3 mistakes learners make with decimal place value, each one named and explained.
Each column to the right of the point is worth a tenth of the one before it, so length tells you nothing about size.
0.45 is written as 4/9 or 45/9, with the digits used as numerator and denominator.
The digits are what you can see, and a fraction is two numbers, so they are made to fit.
Question. 0.45 as a fraction
A common answer. 4/9
The answer. 45/100, which is 9/20
Why. 0.45 means 45 hundredths, so the place value gives the denominator.
Say the decimal out loud: forty five hundredths. The words give you the fraction.
0.125 is chosen over 0.4 because it has more digits.
With whole numbers, more digits does mean bigger, and 125 does beat 4.
Question. 0.4 and 0.125
A common answer. 0.125, because 125 is bigger than 4
The answer. 0.4
Why. 0.4 is four tenths, while 0.125 is one tenth and a bit, so the first column already settles it.
Pad with zeros so both have the same length, then compare from the left.
0.7 is chosen over 0.76, on the basis that fewer digits means a bigger number.
Somebody once explained that longer decimals are not bigger, and the rule got remembered backwards.
Question. 0.7 and 0.76
A common answer. 0.7, because it looks simpler
The answer. 0.76
Why. 0.7 is 0.70, and 0.76 has six more thousandths than that.
Neither length wins. Pad both to the same number of places, then read from the left.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.