Decimal Fractions' Meaning: Completing the sequence

To solve this problem, let's identify the pattern in the sequence:

Given sequence: $0.2, 0.3, 0.4$.

Step 1: Determine the pattern:

• The first number is $0.2$, the second number is $0.3$, and the third number is $0.4$.
• Calculate the difference between consecutive terms: $0.3 - 0.2 = 0.1$ and $0.4 - 0.3 = 0.1$.
• Therefore, the sequence increases by $0.1$ each time.

Step 2: Use this difference to find the missing terms:

• The next term after $0.4$ will be $0.4 + 0.1 = 0.5$.
• The next term after $0.5$ will be $0.5 + 0.1 = 0.6$.
• The next term after $0.6$ will be $0.6 + 0.1 = 0.7$.

Thus, the completed sequence is $0.2, 0.3, 0.4, 0.5, 0.6, 0.7$.

Comparing the given choices, the correct sequence is choice 3: $0.5, 0.6, 0.7$.

Therefore, the missing terms are $0.5, 0.6, 0.7$.

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

• Step 1: Identify the pattern in the given sequence.
• Step 2: Continue the pattern to find the missing terms.

Now, let's work through each step:

Step 1: Look at the given sequence: $0.5, 0.6, 0.7$. We notice that each term increases by $0.1$.

Step 2: To continue the pattern, add $0.1$ to the last given term, $0.7$:

• Next term: $0.7 + 0.1 = 0.8$
• Next term after $0.8$: $0.8 + 0.1 = 0.9$
• Final term to find: $0.9 + 0.1 = 1.0$

Therefore, the complete sequence is: $0.5, 0.6, 0.7, 0.8, 0.9, 1$.

We can verify this matches choice number 1 in the provided answers:

$0.8, 0.9, 1$.

To determine the sequence's missing numbers, follow these steps:

• Step 1: Analyze the given sequence: $0.9, 0.8, 0.7$.
• Step 2: Calculate the common difference by subtracting consecutive terms. For instance, $0.8 - 0.9 = -0.1$ and $0.7 - 0.8 = -0.1$, confirming a common difference of $-0.1$.
• Step 3: Continue the pattern using this common difference: - Starting from $0.7$, subtract $0.1$, giving $0.6$ as the next number. - From $0.6$, subtract $0.1$ again, resulting in $0.5$. - Finally, subtract $0.1$ from $0.5$, yielding $0.4$.

Thus, the completed sequence is $0.9, 0.8, 0.7, 0.6, 0.5, 0.4$.

The correct answer to complete the sequence is $0.6, 0.5, 0.4$.

To solve this problem, let's determine the rule for creating the sequence:

• Step 1: Identify the given numbers in the sequence: 1, 0.9, 0.8.
• Step 2: Determine the difference between consecutive terms:
  • From 1 to 0.9, the difference is 0.1 (i.e., 1 - 0.9 = 0.1).
  • From 0.9 to 0.8, the difference is also 0.1 (i.e., 0.9 - 0.8 = 0.1).
• Step 3: Notice the pattern is a decrease of 0.1 between each term.
• Step 4: Apply this pattern to find the next terms:
  • The next term after 0.8 is 0.8 - 0.1 = 0.7.
  • Following 0.7, the next term is 0.7 - 0.1 = 0.6.
  • Finally, after 0.6, the term is 0.6 - 0.1 = 0.5.

Therefore, the next three terms in the sequence are $0.7, 0.6, 0.5$.

To solve this problem, we'll look for a consistent pattern in the given sequence:

• Step 1: Identify the difference between consecutive terms.
  - From $1$ to $0.8$, the difference is $0.2$ (i.e., $1 - 0.8 = 0.2$).
  - From $0.8$ to $0.6$, the difference is $0.2$ (i.e., $0.8 - 0.6 = 0.2$).
• Step 2: Determine the next terms using this difference.
  - The next term after $0.6$ will be $0.6 - 0.2 = 0.4$.
  - The term after that will be $0.4 - 0.2 = 0.2$.

Therefore, the sequence $1, 0.8, 0.6, ?, ?$ continues as $0.4, 0.2$.

The correct answer is $0.4, 0.2$, which corresponds to choice 4.

