All questions of Chapter 7 - Can You See the Pattern? for Class 5 Exam

Indian Place Value Chart

The Indian Place Value Chart is a system of numeration in which the position of each digit in a number determines its value. It is based on the decimal system, with each place value being ten times the value of the place to its right.

The period which is just right to the period “Arabs” in the Indian Place Value Chart is Crores.

Understanding the Periods in Indian Place Value Chart

The Indian Place Value Chart is divided into four periods, each consisting of three digits. These periods are named as follows:

1. Units Period - Ones, Tens, Hundreds
2. Thousands Period - Thousands, Ten Thousands, Lakhs
3. Crores Period - Crores, Ten Crores, Hundred Crores
4. Billions Period - Thousands of Crores, Ten Thousands of Crores, Lakhs of Crores

The value of each period increases from right to left by a factor of ten. For example, the units period has a value of 1, the thousands period has a value of 10^3 (or 1,000), the crores period has a value of 10^7 (or 10,000,000), and so on.

Identifying the Period Just Right to Arabs

The period just right to Arabs is Crores. This is because the Arabs period represents numbers from 10^12 (one trillion) to 10^15 (one quadrillion), while the Crores period represents numbers from 10^7 (ten million) to 10^10 (ten billion).

Therefore, if we have a number in the Arabs period, we can convert it to the Crores period by dividing it by 10^5 (or multiplying it by 0.00001).

Conclusion

The Indian Place Value Chart is an important system of numeration used in India and other parts of the world. Understanding the periods and their values is essential for performing arithmetic operations and working with large numbers. In this case, we identified the period just right to Arabs as Crores, based on the value of each period and its position in the chart.

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Splitting of Periods in Indian Place Value Chart

The Indian place value chart has four periods: ones, thousands, lakhs, and crores. Each period represents a group of digits that are separated by commas. Let's take a look at how each period is split:

1. Ones Period: This period represents the units or ones place. It is the smallest period and contains only one digit.

2. Thousands Period: This period represents the thousands place. It contains three digits and is separated from the ones period by a comma.

3. Lakhs Period: This period represents the hundred thousands place. It contains six digits and is separated from the thousands period by a comma.

4. Crores Period: This period represents the ten millions place. It contains seven digits and is separated from the lakhs period by a comma.

Answer: Option A

From the above explanation, we can see that none of the periods have been split into three places except for the ones period. Therefore, the correct answer is option A - Ones.

In the sequence, there is a gap of 13, so we should add 13 to 39 and the answer we get is 'A' 52

Given number: 205,076,306,006,306,005,023
To find the successor of the given number, we need to add 1 to it.

Steps to add 1 to the given number:

1. Add 1 to the last digit (3 + 1 = 4).
2. If the result of step 1 is 10, then carry over 1 to the next digit and add it (6 + 1 = 7).
3. Repeat steps 1 and 2 until the first digit (2) is reached.

So, the successor of the given number is:

205,076,306,006,306,005,024 (Option D)

Because we're adding 7

Explanation:
To find the greatest 5-digit number, we need to use all the digits from 0-9 but the digit at the ten-thousands place cannot be zero. So the greatest 5-digit number is 99990.

To find the greatest 6-digit number, we also need to use all the digits from 0-9 but the digit at the hundred-thousands place cannot be zero. So the greatest 6-digit number is 999990.

Now we need to find the sum of X and Y:

X = 99990
Y = 999990

X + Y = 99990 + 999990 = 1099980

So the sum of X and Y is 1099980, which is option (D), 1099998.

Expanded Form of 19,735,800,000,000

To write the expanded form of a number, we need to break it down into its place values. In this case, the number is nineteen trillion seven hundred thirty-five million eight hundred.

Step 1: Identify the place values

- Trillions (1,000,000,000,000)
- Billions (1,000,000,000)
- Millions (1,000,000)
- Thousands (1,000)
- Hundreds (100)
- Tens (10)
- Ones (1)

Step 2: Write the number in expanded form

- 19 trillion = 19,000,000,000,000
- 735 billion = 735,000,000,000
- 800 million = 800,000,000
- 0 thousands = 0
- 0 hundreds = 0
- 0 tens = 0
- 0 ones = 0

Step 3: Combine the place values

- 19,000,000,000,000 + 735,000,000,000 + 800,000,000 + 0 + 0 + 0 + 0 = 19,735,800,000,000

Therefore, the expanded form of 19,735,800,000,000 is 19,000,000,000,000 + 735,000,000,000 + 800,000,000 + 0 + 0 + 0 + 0 = 10,973,580,000,000.

