High School

I. Choose the correct option:

1. What is the place value of 6 in the greatest 4-digit number formed using the digits 4, 5, 6, and 9 without repetition?
- a. 6
- b. 60
- c. 600
- d. 6000

2. The expanded form of a number is \(6 \times 10000 + a \times 1000 + 6 \times 100 + 5 \times 10 + 4\). What is the greatest possible value of \(a\) from the given options, if the number is smaller than 64,000?
- a. 7
- b. 4
- c. 3
- d. 8

3. A clock in our house loses a second every half a minute. How many minutes will it lose in a day?
- a. 24
- b. 48
- c. 1440
- d. 2880

4. A customer purchases a new computer under an exchange scheme by giving his old computer and paying ₹15,200 cash. If the actual price of the new computer is ₹24,800, how much is the old computer worth?
- a. ₹9,600
- b. ₹6,900
- c. ₹7,900
- d. ₹9,800

5. The smallest 4-digit number formed by using the digits 3, 0, 5, 7, and 1 without repetition will have:
- a. 0 in the thousand's place
- b. 0 in the unit's place
- c. 7 in the thousand's place
- d. 1 in the thousand's place

II. Do as directed:

1. Write the number 93,345,637 in the Indian and International system of numeration using commas.
2. Form the greatest 6-digit number using the digits 8, 7, 0, 1, 9, and 3 without repetition.
3. Find the difference between the place values of 4 in 32,246,245.
4. Arrange the following numbers in ascending order:
- 1,84,31,056; 37,90,423; 9,84,671; 1,83,40,217; 37,63,214
5. Arrange the following numbers in descending order:
- 1,84,31,056; 37,90,423; 9,84,671; 1,83,40,217; 37,63,214

Answer :

1. Place Value of 6

To find the place value of 6 in the greatest 4-digit number formed using the digits 4, 5, 6, and 9 without repetition, we arrange the digits in descending order: 9654. Here, the place value of 6 is in the hundreds place. Thus, the place value of 6 is $600$.

Answer: c. 600

2. Greatest Possible Value of 'a'

The expanded form of the number is given as $6 \times 10000 + a \times 1000 + 6 \times 100 + 5 \times 10 + 4$. We need the number to be smaller than 64,000. Start by estimating:

  • If [tex]a = 7[/tex]: 60,000 + 7,000 = 67,000 (Too large)
  • If [tex]a = 4[/tex]: 64,000 exactly, which is not smaller, hence, incorrect.
  • If [tex]a = 3[/tex]: 63,000, which fits as smaller.

Therefore, using the trial method, [tex]a=3[/tex] yields a number less than 64,000.

Answer: c. 3

3. Time Lost by the Clock

The clock loses 1 second every 30 seconds. To find how many seconds it loses in a day (24 hours or 86,400 seconds), calculate:

[tex]\frac{86400}{30} = 2880 \text{ seconds}\, \text{lost per day}.[/tex]

Convert this time to minutes:

[tex]\frac{2880}{60} = 48 \text{ minutes}.[/tex]

Answer: b. 48

4. Worth of the Old Computer

The actual price of the new computer is ₹24,800. The customer paid ₹15,200 in cash.

Calculating the old computer's value:

[tex]24,800 - 15,200 = ₹9,600.[/tex]

Answer: a. ₹9,600

5. Smallest 4-digit Number

To form the smallest 4-digit number using digits 3, 0, 5, 7, and 1 without repetition (must start with non-zero), place the smallest digit first. Starting with 1, place the next smallest: 1,035. The zero cannot be in the thousand's place.

Answer: d. 1 in thousand's place

II. Specific Tasks

  1. Write the number 93,345,637 in systems:

    • Indian System: 9,33,45,637
    • International System: 93,345,637

  2. Greatest 6-digit number without repetition from 8, 7, 0, 1, 9, 3:

    • Arrange in descending order: 987,310

  3. Difference in place values of 4 in 32246245:

    • First 4 (thousand's place): 4000
    • Second 4 (units): 4
    • Difference: [tex]4000 - 4 = 3996[/tex]

  4. Ascending Order:

    • 9,84,671; 37,63,214; 37,90,423; 1,83,40,217; 1,84,31,056

  5. Descending Order:

    • 1,84,31,056; 1,83,40,217; 37,90,423; 37,63,214; 9,84,671

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