You are correct. The coefficient of 10 − 1 is the number telling how many .1’s are used in the number 142.67.
10 − 1 = (1)/(101) = .1.
Very well, we have seen that the digits in a decimal number are simply the coefficients in a sum of multiples of powers of ten. The decimal number
142.67
may be regarded as standing for the expression
1(102) + 4(101) + 2(100) + 6(10 − 1) + 7(10 − 2).
We shall call the expression above the expanded form of the decimal number. The expanded form of a decimal number shows the powers of ten arranged in descending order from left to right. When we write a decimal number in the ordinary way, we are simply writing the coefficients that would appear in the expanded form. The decimal point is placed at the right of the coefficient of 100, if the number involves a decimal fraction.
Which of the expressions below could be the expanded form of a decimal number?
