why is two hundredths written as 1.02 and not as 1.2?
"two hundredths" is written as 0.02 , not 1.02
1.02 is "one and two hundredths
1.2 is "one and 2 tenths
Two hundredths is written as 0.02, not 1.02. When you say "1.02," it represents one whole unit (1) plus two hundredths (.02), which is written as "1.02". However, if you are referring to "0.02", it represents only two hundredths, where the zero before the decimal point indicates there are no whole units.
The reason why two hundredths is written as 1.02 instead of 1.2 is because the decimal place value system is based on powers of 10. In the decimal system, each place value represents a power of 10. The first place to the right of the decimal point represents tenths (10^-1), the second place represents hundredths (10^-2), and so on.
So, when we have "1.02", the digit 1 represents one whole, the digit 0 represents zero tenths, and the digit 2 represents two hundredths. Hence, 1.02 means one whole unit plus two hundredths, or 1 + 0.02.
If we were to write it as 1.2, it would actually represent one whole unit plus two tenths, or 1 + 0.2. This would be incorrect since we want to represent two hundredths, not two tenths.
So, in summary, the digit 2 in the hundredths place, with a decimal point, signifies two hundredths (0.02), and not two tenths (0.2).