Regrouping place values

In your book, Maths Mela (Chapter 1), a number is split into places in a new way. We know 983 = 9 hundreds + 8 tens + 3 ones. But we can also say 983 = 90 tens + 83 ones. Why? Each hundred is 10 tens, so 9 hundreds are 90 tens, which is 900. What is left is 83, and we count all of it as ones.

This is called regrouping: we change some of a bigger unit into a smaller unit. 68 = 6 tens + 8 ones, but it is also 5 tens + 18 ones, because we broke 1 ten into 10 ones. 7,069 = 5 thousands + 20 hundreds + 69 ones: 5 thousands is 5,000, and 20 hundreds is 2,000, which together make 7,000, and 69 ones are left. And 37,608 = 2 ten thousands + 17 thousands + 6 hundreds + 8 ones, because 20,000 + 17,000 = 37,000.

Regrouping helps us count notes. How many ₹10 notes are there in ₹7,934? Every 10 rupees is one ₹10 note. 7,934 is 793 tens and 4 ones, so there are 793 notes of ₹10 (with ₹4 left over). In the same way, 7,934 is 79 hundreds and 34 more, so there are 79 notes of ₹100. And 7,934 has 7 thousands.

How many ₹500 notes? Two ₹500 notes make ₹1,000, so 7 thousands make 7 × 2 = 14 notes of ₹500. The 934 that is left is more than 500, so one more ₹500 note fits. That makes 15 notes of ₹500.