Comparing Decimals
Comparing Decimals
Might 1.25 be greater than 1.4?
- maybe, because 125 is bigger than 14?
- or even, because 25 is bigger than 4 ?
Where a digit is positioned is crucially important to how much
it contributes to the number.
The further to the left a digit lies, the greater its weight.
Consider 2111 and 1999.
Each of these numbers has the same number of digits. 2111 is
the larger number because in its leftmost position it has a 2,
whereas 1999 has a 1 in that position (and so the contribution of
all the 9’s to the right of the 1 in 1999 do not help to
‘overcome’ the 1’s in 2111).
The same holds behind the point:
in 1.25 the leftmost position behind the point is 2; 1.4 has
the digit 4 in that position, so, (with the same number to the
left of the point in both cases), 1.4 is greater than 1.25.
The digit in the leftmost position (behind the point) counts
the tenths while the next position to its right counts the
hundredths. One tenth (1, being the smallest non-zero digit) is
always greater than nine hundredths (the largest digit is 9).
So 1.3 is bigger than 1.29, or even 1.29880789…
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simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) |
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finding LCM and GCF |
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operations with complex numbers (simplifying, rationalizing complex denominators...) |
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solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) |
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solving a system of two and three linear equations (including Cramer's rule) |
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graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
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graphing general functions |
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operations with functions (composition, inverse, range, domain...) |
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simplifying logarithms |
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