Word Problem: Numeration

Q1: If you have 3 hundreds, 4 tens, and 2 ones, what number do you have? 
Ans: Hundreds: 3 hundred means you have 3 groups of 100. So, $3\times 100=3003\; \backslash times\; 100\; =\; 300$.
Tens: 4 tens means you have 4 groups of 10. So, $4\times 10=404\; \backslash times\; 10\; =\; 40$.
Ones: 2 ones means you have just 2.
Now, you add them all together: $300+40+2=3420\; +\; 40\; +\; 2\; =\; 342$
So, the number is 342.

Q2: You have 500 marbles. Your friend gives you 150 more marbles. How many marbles do you have now? 
Ans: Start with 500 marbles. Your friend gives you 150 more marbles.
To find out how many you have now, you add: $500+150=6500\; +\; 150\; =\; 650$
Now, you have 650 marbles.

Q3: Sarah has 7,200 stickers. She gives away 1,500 stickers to her friends. How many stickers does she have left?
Ans: Sarah starts with 7,200 stickers. She gives away 1,500 stickers.
To find out how many stickers she has left, you subtract: $7,200-1,500=5,700200\; -\; 1,500\; =\; 5,700$
So, Sarah has 5,700 stickers left.

Q4: If the greatest 5-digit number is 99,999, what is the successor of this number?
Ans: The greatest 5-digit number is 99,999. The successor of a number is what you get when you add 1 to it.
So, you do: $99,999+1=100,00099,999\; +\; 1\; =\; 100,000$
Therefore, the successor is 100,000.

Q5: If you add 1 to the number 1,00,000, what number do you get, and how many digits does it have?
Ans: Start with 100,000. When you add 1, you get:
$100,000+1=100,001$
To find out how many digits this number has, count them: 1, 0, 0, 0, 0, 1. That makes 6 digits.
So, the answer is 100,001, which has 6 digits.

Q6: If you write the number 23,344 in expanded notation, what is its expanded form?
Ans: In expanded notation, we break down each digit by its place value:

• 2 is in the ten thousand place: $2\times 10,000=20,0002\; \backslash times\; 10,000\; =\; 20,000$
• 3 is in the thousands place: $3\times 1,000=3,0003\; \backslash times\; 1,000\; =\; 3,000$
• 3 is in the hundreds place: $3\times 100=3003\; \backslash times\; 100\; =\; 300$
• 4 is in the tens place: $4\times 10=404\; \backslash times\; 10\; =\; 40$
• 4 is in the ones place: $4\times 1=44\; \backslash times\; 1\; =\; 4$

Putting it all together, you get: $23,344=20,000+3,000+300+40+423,344\; =\; 20,000\; +\; 3,000\; +\; 300\; +\; 40\; +\; 4$

Q7: If you have the numbers 12,675, 6,532, 62,392, 18,125, and 29,358, how would you arrange them in ascending order?
Ans: To arrange these numbers in ascending order (from smallest to largest), you compare each number:

• The smallest number is 6,532.
• Next is 12,675.
• Then comes 18,125.
• After that, we have 29,358.
• Finally, the largest number is 62,392.

So, the order is:

Q8: Sarita wants to round off her weight to the nearest ten. If she currently weighs 42 kg, what would her rounded weight be?
Ans: Sarita weighs 42 kg. To round to the nearest ten, we look at the ones digit, which is 2.
Since 2 is less than 5, we round down.
So, 42 kg rounded to the nearest ten is 40 kg.

Q9: If you have 1 lakh rupees and add ₹1 to it, what is the new amount in numerical form?
Ans: 1 lakh is written as 100,000. When you add ₹1, you do:
$100,000+1=100,001,000\; +\; 1\; =\; 100,001$
So, the new amount is 100,001 rupees.

Q10: What is the difference in place value between the digit 5 in the number 56,789 and the digit 5 in the number 5,678?
Ans: In the number 56,789, the digit 5 is in the thousands place, so its place value is: $5\times 1,000=5,000times\; 1,000\; =\; 5,000$
In the number 5,678, the digit 5 is in the hundreds place, so its place value is: $5\times 100=5005\; \backslash times\; 100\; =\; 500$
Now, to find the difference in place values: $5,000-500=4,5005,000\; -\; 500\; =\; 4,500$
So, the difference in place value is 4,500.