Is 0.19 less than 0.40

Answer 1

yes

The way to know is by comparing the numbers' most significant digits, which are the nonzero digits that are farthest to the left with respect to the decimal point. A number is greater if its most significant digit is farther left from the decimal point or closer to the right side of the decimal point. For example, 123.1 is greater than 45.99 because 123.1 has its most significant digit in the hundreds place, the 3rd place left of the decimal point, while the most significant digit of 45.99 is in the tens place. Also, 0.01 is greater than 0.00499 because the most significant digit of 0.01 is closer to the right side of the decimal point (in the hundredths place). In cases like these where the two numbers have their most significant digits in different places, the values of the digits don't matter; the one with the most significant digit farther to the left is always greater.

In cases like the posted question, where the most significant digits are in the same place (in this case, the tenths place), the number whose most significant digit has the greater value is the greater number. It doesn't matter how many other digits are to the right of the most significant digit. For example, 0.23 is greater than 0.198574659, because 2 is greater than 1.