Knowing Our Numbers — Class 6 IMO

Large Numbers, Place Value & Number Systems

In the Indian system the places are Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs and Crores. In the International system they are Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands and Millions.

The two systems link up: 10 lakh = 1 million and 1 crore = 10 million. The place value of a digit is the digit times the value of its place.

Example 1: What is the place value of 7 in 7,53,42,108?

7 is in the Crores place, so its value is 7,00,00,000.

Example 2: How many lakhs make 1 million?

1 million = 10 lakhs.

Quick recap

Indian: …Lakhs, Ten Lakhs, Crores; International: …Hundred Thousands, Millions.
10 lakh = 1 million; 1 crore = 10 million.

✓ Quick check

What is the place value of 5 in 4,56,789?

5 is in the Ten Thousands place, so its value is 50,000.

10 lakh is the same as ___ ?

10 lakh = 1 million.

Comparison, Ordering & Estimation

To compare numbers, the one with more digits is larger; if the digit counts match, compare from the left. Estimation uses rounding to the nearest ten, hundred or thousand to get a quick answer.

To round, look at the digit just after the rounding place: 5 or more rounds up, otherwise round down.

Example 1: Round 6,857 to the nearest thousand.

The hundreds digit 8 is 5 or more, so it rounds up to 7,000.

Example 2: Arrange in ascending order: 45,231 ; 45,213 ; 45,123.

45,123 < 45,213 < 45,231.

Quick recap

More digits means a larger number; otherwise compare from the left.
Round up if the next digit is 5 or more, else round down.

✓ Quick check

Round 3,468 to the nearest hundred.

The tens digit 6 is 5 or more, so it rounds up to 3,500.

Which is the largest number?

98,765 is the greatest of these.

Roman Numerals (up to 1000)

Roman numerals use I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. A letter repeats up to three times to add (XXX = 30).

A smaller letter before a larger one means subtract: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900.

Example 1: Write 49 in Roman numerals.

40 + 9 = XL + IX = XLIX.

Example 2: What number is DCC?

500 + 100 + 100 = 700.

Quick recap

I, V, X, L, C, D, M; repeat up to three times to add.
Smaller before larger means subtract (CD = 400, CM = 900).

✓ Quick check

Write 90 in Roman numerals.

X before C means 100 − 10 = 90.

What number is CM?

C before M means 1000 − 100 = 900.