Explanation:

To find the correct number from the given options, we need to understand the pattern or rule that is being followed.

Pattern:
- The given number is a combination of smaller numbers.
- Each smaller number is obtained by multiplying a digit by a power of 10.
- The powers of 10 used are in descending order from left to right.

Analysis:
Let's analyze the given number and break it down into its smaller components:

- 7000000000: This can be broken down into 7 x 1,000,000,000.
- 500000000: This can be broken down into 5 x 100,000,000.
- 800000: This can be broken down into 8 x 100,000.
- 600: This can be broken down into 6 x 100.
- 9: This is a standalone number.

Using the Pattern:
Now, let's use the pattern we identified to find the correct number from the given options:

- Option A: 7500800609
- This can be broken down into 7 x 1,000,000,000 + 500,000,000 + 8 x 100,000 + 600 + 9.
- This matches the pattern we identified and is equal to the given number.

- Option B: 7508000609
- This can be broken down into 7 x 1,000,000,000 + 500 x 1,000,000 + 8 x 100,000 + 600 + 9.
- This does not match the pattern as the second component is multiplied by 1,000,000 instead of 100,000,000.

- Option C: 7500080609
- This can be broken down into 7 x 1,000,000,000 + 500,000,000 + 80 x 1,000 + 600 + 9.
- This does not match the pattern as the third component is multiplied by 1,000 instead of 100,000.

- Option D: 7500806009
- This can be broken down into 7 x 1,000,000,000 + 500,000,000 + 8 x 100,000 + 600 x 1,000 + 9.
- This does not match the pattern as the fourth component is multiplied by 1,000 instead of 100.

Conclusion:
Based on the analysis and using the pattern, the correct number is option A: 7500800609, as it matches the given number and follows the pattern of multiplying digits by powers of 10 in descending order.

Understanding the Pattern
To solve the missing numbers in the sequence: 8, ____, 16, ____, 24, 28, 32, we need to look for a consistent pattern.
Identifying the Sequence
- The first number is 8.
- The third number is 16.
- The fifth number is 24.
- The sixth number is 28.
- The seventh number is 32.
Looking at the numbers, we see that they increase as follows:
Finding Differences
- 8 to 16 is an increase of 8.
- 16 to 24 is an increase of 8.
- 24 to 28 is an increase of 4.
- 28 to 32 is an increase of 4.
This suggests that the pattern is alternating increases of 8 and 4.
Filling in the Blanks
- After 8, the next number should be 12 (8 + 4).
- After 12, the next number should be 16 (12 + 4).
- After 16, the next number should be 20 (16 + 4).
- After 20, the next number should be 24.
Thus, the missing numbers are 12 and 20.
Conclusion
The correct answer is option 'A': 12, 20. This maintains the consistent pattern of increasing by 4 and 8 in the sequence.

To find the number that follows the given pattern, we need to observe the sequence and identify the pattern. Let's analyze the given numbers:

17, 22, 27, 32, ____

Pattern:
- Starting from 17, each subsequent number is obtained by adding 5 to the previous number.

Analysis:
- The first number, 17, is increased by 5 to get the second number, 22.
- The second number, 22, is increased by 5 to get the third number, 27.
- The third number, 27, is increased by 5 to get the fourth number, 32.

Applying the Pattern:
To find the missing number, we need to add 5 to the last given number, 32.

32 + 5 = 37

Therefore, the missing number in the sequence is 37.

Final Answer:
The number that follows the pattern is 37, which corresponds to option C.

0 , as natural numbers are the positive numbers which begin from 1 and continue till infinity .

Yes

Addition of 7 and 13

To find the sum of 7 and 13, we need to add the two numbers together.

Steps:

1. Write down the numbers 7 and 13 vertically, aligning the digits.

7
+ 13

2. Start by adding the digits in the rightmost column, which is the ones place. In this case, 7 plus 3 equals 10. Write down the 0 in the ones place and carry over the 1 to the next column.

7
+ 13
10

3. Move to the next column, which is the tens place. Add the carried-over 1 to the digit in the tens place, which is 1. 1 plus 1 equals 2. Write down the 2 in the tens place.

7
+ 13
20

4. Since there are no more digits to add in the hundreds place, we can stop here.

Result:

The sum of 7 and 13 is 20.

Therefore, the correct answer is option C) 20.

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