0" represents there are no tenths or hundredths, and "67" fills the thousandths place.

Therefore, the decimal equivalent of $\frac{67}{1000}$ is $\mathbf{0.067}$.

To convert the fraction $\frac{5}{1000}$ into a decimal, consider the following steps:

• Step 1: Recognize that the denominator 1000 represents thousandths. We need to express 5 in terms of thousandths.
• Step 2: Convert the fraction to a decimal by aligning with the place value: $\frac{5}{1000}$ is equivalent to 5 thousandths.
• Step 3: The decimal form therefore has the digit 5 in the thousandths place, which results in the number 0.005.

Since the denominator is 1000, equivalent to three decimal places, the number 5 as part of thousandths results in $0.005$.

Therefore, the solution to the problem is $\frac{5}{1000} = 0.005$. This corresponds to choice 2.

To solve this problem, let us follow these steps:

• Step 1: Understand the given fraction $\frac{100}{1000}$.
• Step 2: Simplify the fraction if possible.
• Step 3: Convert the simplified fraction into a decimal.

Now, let's dive into the details:

Step 1: We are given $\frac{100}{1000}$. This fraction represents 100 divided by 1000.

Step 2: The fraction can be simplified because both the numerator (100) and denominator (1000) have a common factor of 100.
Dividing both by 100 gives:

Step 3: Convert $\frac{1}{10}$ into a decimal:

The fraction $\frac{1}{10}$ means one-tenth, which can be directly written as the decimal $0.1$.

There are also other decimal forms which retain the same value such as $0.10$ and $0.100$, which are legitimate representations with different coverage of decimal precision.

Therefore, the decimal representation of $\frac{100}{1000}$ is 0.1, and among the choices provided, the answer choice representing this is "All answers are correct".

To convert the fraction $\frac{4}{100}$ into a decimal, we follow these steps:

• Step 1: Identify that we need to divide 4 by 100. In mathematical terms, this is written as $4 \div 100$.
• Step 2: Perform the division. When dividing 4 by 100, we can move the decimal point in 4 two places to the left because there are two zeros in 100.
• Step 3: Moving the decimal point in 4 (which is 4.0) two places to the left, we shift from 4.0 to 0.04.

Therefore, the decimal representation of $\frac{4}{100}$ is $0.04$.
Upon reviewing the provided choices, we see that option 3, $0.04$, corresponds exactly to our calculated result.

To solve the problem of converting the decimal 0.0157 into a fraction, follow these steps:

• Step 1: Identify the Decimal Places
  The decimal number 0.0157 has four decimal places.
• Step 2: Convert to a Fraction
  A decimal with four decimal places can be expressed as a fraction over 10,000. Therefore, 0.0157 is $\frac{157}{10000}$. This arises because 0.0157 is $\frac{157}{10000}$ when directly considering its placement over 10000 as a power of ten.
• Step 3: Simplification (if applicable)
  In this case, $\frac{157}{10000}$ is already in its simplest form since 157 and 10000 have no common factors other than 1.

Therefore, the fractional representation of the decimal 0.0157 is $\frac{157}{10000}$.

To solve this problem, we will convert 0.708 into a fraction step-by-step:

• Step 1: Identify the decimal and its place value. Since 0.708 has three decimal places, it is equivalent to having a denominator of 1000.
• Step 2: Write the decimal as a fraction. Place the number 708 on the numerator and 1000 as the denominator, resulting in $\frac{708}{1000}$.

Therefore, the solution to converting 0.708 to a fraction is $\frac{708}{1000}$.