Comparing two numbers sounds simple until one has a minus sign, another is written as a decimal and a third appears in scientific notation. The same core principle works every time: put the values on a common scale and ask which is farther to the right on the number line.
This is a practical skill for shopping, measurements, temperatures, statistics and school maths. You do not need a complicated calculator for most comparisons, but you do need to notice signs, units and place value.
Understand greater than and less than
The symbol > means 'greater than'. Write 8 > 5 because eight is larger than five. The symbol < means 'less than', as in 3 < 7.
The wide opening faces the larger value. If you are unsure which way to draw the symbol, read the statement as a sentence: 'Three is less than seven.'
The equals sign means the two expressions have the same value. For instance 6 = 2 × 3, even though one side is one number and the other is a multiplication.
Compare positive whole numbers
Begin at the highest place value. A four-digit positive integer is larger than a three-digit positive integer, so 1200 > 999.
For two numbers with the same number of digits, compare from the left. In 6428 and 6399, the thousands match at 6, but the hundreds are 4 and 3. Therefore 6428 is larger.
There is no reason to examine the last two digits once a higher-value position decides the result.
Learn why negative numbers reverse intuition
On a number line, -2 lies to the right of -7. Therefore -2 is larger even though the digit 7 is greater than 2.
A negative number farther from zero has a smaller value. That is why -100 < -1. This matters when comparing debt, freezing temperatures or positions below sea level.
All positive numbers are greater than all negative numbers, and zero separates them. But remember that the magnitude of a negative number is not the same as its signed value.
Compare decimals correctly
When whole-number parts match, compare tenths, then hundredths, then thousandths. For example 4.6 = 4.60, which is greater than 4.58.
Adding trailing zeroes can make the positions easier to see. The values 0.7 and 0.700 are identical, not different because one is written with more digits.
For negative decimals, keep the sign in mind. -0.7 is less than -0.6 because -0.7 lies farther left on the number line.
Convert fractions to a common form
To compare 2/3 and 3/5, use a common denominator of 15. Two-thirds becomes 10/15 and three-fifths becomes 9/15, so 2/3 is larger.
You can also convert to decimals: 2/3 is approximately 0.666... and 3/5 is 0.6. Just do not round a recurring decimal too early.
When comparing a fraction to a whole number, converting the fraction to an improper form or decimal can help. For example 7/4 = 1.75, so it is greater than 1.
Compare numbers written with different units
A number can represent a measurement rather than a pure amount. The values 100 centimetres and 1.2 metres cannot be compared by looking only at 100 and 1.2.
Convert both to the same unit. One hundred centimetres is 1 metre, so 1.2 metres is longer. In millimetres the values are 1000 and 1200, giving the same result.
Always verify the units when comparing prices per kilogram, speeds, energy use or distances. A unit mismatch can produce a confident but meaningless answer.
Large numbers and commas
Commas or spaces can group thousands and help you read long numbers. In standard UK notation, 1,000,000 is one million.
Compare 2,500,000 with 2,050,000 by their digit positions. Both have two million, but the first has five hundred thousand while the second has only fifty thousand more, so the first is larger.
Do not confuse decimal separators and grouping separators when reading numbers from other countries. Some systems use commas where British notation would use decimal points.
Scientific notation
Very large or very small values may be written using powers of ten. For example 3.2 × 10^6 means 3,200,000, while 4.1 × 10^5 means 410,000.
For positive numbers in standard scientific notation, the greater power of ten normally decides the comparison. If the powers match, compare the leading coefficients.
With negative exponents, 2 × 10^-3 is 0.002 and 9 × 10^-4 is 0.0009, so the first is larger despite the 9 in the second expression.
Significant figures and measurement accuracy
Measurements may look different because one is rounded more heavily. For example, 2.50kg and 2.5kg represent the same numerical value, but they can imply different recorded precision.
If one measurement says 2.48kg and another says 2.5kg, the second is numerically greater. Whether the difference is meaningful depends on the accuracy of the measurement.
Do not treat reported values as more precise than the instrument or source allows. An apparent difference in the last decimal place may not be practically significant.
Order a list from smallest to largest
Suppose you have -1.5, 0.2, -0.75, 1/4 and 0. The correct ascending order is -1.5, -0.75, 0, 0.2, 1/4.
Converting 1/4 to 0.25 makes the final comparison straightforward. Sorting mixed forms becomes easier if you rewrite them consistently before ordering.
Check that negative values come before zero, with the most negative first. Then place positive numbers in increasing order.
Compare numbers in everyday decisions
A supermarket price of £1.80 for 300g cannot fairly be compared with £2.40 for 500g without calculating unit prices. The first is £6 per kilogram; the second is £4.80 per kilogram, so the second is cheaper for the same amount.
For electricity use, 0.6kWh is greater than 450Wh because 450Wh equals 0.45kWh. A correct comparison requires matching units.
When deciding between products, also consider quality, quantity and actual usefulness. The smaller numeric price is not always the better deal.
Make a reasonableness check
If your comparison tells you that -10°C is warmer than -2°C, reconsider the number line. If a decimal with more digits appears larger simply because it has more characters, align the positions.
Use estimation to spot errors. A number just under one should not be reported larger than a number just over one.
A calculator is useful for awkward conversions, but it cannot decide whether you entered the correct unit or interpretation.
The reliable order of operations
Check signs, match units, rewrite fractions or decimals if necessary, then compare from the highest place value. For scientific notation, convert or compare exponents with care.
Explaining why one number is greater helps you detect your own mistakes. The purpose is not memorising symbols but understanding what the quantities actually represent.