How to Compare Numbers Up to a Billion: A Step-by-Step Guide

To compare two whole numbers, count their digits: the one with more digits is larger. If they have the same number of digits, read left to right and stop at the first place where they differ. Below: the method, worked examples up to the billions, and practice questions.

Count the digits first

The quickest comparison needs no place value at all. A whole number with more digits is always the larger one: 1,000,000 beats 999,999 because seven digits beat six. This only works once leading zeros are stripped, so write both numbers plainly before you start.

When the two numbers have the same number of digits, work left to right. Compare the leftmost digits; if they match, move one place right, and keep going. The first place where the digits differ decides the whole comparison, and nothing to its right can change the answer.

Worked example: 3,941 and 3,986

Thus, you compare the tens digits. The tens digit in 3941 is 4 and the tens in 3986 is 8. So, 3941 is less than 3986.

Hence, 3941<3986.

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Numbers into the millions and billions

Large numbers are grouped into periods of three digits, separated by commas: ones, thousands, millions, billions. Comparing them is the same left-to-right walk, but it is easier to compare period by period.

Take 4,308,000,000 and 4,380,000,000. Both are billions with a 4 in the billions period, so move to the millions period: 308 against 380. Since 308 is less than 380, 4,308,000,000 < 4,380,000,000. Everything after that point is zeros and cannot affect the result.

Lining the numbers up with the right-hand digits flush makes this visible. If one number is shorter, it has fewer periods and is smaller.

Common mistakes

• Comparing from the right. The ones digit is the least important. Starting there gives the wrong answer whenever a larger place differs.
• Judging by the size of individual digits. 1,999 has bigger digits than 2,000 but is smaller. Only position counts.
• Miscounting digits. Commas help: 1,000,000 has two commas and 999,999 has one, so the first is larger without reading a single digit.
• Mixing up the symbols. The open end of < and > always faces the larger number.

Practice questions on comparing large numbers

Write <, > or = between each pair.

1. 58,207 and 58,270
2. 903,415 and 93,415
3. 7,000,000 and 6,999,999
4. 412,608,000 and 412,608,000
5. 1,250,000,000 and 1,205,000,000

Answers

1. 58,207 < 58,270. The thousands and hundreds match; the tens are 0 against 7.
2. 903,415 > 93,415. Six digits against five.
3. 7,000,000 > 6,999,999. Seven digits each, but the leading 7 beats the leading 6.
4. 412,608,000 = 412,608,000.
5. 1,250,000,000 > 1,205,000,000. The billions and the hundred-millions match; the ten-millions are 5 against 0.

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