To determine the next numbers in the sequence $0, 0.2, 0.4, 0.6$, we proceed by identifying the pattern:

• Evaluate the difference between the first two terms: $0.2 - 0 = 0.2$.
• Verify this difference remains the same between the subsequent terms: $0.4 - 0.2 = 0.2$ and $0.6 - 0.4 = 0.2$.

Each term increases by $0.2$. Therefore, this sequence follows an arithmetic progression with a common difference of $0.2$.

To find the next term in the sequence: add $0.2$ to the last known term.

• Next term after $0.6$ is $0.6 + 0.2 = 0.8$.
• To find the term following $0.8$, add $0.2$ again: $0.8 + 0.2 = 1$.

Thus, the next two numbers in the sequence are $0.8$ and $1$.

The correct answer, therefore, is $0.8, 1$.

To complete the sequence, let's observe the given numbers: $0, 0.01, 0.02$.

Step 1: Calculate the difference between the consecutive terms:

• Difference between $0$ and $0.01$: $0.01 - 0 = 0.01$.
• Difference between $0.01$ and $0.02$: $0.02 - 0.01 = 0.01$.

Step 2: The difference between each term is $0.01$, suggesting a pattern where each term increases by $0.01$.

Step 3: Apply this pattern to find the next terms:

• The term after $0.02$ is $0.02 + 0.01 = 0.03$.
• The term after $0.03$ is $0.03 + 0.01 = 0.04$.

Therefore, the completed sequence is $0, 0.01, 0.02, 0.03, 0.04$.

Comparing this with the choices provided, the correct choice is:

$0.03,0.04$

The sequence provided is $0.1, 0.09, ?, ?, 0.06, 0.05$.

First, observe the difference between the first two numbers of the sequence:

$0.1 - 0.09 = 0.01$.

This indicates that the sequence decreases by $0.01$ between consecutive terms.

Apply this pattern to find the missing numbers:

1. From $0.09$, subtract $0.01$ to find the next term:
$0.09 - 0.01 = 0.08$.

2. From $0.08$, again subtract $0.01$:
$0.08 - 0.01 = 0.07$.

This reveals the sequence as:

$0.1, 0.09, 0.08, 0.07, 0.06, 0.05$.

Therefore, the missing terms in the sequence are $0.08$ and $0.07$.

The correct answer, matching the choice is $0.08, 0.07$.

To solve this mathematical sequence problem, we need to identify the common difference and use it to find the missing numbers. Let's follow these steps:

• Step 1: Identify the given numbers and their positions in the sequence.
• Step 2: Calculate the common difference between successive terms.
• Step 3: Use the common difference to determine the missing numbers.
• Step 4: Validate the completed sequence with the original pattern.

Now, let's work through each step:

Step 1: The given numbers in the sequence are $0.1, ?, 0.06, 0.04, ?, 0$.

Step 2: Calculate the common difference. The difference between $0.06$ and $0.04$ is $0.06 - 0.04 = 0.02$. The difference between $0.04$ and the next number $(0)$ is also $0.04 - 0 = 0.04$. This suggests a pattern of reducing by $0.02$ each time.

Step 3: Deduct $0.02$ from each preceding term to find the subsequent numbers:

• Before $0.06$, the number must be $0.06 + 0.02 = 0.08$.
• Before $0$, the number must be $0 + 0.02 = 0.02$.

Step 4: By substituting the above values into the sequence, we have the completed sequence: $0.1, 0.08, 0.06, 0.04, 0.02, 0$.

Therefore, the missing numbers in the sequence are $0.08$ and $0.02$.

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

• Step 1: Identify the sequence pattern.
• Step 2: Calculate the differences between known terms.
• Step 3: Use the difference to find missing terms.
• Step 4: Validate against the given choices.

Now, let's work through each step:
Step 1: Identify the sequence pattern from the given terms $0.9$ and $0.6$.
Step 2: Calculate the difference between $0.9$ and $0.6$, which is $0.9 - 0.6 = 0.3$. This indicates the sequence decreases by $0.3$ with each term.
Step 3: Apply this difference to find the next terms:
- Subtract $0.3$ from $0.6$: $0.6 - 0.3 = 0.3$
- Subtract $0.3$ from $0.3$: $0.3 - 0.3 = 0$
Step 4: Validate against the given choices; the only choice that matches this sequence is $0.3, 0$.

Therefore, the solution to the problem is $0.3, 0$.