Large Numbers Around Us | FIO

Question 21

You are given two sets of number cards numbered from 1-9. Place a number card in each box below to get the

(a) largest possible sum

(b) smallest possible difference of the two resulting numbers.

Solution

We need to arrange digits to form two numbers for sum and difference.

Step 1 — Largest possible sum

Let the 6-digit number be $N_1$ . Let the 5-digit number be $N_2$ . We have two sets of digits from 1 to 9. This means we have two of each digit. To maximize the sum, we place largest digits. We place them in the highest place values. The $10^5$ place is the highest. We assign the largest digit, 9. It goes to $N_1$ 's $10^5$ place. $N_1 = \mathbf{9} \_ \_ \_ \_ \_$ The next highest place is $10^4$ . We assign the next two largest digits. These are 9 and 8. We give 9 to $N_1$ and 8 to $N_2$ . $N_1 = 9\mathbf{9} \_ \_ \_ \_$ $N_2 = \mathbf{8} \_ \_ \_ \_$ We continue this process. Assign next largest digits to next place values. For $10^3$ : 8 to $N_1$ , 7 to $N_2$ . $N_1 = 99\mathbf{8} \_ \_ \_$ $N_2 = 8\mathbf{7} \_ \_ \_$ For $10^2$ : 7 to $N_1$ , 6 to $N_2$ . $N_1 = 998\mathbf{7} \_ \_$ $N_2 = 87\mathbf{6} \_ \_$ For $10^1$ : 6 to $N_1$ , 5 to $N_2$ . $N_1 = 9987\mathbf{6} \_$ $N_2 = 876\mathbf{5} \_$ For $10^0$ : 5 to $N_1$ , 4 to $N_2$ . $N_1 = 99876\mathbf{5}$ $N_2 = 8765\mathbf{4}$ The two numbers are 998765 and 87654. Let us calculate their sum.

$N_1 + N_2 = 998765 + 87654$

$= 1086419$

$\boxed{1086419}$

Diagram 1

Step 2 — Smallest possible difference

Let the 6-digit number be $N_1$ . Let the 5-digit number be $N_2$ . We want to minimize $N_1 - N_2$ . $N_1$ must be a 6-digit number. $N_2$ must be a 5-digit number. So $N_1$ will always be larger than $N_2$ . To make the difference smallest. $N_1$ should be as small as possible. Also, $N_2$ should be as large as possible. For $N_1$ , its first digit must be smallest. The smallest non-zero digit is 1. So, $N_1 = \mathbf{1} \_ \_ \_ \_ \_$ For $N_2$ , its first digit must be largest. The largest digit is 9. So, $N_2 = \mathbf{9} \_ \_ \_ \_$ We have used one '1' and one '9'. Now we fill $N_1$ 's remaining digits. We use the smallest available digits. These are 1, 2, 2, 3, 3. So, $N_1 = 112233$ . Now we fill $N_2$ 's remaining digits. We use the largest available digits. The digits used are 1, 1, 2, 2, 3, 3, 9. The largest 4 digits for $N_2$ are 9, 8, 8, 7. So, $N_2 = 99887$ . Let us calculate their difference.

$N_1 - N_2 = 112233 - 99887$

$= 12346$

$\boxed{12346}$

Diagram 2

Answer

(a) The largest possible sum is 1086419. (b) The smallest possible difference is 12346.

More questions in FIO

According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?

The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?

By how much did the population of Chintamani increase from 2011 to 2024?

For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative.

(a) 8300

(b) 40629

(d) 66666

(e) 367813

For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression.

Do you see any connection between each number and the corresponding smallest number of button clicks?

If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.

Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:

(a) 4050678

(b) 48121620

(d) 246813579

(e) 345000543

(f) 1020304050

Write the following numbers in Indian place value notation:

(a) One crore one lakh one thousand ten

(b) One billion one million one thousand one

(d) Nine billion eighty million seven hundred thousand six hundred

Q10

Compare and write '<', '>' or '=':

(a) 30 thousand ______ 3 lakhs

(b) 500 lakhs ______ 5 million

(d) 640 crore ______ 60 billion

Q11

Find quick ways to calculate these products:

(a) $2 \times 1768 \times 50$

(b) $72 \times 125$ [Hint: $125 = \frac{1000}{8}$ ]

Q12

Calculate these products quickly.

(a) $25 \times 12 =$ _______

(b) $25 \times 240 =$ _______

(d) $2500 \times 12 =$ _______

(e) _______ $\times$ _______ $= 120000000$

Q13

Using all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-digit number, write the —

(a) Largest multiple of 5

(b) Smallest even number

Q14

The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 42 letters. Give a 7-digit number name which has the maximum number of letters.

Q15

Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?

Q16

Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.

Q17

The words 'zero' and 'one' share letters 'e' and 'o'. The words 'one' and 'two' share a letter 'o', and the words 'two' and 'three' also share a letter 't'. How far do you have to count to find two consecutive numbers which do not share an English letter in common?

Q18

Suppose you write down all the numbers 1, 2, 3, 4, ..., 9, 10, 11, ... The tenth digit you write is '1' and the eleventh digit is '0', as part of the number 10.

(a) What would the 1000th digit be? At which number would it occur?

(b) What number would contain the millionth digit?

Q19

A calculator has only '+10,000' and '+100' buttons. Write an expression describing the number of button clicks to be made for the following numbers:

(a) 20,800 (b) 92,100 (c) 1,20,500 (d) 65,30,000 (e) 70,25,700

Q20

How many lakhs make a billion?

Q21

You are given two sets of number cards numbered from 1-9. Place a number card in each box below to get the

(a) largest possible sum

(b) smallest possible difference of the two resulting numbers.

Q22

You are given some number cards; 4000, 13000, 3000, 70000, 150000, 20, 5. Using the cards get as close as you can to the numbers below using any operation you want. Each card can be used only once for making a particular number.

(a) 1,10,000: Closest I could make is 4000 × (20 + 5) + 13000 = 1,13,000

(b) 2,00,000:

(d) 12,45,000:

(e) 20,90,800:

Q23

Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick.

Q24

Grey-headed albatrosses have a roughly 7-feet wide wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900 – 1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?

Q25

A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560 km from Alaska to Australia without stopping. Its journey started on 13 October 2022 and continued for about 11 days. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.

Q26

Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is about 8850 m high. Aeroplanes can fly as high as 10,000 – 12,800 m. How many times bigger are these heights compared to Somu’s building?