why is .4 equal to .40

0.4 = 4/10

0.40 = 40/100

When you simplify or reduce 40/100, you get 4/10.

Adding zeroes to the end of a decimal number does not change it's value.

0.4 also = 0.4000000000

When we write the decimal number 0.4, it is equivalent to writing 0.40. This is because the trailing zero in 0.40 has no significant effect on the value of the number.

To understand this concept further, let's look at the place value of the digits in decimal numbers. The digit to the left of the decimal point represents the "tenths" place, and the digit to the right represents the "hundredths" place.

In the number 0.4, the digit 4 is in the tenths place. The decimal has only one significant digit, indicating that there are no other digits beyond the tenths place. Therefore, by omitting the trailing zero, we can still represent the same value as 0.40.

Mathematically, 0.4 is equal to 0.40 because the value in the hundredths place is zero, and any additional trailing zeros after the decimal point do not change the overall value of the number.