how to explain 0.26 and 0.260 are same
To explain that 0.26 and 0.260 are the same, consider the following steps:
Step 1: Understand the concept of decimal representation.
In our number system, decimals represent fractional quantities. The digits to the right of the decimal point become smaller as they move from left to right. One important property of decimals is the concept of place value, where each digit's value is determined by its position relative to the decimal point.
Step 2: Analyze the digits in both numbers.
In the number 0.26, the digit 2 is in the hundredths place (or 10^-2 place), while the digit 6 is in the tenths place (or 10^-1 place). In the number 0.260, the digit 0 is in the thousandths place (or 10^-3 place), the digit 6 is in the hundredths place, and the digit 2 is in the tenths place.
Step 3: Realize that trailing zeros don't affect the value.
Since the digit 0 has a place value one position to the right of the decimal point, it represents a value of 0. Thus, adding trailing zeros after the final nonzero digit does not change the numerical value of the number. Therefore, 0.260 is equivalent to 0.26.
In conclusion, 0.26 and 0.260 are exactly the same number when considering their numerical value or quantity, as the additional trailing zero after 0.26 doesn't affect its value.
To explain why 0.26 and 0.260 are the same, let's break down the concept of decimal numbers. In decimal notation, each digit has a specific place value. The digit to the right of the decimal point represents a fraction of the whole number, and the places to the right get progressively smaller.
Now, looking at the numbers 0.26 and 0.260, the digits after the decimal point indicate the fraction of the whole number. In both cases, the two digits after the decimal point are the same, i.e., "26". The difference lies in the number of digits that come after the "26".
In the case of 0.26, there are no additional digits after "26." Thus, it represents the number as it is - 0.26.
On the other hand, in the case of 0.260, there is an additional zero after "26". However, zeros after the last non-zero digit do not change the value of the number. Therefore, 0.260 is equivalent to 0.26.
In conclusion, both 0.26 and 0.260 represent the same number, and the difference lies in how the numbers are expressed in decimal notation.
.26 = 2 tenths + 6 hundredths
.260 = 2 tenths + 6 hundredths + 0 thousandths
the 0 thousandths don't add anything to the value.
It's the same for
12 = 012 = 00000012
The leading zeros have no value.